Kim H. Veltman
The Sources of Perspective
THE SOURCES AND LITERATURE OF PERSPECTIVE, VOLUME I
To B.A.R. Carter, Sir Ernst Gombrich and Luigi Vagnetti
TABLE OF CONTENTS
Acknowledgments
Introduction
iv-v
vi-viii
1.
DEFINITIONS AND ORIGINS
1-17
1. Introduction 2. Pseudo-perspectival Methods 3. Parallel-Perspective
4. Standard Methods 5. Picture Plane 6. Angular, Conic and Cylindrical Planes
7. Spherical Planes and Surfaces 8. Perspective and Anamorphosis 9. Geometry
and the Distance Point 10. Optics and the Legitimate Construction 11. Practice
and Theory 12. Architecture and Ruins 13. Surveying and Topography
14. Problems of Definition. 15. Conclusions.
2.
CENTRES
1. Introduction 2. Europe 3. Greater Europe 4. Britain 5. America
6. Far East and Elsewhere 7. Conclusions.
18-61
3.
TREATISES
1. Introduction 2. Early Treatises 3. Optics 4. Geometry 5. Architecture.
6. Themes 7. Categories 8. Conclusions.
62-90
4. CLASSIFICATION
1. Introduction 2. Optics 3. Architecture
6. Mathematics 7. Conclusions.
91-108
4. Drawing 5.Drawing Education
5.
INSTRUMENTATION AND SCIENCE
1. Introduction 2. Astronomy 3. Optics 4. Perspective 5. Mathematics
6. Mechanics and Physics 7. Centres 8. Modern Developments.
109-124
6.
ART AND REPRESENTATION
1. Introduction 2. Objects 3. Functions
6. Conclusions.
125-139
7.
4. Narrative
5. Contexts
ARCHITECTURE AND ENVIRONMENT
1. Introduction 2. Italy 3. Netherlands 4. France 5. England
140-152
6. Conclusions.
8.
IMAGINATION AND FREEDOM
1. Introduction 2. Illusion and Metaphor 3. Theatre and Spectacle
4. Trompe l'Oeil 5. Old and New 6. Real and Imaginary 7. Literacy
and Levels of Distance 8. New Functions of Art 9. Conclusions
153-171
9.
10.
11.
12.
CONCLUSIONS
NOTES
ILLUSTRATIONS
INDEXES
172-181
182-234
235-335
336-366
1
ACKNOWLEDGMENTS
Projects such as this would be unthinkable without long term support. From
September 1977 through September 1984 a generous series of fellowships from
the Volkswagen, Humboldt, Thyssen and Gerda Henkel Foundations made it
possible to concentrate on Leonardo da Vinci's perspective and optics and work
part-time on the bibliography at the great Herzog August Bibliothek in
Wolfenbüttel. From September 1986 through June 1987 support from the Getty
Trust made it possible to concentrate full time on the project. This continued from
July 1987 to July 1989 with the aid of a Canada Research Fellowship.
In the course of the past decade, hundreds of individuals have contributed to the
bibliography. A number of these are mentioned in the introduction. Professors
André Chastel, Decio Gioseffi, Kaori Kitao and Corrado Maltese kindly sent lists
of titles and references. Particular thanks go to a handful of mentors whose
interest, criticisms and counsel have helped to shape this project: Professors
Eugenio Battisti, B.A.R. Carter, Samuel Y. Edgerton, Jr., Sir Ernst Gombrich and
Luigi Vagnetti. Special thanks go to Professoressa Marisa Dalai-Emiliani who has
patiently followed and encouraged every phase of the project.
In Wolfenbüttel there were also three individuals, unflinching in their support,
whom I thank particularly: Professor Paul Raabe, Director of the Herzog August
Bibliothek; Dr. Sabine Solf, Leiterin des Forschungsprogramms and Dr. HansHeinrich Solf. There was also Dr. Marie-Luise Zarnitz, of the Volkswagen
Foundation, who visited regularly from Hanover. At the library, Anne-Marie
Deegen was exemplary in her helpfulness. Ulrich Kopp gave advice. Gaby (neé
Jöckel) Lüddecke, heroically ordered seven meters of photocopies through
interlibrary loan. Uwe Jumtow, and subsequently Miss Schultze, kindly drove me
to Göttingen and helped in the search. At the Niedersächsische Staats-und
Universitätsbibliothek Messieurs Grobe and Münther, patiently introduced me to
standard reference works (Art Index, Répertoire d'Art and R.I.L.A.); national book
catalogues (Brinkmans, Estreicher, Lorenz, Pagliaini, etc.); then, via the mysteries
of the 800-volume Real-Katalog, to specialized bibliographies (Draud, Lipenius,
Murr, Murhard, Riccardi and thirty others, see Index I.A.). Reimar Eck, head of
user services, was tireless in his patient help and counsel.
By August 1986, the bibliography was based on the lists of 125 libraries. In
addition books and manuscripts had been consulted in 34 libraries, particularly
Göttingen, Leiden, London, Madrid, Paris and Wolfenbüttel. Index I.C. lists
cooperating libraries, plus many of the librarians who helped in consulting texts or
answering queries concerning rare and spurious editions.
As the information arrived it was transferred to handwritten file cards. In August
1986, Dr. Richard Dolen began preparing a preliminary programme which permits
the information to be entered into an IBM PCAT using a DBase III Plus system.
2
At the Getty Center, the 15,000 titles were entered into a machine largely by Coley
Grundmann and partly by Joseph Leon, with some help from Victor Bonino and
Clay Stalls, two research assistants, who also continued the painstaking work of
verifying titles and locations. Since 1987, Alan Brolley (Toronto) has continued to
develop the computer version.
At the Getty Center, Dr. Herbert Hymans, Peter Holliday, Steven Lanzarotta and
Marianne Tegner were constantly helpful as were Dr. Marilyn Schmitt, Celine
Alvey and John Logan at the Getty's Art History Information Program. Megan
McFarland and Michelle Nordon kindly typed the first chapters of the draft. In
Toronto, Shirley Fulford patiently typed the manuscript, which Professors B.A.R.
Carter, M. Dalai Emiliani and Samuel Edgerton Jr. and Rocco Sinisgalli read fully.
Professors Sir Ernst Gombrich, André Corboz, Dan Blickman, Ruth Mellinkoff
and Drs. R. N. D Martin, and Richard Dolen kindly read sections.
The original vision of the project owes much to my friend, Dr. Rolf Gerling
(Zürich), who in the spring of 1981 generously took me on a three-month tour of
the Mediterranean. As he drove the range rover its 12,000 miles from the straits of
Gibraltar, through the mountains and plains of Tunisia, Sicily and Greece, along
the coasts to Tarsus and finally back across the vast expanses of Turkey, he played
Socrates, and challenged me to articulate a new approach to knowledge. Other
friends, Udo Jauernig (Wolfenbüttel), and Ian Stuart (London) listened many
hours, as this approach gradually evolved as a multivalent bibliography. In the
spring of 1986 a series of three lectures at Brigham Young University, generously
arranged by my friend Professor Dan Blickman, helped clarify my ideas, as did the
lecture with the Gesellschaft für Klassifikation in Münster arranged by Dr.
Ingetraut Dahlberg. In Toronto my ideas were further developed with my
colleague, Professor Ian Hacking, and friend, Sergio Sismondo, Jr. There was also
the loyal encouragement of friends, particularly Professors Syd Eisen, Deirdre
Vincent, Dr. Pauline and Don McGibbon and Diane Everett.
Between the preparations in London, the ideas in Wolfenbüttel and their
accomplishment in Santa Monica and Toronto lay the vision of Dr. Kurt Forster,
director of the new Getty Center for the History of Art and the Humanities as well
as the generous support of the Getty Trust, the encouragement of the Director of
the Institute for the History and Philosophy of Science and Technology, Professor
M. P. Winsor, and the support of the Social Sciences and Humanities Research
Council of Canada. To these and to all who have contributed I am very grateful.
In a sense, this project has been over thirty years in the making, although it has
only begun to take serious shape in the past decade. As I read through the text, I
am profoundly conscious of how much more there is to do, that this is an
introduction in fact, as well as in name. And yet, if it proves to be truly that, if it
can introduce more critical and discerning minds to a vast realm of human activity,
whereby we render things visible, the many invisible hours will not have been in
vain.
3
INTRODUCTION
1. Beginnings 2. Problems of method
and More Problems of Method
3. Scope of the book
4. Further Delays
1. Beginnings
In March 1977, Professoressa Marisa Dalai Emiliani, was in London organizing
the first world conference on perspective at the behest of Professor Eugenio
Battisti. At the suggestion of Professors B.A.R. Carter, Sir Ernst Gombrich and
John White she visited a young man who had recently finished a doctorate on the
history of perspective and invited him to do a bibliography for the conference.
The young man's interest in the subject went back to childhood. At fifteen, he had
decided to learn about perspective and had asked the art teacher at his high school
for instruction. The teacher went to the blackboard, drew an horizon line, put a
vanishing point in the center and explained that in perspective all lines at right
angles to the viewer converge at this point. By way of example he drew two boxshaped houses. Within five minutes the pupil had learned "all there was to know"
as far as the teacher was concerned. The pupil went away both delighted that the
truth was so wonderfully simple, and disappointed: How was it possible that
myriad effects of depth with vast vistas real and imaginary as well as all those
mysterious feats of illusionism and trompe l'oeil were governed by a simple dot on
the blackboard?
While preparing an undergraduate thesis on concepts of perfection and infinity
with Professor Brayton Polka, (York University), the student found claims (Ivins,
Foss)1 that the Greeks' concept of perfection had led them to emphasize tactile
sensibility, which led them to prefer sculpture over painting. By contrast, a
concept of infinity in the Renaissance had allegedly led them to emphasize things
visual, to prefer painting to sculpture and to develop perspective. The student was
puzzled. If it took eyes to look at both sculpture and painting in what sense was
Renaissance painting more visual than Greek sculpture? He decided he would
study the history of theories of vision and their relation to theories of
representation, but for the purposes of an M.A., Professor Stillman Drake
(University of Toronto), wisely persuaded him to focus on the history of optics.
Dr. A.I. Sabra, at the Warburg Institute, in London challenged him to define the
problem more carefully when he began his doctoral studies. What, if anything, set
Renaissance theories of vision apart from those of Antiquity? In the quiet of the
North Library the student found a provisional answer: a new emphasis on distance,
particularly in relation to size. He would study the history of distance even if his
contemporaries found the topic way out. Accordingly he read texts in the history
of optics, perspective, surveying and even cartography. When Dr. Sabra left for
Harvard the orphan was adopted by Sir Ernst Gombrich who plunged him into the
psychological dimensions of perspective and led him to consult two other mentors:
4
Professor Robert A. Weale, Director of Visual Science at the Institute for
Ophthalmology and B.A.R. Carter, professor of perspective at the Slade and later
at the Royal Academy. Meanwhile, almost by chance he met at the Wellcome
Institute for the History of Medicine, another mentor, Dr. Kenneth D. Keele, under
whose guidance a reconstruction of Leonardo da Vinci's perspectival experiments
took place.
The young man soon learned that even the principle of the picture plane was not
nearly as obvious in practice as it was often assumed to be in theory. He learned
the problems of the standard opinions. His mentors revealed that the usual
analogies between optics and perspective were too facile, and that most questions
with respect to perspective and psychology were still unanswered. And as he
continued to read quietly in the North Library he began to uncover a wealth of new
material. By August 1977 when he left London it had become clear to him that
perspective was an open field.
By the autumn of 1978 the publisher, Dr. De Marchi of Centro Di, grew impatient
and announced that the bibliography would appear in the spring. Professor
Vagnetti also announced that his bibliography, thirty years in the making, would
appear in March 1979. When this great work appeared it seemed petty to publish a
version which had only a few hundred titles more. When the young man wrote to
Professor Vagnetti asking for advice, he was invited to Rome.
It was a remarkable encounter only a few weeks before the professor's final stroke.
He explained calmly that although he had studied the subject for fifty years he
knew nothing about perspective in China, Japan, India, South America, Africa or
Australia. Nor, he added, did anyone else. He was old. His colleague was young.
If the young man would write letters to the major libraries of these countries the
official bibliography could achieve something more than his. Challenged, the
young man wrote sixty letters to places including Beijing, Calcutta, Canberra,
Moscow and Rio de Janeiro. The next six months saw fifty-five replies with lists
ranging from six to six hundred titles, many cursory, with no indication of place of
publication, publisher or format. A slow process of verification now began.
2. Problems of method
By 1981, three problems of method dominated his attention: 1) how much of a
book needs to deal with a subject for it to be included as a title; 2) how does one
handle meanings of a term changing over time, or 3) definitions which change
from place to place? Each of these problems will be explained briefly. In the first
case one obviously included all books dealing strictly with perspective. But what
about a four-volume work on drawing with one volume on perspective? Or a
single volume on drawing with a major section or perhaps a minor section, a
chapter or only a few pages on perspective?
5
A computer would be needed in order that one could search for books or articles
separately. Individual volumes, sections or chapters contained in a larger work
could be searched either with respect to the part or the whole and their relation
would be indicated in terms of: contains or contained in. In the case of individual
volumes, sections, or chapters, the general title which contains them would be
listed first, then the title of the part.
The second problem was which titles one should include if the meaning of a term
changed with time. In 1983 he joined the Gesellschaft für Klassifikation hoping
that they would have an answer. Finding none he developed his own preliminary
solution. Again a computer would be needed. First there would be a master list of
titles including all possible connotations. Then there would be various levels. One
level would identify standard categories of the term: axonometric, cylindrical,
isometric, parallel, spherical, etc. Another level would identify titles which earlier
bibliographers had included but which he would exclude. Peckham's Common
perspective is an example. Being a work on optics, on theories of vision rather
than theories of representation he would exclude it, or rather, wish to identify all
optical works in the list which are borderline with respect to perspective. A further
level would identify titles which earlier bibliographers had excluded but which he
would include. Jacques Androuet du Cerceau's Twenty optical views which they
call perspective is a case in point. Others have classed this under Roman ruins,
architectural views or the so-called Vedute(n) literature. But given the title, and
the perspectival nature of the views, which are as convincing as those by
Vredeman de Vries whose work is accepted as being perspective, he felt it should
be included. Yet another level would identify which titles had been included in
each of the earlier bibliographies. Proceeding chronologically one could trace how
awareness of the scope of the field grew with time. This new approach to
bibliography would thus bring to light the historical dimensions of a subject. The
printed bibliography would simply publish all these works including borderline
cases.
Even so this solution could not resolve deeper problems concerning classification.
In the fifteenth century there had been no well-established category for linear
perspective and thinkers accordingly classified the idea under optics, architecture,
surveying or geometry. As the concept of linear perspective developed so too did
its connotations and related fields including chiaroscuro, conic sections, drawing,
geometry, instruments, projection, proportion, scenography, shades and shadows,
space and time. Each of these terms also changed with time.
To make matters worse, and this was the third problem of method, the meaning of
perspective and each of these related terms changed from place to place. They
changed from country to country as witnessed by book catalogues. In France,
Lorenz listed perspective and dessin together in a way that catalogues in Britain,
Germany or Italy did not. The meanings and connections between them changed
6
Anatomy
Roman Ruins
Architectural Sketch Books
Shades and Shadows
Chiaroscuro
Scenography
Drawing
PERSPECTIVE
Proportion
Geometry
Projection
Conic Sections
Space and Time
Instruments
Optics
Anatomy
Roman Ruins
Shades and Shadows
Scenography
Architectural SketchBooks
Chiaroscuro
Perspective
DRAWING
Proportion
Geometry
Projection
Conic Sections
Space and Time
Instruments
Optics
7
Fig. 1 Schematic view of perspective and drawing with their satellite concepts
also with every major system of classification. They were different in Dewey than
in Bliss or Ranganathan. They even changed with every major library which had
its own classification scheme. In Göttingen one looked for perspective under
mathesis optica and artes plastices. In the Library of Congress one looked under
architectural drawing (NA 2710), drawing technique (NC 749-753), descriptive
geometry (QA 515) and in the technology section under projection (T369).
To handle such problems library catalogues had their "see also" signs. But these
too varied from place to place. At Stanford if one looked under perspective one
was referred to drawing and under drawing in turn asked to see thirteen other
headings including anatomy, artistic; architectural drawing, caricature, and design,
decorative. In Seattle under the same heading, drawing, one was asked to see
thirty-six other headings including brush, charcoal, crayon, fashion and figure
drawing. At the Library of Congress, in the Scorpio system, under drawing one
was asked to see 175 other headings including drawing materials, drawing of the
hand, drawing pets, sharks, and spaceships.
These problems of method implied that there could be no definitive list of books
on a single subject. At best, any list which aimed to be exhaustive would become
a (temporary) full bibliography on that subject and a partial bibliography on all its
related terms. A complete study would require full bibliographies for each of the
satellite terms in which the original subject would in turn be treated partially (fig.
1). Thus an exhaustive approach to perspective pointed to a comprehensive
bibliography on all the theoretical literature on art: Julius von Schlosser's vision2
in a new dimension.
Indeed, considerably more than a bibliography in the old sense was needed. Since
definition and meaning played such an essential role in defining boundaries one
would wish eventually to integrate existing dictionary definitions and encyclopedia
explanations with the titles. Given the new possibilities of video discs which allow
one to record 100,000 pages on a single diskette, the complete corpus of primary
literature on perspective could be recorded on a handful of discs. The Saur Verlag
was approached and steps to accomplish this are underway. The existence of a
corpus will make it possible for students and researchers to study systematically
the contents of the texts: to identify which images become part of a stock
repertoire, to trace when certain themes such as secular architecture, gardens,
landscapes or seascapes enter the tradition. In the long term these results could
then be compared with parallel trends in painting, sculpture and other arts such
that, for the first time, a practical confrontation of theory and practice would be
possible.
The above-mentioned problems of method had led previous thinkers to begin each
time with the premise that one needed to discover or invent a new system of
classification which would replace all others and then see where a book fitted in.
8
But could one not reverse the process: start with the title of a book and then record
the different ways in which it had been classed? Thereby the differences between
international classification systems, national book catalogues and local library
catalogues were no longer an embarrassment or a threat. Indeed these different
cubbyholes which changed with time and place offered unexpected insights into
the history of mentalities. This was a way of watching how cultural differences
led to different structures of knowledge. In the case of perspective one could trace
how some mind sets emphasized its mathematical dimensions, others its technical
qualities, others its purely artistic functions.
Implicit in this approach was a whole new way of perceiving the function of texts.
Some texts, for instance, by nature of their being very specialized, would find
themselves being slotted into a minimal number of cubbyholes. Other texts, by
contrast, would involve various fields and thus appear in many more cubbyholes.
Alberti's On Painting, for example, would appear under painting, painting
technique, perspective, optics, aesthetics of art, artes plastices and so on. This
would provide one dimension of a book's field of influence. Such an approach
offered more than a thermometer of popularity. It offered a means of identifying
which books had affected both art and science, which books had functioned as
bridges between what are now seen as two cultures.
Thus it was that a project which had begun in 1977 with the intent of producing an
official bibliography had expanded by 1983 into a vision of a new approach to
knowledge. When representatives of the Research Libraries Group came to
Wolfenbüttel in 1983, Professor Paul Raabe, the Director of the Herzog August
Bibliothek, kindly persuaded two members, Drs. Marcus McCorison and David
Stam to consider the idea informally. The former of these felt the project should
be taken up by the Getty Trust and wrote them personally. On 10 April, 1984 the
idea was presented formally as the inaugural address at the annual meeting of the
Gesellschaft für Klassifikation. In November 1984 came an invitation to become
Canada's first Getty Scholar. Commitments made it necessary to delay the
invitation for a year, during which time the plan was further developed.
3. Scope of the book
A distinction is made between primary and secondary literature: primary referring
to treatises and textbooks giving theoretical instructions how to do perspective;
secondary referring to works which deal with historical, metaphorical and
philosophical dimensions. In rare cases, a primary treatise, such as Danti's edition
of Barozzi (1583) contains important historical material such that it functions also
as secondary literature. For the purposes of this bibliography a distinction between
treatises and manuals has yet to be made.
The published version is not merely a paper copy of the computerized version. It
is in four volumes, the first two dealing with primary literature, the third and fourth
devoted to secondary literature. Volume one offers an historical survey of the
9
primary literature. In volume two the bibliography is presented chronologically
including: basic texts, manuscripts, articles, and some texts in related fields (as
explained above). With respect to locations, the reader is informed whether a title
is in the National Union Catalogue (NUC for cases pre-1956) or in the Research
Libraries Information Network (RLIN, for post-1956 imprints), and given one
European holding where possible. In the case of lost or spurious works a standard
bibliographical reference is given instead. Appendices provide lists by author, lists
of editors, translators and publishers plus cross-references to works on specific
branches of perspective and related terms. Volumes three and four will do the
same for the secondary literature.
The volumes offer an historical survey of the literature and provide a bibliography
in short title catalogue (STC) form, thus serving both as introduction and reference
work with respect to the more comprehensive computerized version. As such they
represent work in progress, are intended to assess the state of the field, to ask new
questions and point to new avenues of research.
The survey of primary literature is in two parts. An opening chapter gives
definitions of pseudo- and standard perspectival methods, analyzes the effects of
different projection planes, outlines the origins of the two chief perspectival
methods, explores the interplay of perspective with cartography, astronomy,
geometry, optics, architecture and surveying, and traces how early thinkers classed
perspective in terms of these established disciplines. It is shown that the
development of perspective was intimately connected with the rise of the
mathematical sciences in the Renaissance. A second chapter outlines the Italian
centres where perspective evolved, identifying some of the key theoreticians and
practitioners and suggesting their connections with Northern centres in Burgundy,
France, the Netherlands and Germany. The initial interplay between South and
North is examined; their different approaches to oral, manuscript and printed
traditions contrasted and the gradual dominance of the North by the mid-sixteenth
century traced. The rise of Paris in the seventeenth and London in the eighteenth
centuries as the leading European centers is documented briefly.
Most of the second chapter concerns patterns of publication in major centres since
1600. A thorough treatment of this vast subject would have been a major book in
itself. Since our purpose is to provide an orientation with some hint of
relationships between three areas, artistic perspective, mathematics and various
branches of drawing, the treatment often becomes rather dry, sometimes
resembling a list. Persons who find this tedious are advised to use this chapter
only as a reference tool and a move directly to the next chapter.
A third chapter outlines the chief themes contained in the early treatises and
identifies major trends in the contents of texts from the seventeenth century,
through to the present. A fourth chapter examines how the intended readership of
texts expanded gradually to include amateurs, outlining how this went hand in
hand with the emergence of different levels of dissemination and the spread of
10
more specialized literature; trying to map out what role was played by perspective
in the extraordinary proliferation from a single type of model book of the
thirteenth century to individual treatises on machine drawing, architectural
drawing, flower drawing, furniture drawing and so on by the nineteenth century
and asking what effects this proliferation of literature had on the classification of
perspective?
Part two of the survey explores the consequences of perspective on science, art, the
environment and the imagination. In terms of science it is shown that the
development of perspective was integrally connected with the rise of
instrumentation and that this focussed attention on proportion, scale and finally
quantification in science.
It is claimed that the nature of perspectival
representation, which permitted a systematic treatment of both views and scales of
an object, also played a role, leading away from questions of essence to those of
distinct functions which could be isolated and catalogued. This approach was
applied to machines, extended to living organisms, as if they were mechanical
objects, and eventually used also in cataloguing what had hitherto been abstract
powers of nature. In the process, perspective introduced a visual standard for
scientific truth which led to observation, experiment, measurement and the other
familiar characteristics of early modern science.
A second chapter shows that the consequences for art were no less profound. By
way of introduction Gombrich's approach in terms of various goals and functions
of art is used to explain why many cultures, including the Greeks, were ultimately
uninterested in perspective. Connections between perspective, literacy and the
narrative function are explored in order to show how this transformed the spatial
contents of pictures, leading eventually to an integration of spatio-temporal factors.
Meanwhile, another strand of perspective focussed attention on the frames of
pictures more than their contents and led to paradoxical plays on form without
content which offer new insights into differences between renaissance, mannerist
and baroque art. The third chapter explores the transformative effects of
perspective on architectural and environmental spaces, while a final chapter
explores the function of perspective as a visual metaphor in order to emphasize its
links with concepts of freedom and imagination.
A central thesis of this book is that the history of perspective involves two distinct
stories. One is the development of an objective method for recording or copying
the physical world at different levels of abstraction in the form of photographs and
maps. This is the story which Samuel Edgerton, Jr.,3 has emphasized and which
James Burke has popularized in his programme on perspective in the television
series The Day that the World Changed. What needs to be emphasized is that the
theoretical texts on perspective did not play a crucial role in these developments.
The breakthroughs were made by practitioners, were only subsequently integrated
into the theoretical texts, and even then constituted a small part of the contents of
the treatises.
11
The so-called conquest of realism involved a surprisingly small number of spatial
forms which were gradually mastered from the 12th through the 15th centuries. I
shall suggest that there is an implicit logic behind perspective which involves not
only the window principle, but also doors, cupolas, vaults, columns, porticos, and
colonnades, interiors and exteriors. A key aspect of this approach was that persons
began to approach the same objects systematically from different viewpoints and
in different scales.
If perspective had been nothing more than this, its discovery should have
threatened the creative imagination and its development should have reduced art to
an process of dull reproduction. But the Renaissance was hardly that and that is
why there is a second story to be told. The contents of the perspective texts were
primarily devoted to something other than realism. The treatises were in fact
repositories for a whole range of new images: regular solids, semi-regular solids,
lutes, chairs, stairs, complex plays of shadow and reflections, grotesques and
caryatids, imaginary gardens, fountains, idealized ruins and phantasy architecture.
These new perspectival images led to an emphasis on illusionism and trompe-l'oeil
involving a new interplay between real scenes, realistic scenes as if theatrical and
theatrical scenes as if realistic; an interplay between reconstructions of past
structures and interpretations of existing, possible and ideal ones. I shall argue that
it was precisely this blurring of boundaries between the natural and the fictive
which inspired that extraordinary proliferation of visual images which is unique to
the West and that herein lies the true significance of linear perspective: not simply
as a tool for realism, but as a catalyst to our imagination, playfulness, creativity
and freedom.
4. More Problems of Method and Further Delays
The invitation in November 1984 to become a Getty Scholar provided an ideal
opportunity to advance the bibliography. It also arrived at a delicate time: three
months after beginning a three year contract as an Assistant Professor at the
University of Toronto, Colleagues urged that the invitation should postponed for a
year. This was done and in August 1986 there began an inspiring year of living in
Santa Monica.
12
I. DEFINITIONS AND ORIGINS
1. Introduction
2. Pseudo-Perspectival Methods
3. Parallel-Perspective 4.
Standard Methods 5. Picture Plane 6. Angular, Conic and Cylindrical Planes 7.
Spherical Planes and Surfaces 8. Perspective and Anamorphosis 9. Geometry
and the Distance Point 10. Optics and the Legitimate Construction 11. Practice
and Theory 12. Architecture and Ruins 13. Surveying and Topography 14.
Problems of Definition 15. Conclusions.
1. Introduction
Perspective is a mathematical method of representation, which demonstrates how
images change size with distance and change shape when they intersect planes of
different shapes in various positions. It is sometimes used in a broader sense to
mean all systematic, mathematical methods of representation, including various
branches of parallel perspective, where distance plays no role. Hence, we need to
distinguish at the outset between perspective, which is quantitative and objective,1
and pseudo-perspectival methods, which are qualitative and subjective. By way of
introduction we shall also define the standard branches of perspective, identify
some properties of rectilinear picture planes and examine the effects of angular,
conic, cylindrical and spherical planes in order to explain the reciprocal relation
between perspective and anamorphosis (trick-perspective). We shall then
reconsider the two chief Renaissance methods of perspective and the question of
their origins. The role of astronomy, geography, geometry, optics, surveying,
topography, architecture and archaeology will be mentioned, as will the relation
between early practice and theory. Finally some questions of definition will be
raised concerning fifteenth and sixteenth century treatises on perspective.
2. Pseudo-Perspectival Methods
Vitruvius, in the introduction to book seven of his De architectura reports that
Agatharcus, a contemporary of Aeschylus painted a scene and left a commentary
about it:
This led Democritus and Anaxagoras to write on the same subject, showing
how, given a centre in a definite place, the lines should naturally
correspond with due regard to the point of sight and the divergence of the
visual rays, so that by this deception a faithful representation of the
appearance of buildings might be given in painted scenery, and so that,
though all is drawn on a vertical flat facade, some parts may seem to be
withdrawing into the background, and others to be standing out in front.2
Those who have interpreted these lines as proof of perspective in Antiquity3 have
ignored the wider context of the discussion. In the same book (VII, Chapter V),
13
Vitruvius laments the decadence of contemporary fresco paintings noting that,
whereas the ancients required realistic pictures of real things, subsequent artists
represented "the forms of buildings and of columns and overhanging pediments"
as well as the facades of scenes in tragic, comic or satyric style. Vitruvius adds
that:
Those subjects which were copied from actual realities were scorned in
those days of bad taste. We now have fresco paintings of monstrosities
rather than of truthful representations of definite things.. Such things do not
exist and cannot exist and never have existed.4
If linear perspective had been involved Vitruvius, as a pragmatic architect, should
have emphasized the practical applications of these methods for architecture and
their significance in recording the natural world quantitatively. His deliberate
opposition between truthful representation of the natural world and the unreal
objects produced in these scene paintings and frescoes confirms that something
else was involved.
The evidence of the extant frescoes at Pompeii (pl. 1.4), Herculaneum5 and
Oplontis6 supports this conclusion. Most of the buildings represent imaginary
inventions, which are architectural impossibilities. In most cases the depth
represented involves only a few feet. The scenes serve to close spaces7 rather than
to open them. Nor do all the lines converge to a single point. In the rare cases
where most lines observe this rule, the rest still converge to other points along an
axis. This suggests that Vitruvius' description of scene painting probably involved
a pseudo-perspectival method variously known as axial, vanishing vertical axis or
fish-bone perspective (fig. 2b, pl. 1.3-4). In which case, the centre which Vitruvius
mentions, refers to an axis running through the central point of a Greek theatre, an
axis being involved in order to accommodate the different heights of the viewers.
Other evidence has also been cited to claim that the Greeks were acquainted with
the laws of perspective. Greek optical theory asserted that visual angles govern
apparent size. This theory, when applied to their practice of representation, invited
two solutions: to represent objects higher up as smaller (pl. 1.1) or to make a
higher object larger in order that it appear the same size (pl. 1.2.). These are again
pseudo-perspectival methods variously termed negative perspective, optical
adjustments or visual angles methods (fig. 2a). According to Pennethorne, the
method of making objects higher in order that they appear the same size was used
in the temple of Thebes in the 13th century B.C. and with the letters on the temple
of Priene in the 5th century B.C.8
In Antiquity such a method probably inspired Plato's complaints against sculpture
in the Sophist.9 The method remained popular throughout the Renaissance. Dürer
described it in his Instruction of Measurement (1525). Michelangelo used it in the
figures above the altar of the Sistine Chapel,10 and Serlio described it in his first
book on architecture, as did Barbaro in his Practice of perspective (1568).
14
Most Renaissance thinkers were so convinced that the visual angles principles
taken from Euclid's Optics provided a theoretical basis for linear perspective that
they overlooked a basic contradiction between their practice of perspective and
theory of vision, namely, that perspective deals with planes and not with angles.
Imagine (fig. 2a)
a viewer at A looking at three equally sized objects BC, DE and FG. As long as
the interposed plane HI is parallel with BG, the projected size of B1C1, D1E1, and
F1G1 will be equal even though the angles subtended at the eye become smaller.
In other words, although Euclid's theory of vision predicts that GF appears smaller
than BC, Euclid's geometry predicts that G1F1 is projected the same size as B1C1.
Desargues (1636) recognized this contradiction between planes and angles and
hence when Dubreuil continued to espouse optical adjustments methods in his
Practice of perspective (1642), Desargues tried to clarify the issue. His student,
Abraham Bosse, the first professor of perspective at the Académie Royale, went
further and set out "to prove that one must not draw or paint as the eye sees."
Bosse's colleagues did not understand his plea to distinguish the objective laws of
perspectival planes based on geometry from subjective theories of vision based on
psychological optics and they conveniently hid their incomprehension by expelling
him from the Academy.11 Although more than three centuries have passed Bosse's
distinction continues to be overlooked. Even highly educated individuals when,
under extreme conditions, they discover discrepancies between their subjective
visual impressions and the objective laws of perspectival representation, assume
that perspective must be a simple convention. Some also continue to associate
optical adjustments methods based on visual angles with perspective.
15
Underlying optical adjustments is a principle of compensation: one adds to the
object's physical size, an amount that it would otherwise have lost in apparent size.
But this addition usually occurs only in a vertical plane. In a third pseudoperspectival method, inverted perspective, (fig.2c), one applies this principle to
both the vertical and horizontal planes simultaneously such that parts further away
are both higher and wider (pl. I.5-6). However, the extent of this adjustment is not
fixed and it is used so subjectively in many pre-literate cultures that it is difficult to
think of it as a systematic method as Shegin12 claimed. While creating a sense of
depth this method also remained subjective. In all three of these pseudoperspectival methods there is no way of studying the picture in order to determine,
post facto, the original distance of the viewer. Others have been exploring
spherical or cylindrical methods of perspective which they hope will objectively
record their subjective impressions (cf. below, pp. ).
3. Parallel perspective
Parallel perspective is another method in which the original distance of the viewer
cannot be determined because the viewer's position is taken to be at infinity. In
parallel perspective further distinctions are now made between orthographic or
axonometric projection where the faces of an object are oblique or tilted relative to
the picture plane and multiview projection when the face of an object remains
parallel to the picture plane. These categories are in turn subdivided. Multiview
projection may involve first angle (also termed first quadrant) projection,
commonly used in Britain (fig. 3.3 cf. fig. 3.2), where one looks out at the
projection: or third angle projection, commonly used in the United States (fig. 3.5),
where one looks in at the projection as if it were in a transparent glass box (fig.
3.7). Axonometric projection (fig. 4.1) is subdivided into isometric, dimetric and
trimetric projection. In isometric projection all three faces are equally oblique (fig.
4.2). In dimetric, two faces are equally oblique (fig. 4.3). In trimetric, only one
face is equally oblique (fig. 4.4). In addition, there are two other oblique parallel
projections known as cavalier projection, where the object is at 45o relative to the
picture plane (fig. 4.5) and cabinet projection, where the object is at arc tan 2
relative to the picture plane (fig. 4.6), and some include a third, military projection
(fig. 4.7).
Parallel perspective is often a misleading term because historically these technical
distinctions did not apply. In the seventeenth century, for example, cavalier and
military perspective were often interchangeable, and usually referred to rough and
ready methods involving a bird's eye view of a fortification (cf. below, p.
) In
addition, perspective is used to describe practical conventions in Oriental art which
appear to be without a theoretical basis.
4. Standard Methods
Linear perspective, according to the Oxford English Dictionary is
16
an application of projective geometry in which the drawing is such as
would be made upon a transparent vertical plane (plane of delineation)
interposed in the proper position between the eye and the object, by
drawing straight lines from the position of the eye (point of sight) to the
several points of the object, their intersections with the plane of delineation
forming the corresponding points of the drawing.
Linear perspective is generally accepted as being synonymous with central, plane,
Brunelleschian or Albertian perspective. A distinction has arisen between one-,
two- and three-point perspective. In one-point or central perspective only one
dimension (depth) is not parallel to the picture plane. In two-point perspective two
dimensions (depth and breadth) are not parallel to the interposed plane. In threepoint perspective all three dimensions (depth, breadth, and height) are not parallel
with the picture plane (fig. 5). Fifteenth century authors dealt almost exclusively
with one-point perspective and hence this method is sometimes treated as
synonymous with Renaissance perspective. One-point perspective is also
occasionally treated as synonymous with linear perspective but this is misleading.
Linear perspective includes one, two and three point methods.
Two-point perspective was made popular in the early sixteenth century by Jean
Pélerin, le Viateur (1505) and Joachim Fortius Ringelbergius (1531). This method
is synonymous with angular perspective. In England two-point and oblique
perspective are also synonymous. In America, by constrast, oblique perspective is
used as a synonym for three-point perspective. In both countries three point and
inclined picture plane perspective are synonymous.
Because parallel perspective as well as one-and two-point perspective all have
their frontal plane or height dimension parallel to the picture plane, these three
methods are classed by some under a more general heading of orthogonal
perspective. Nonetheless, mathematicians continue to distinguish between
orthogonal, parallel and central projections.
5. Picture-Plane
One of the distinguishing characteristics of linear perspective is the principle of the
window or picture plane (pl. 58. 1-2. cf. pl. 30, 54) whereby a transparent plane is
used in arriving at a perspectival foreshortening.13 Alberti, in the Latin version of
his On Painting, (1435) claims to have invented this principle. In the Italian
version, dedicated to Brunelleschi, this claim is carefully avoided, which makes it
likely that Brunelleschi was actually the first to use it when he made his famous
rendering of the Baptistry of San Giovanni between 1420 and 1425.
The inverse size/distance law of linear perspective applies in the case of objects
positioned parallel to this picture-plane. Hence, when an object is twice as far
away from the picture plane as the distance from the eye to the picture plane, its
17
size on the picture plane is one half its original size. When an object is three times
as far away, its size on the picture plane is one third. When it is four times as far
away it is one fourth and so on. In this process there are three variables: eye,
picture plane and object. Normally two variables are kept constant while a third is
moved systematically. If the object is moved away from the eye the object's
projected size becomes proportionately smaller. If the picture plane is moved
away from the eye, the object's projected size becomes proportionately larger. If
the eye is moved away from the object and picture plane, the object's projected
size becomes proportionately larger, while other objects at right angles to the
picture plane become increasingly foreshortened (fig. 6).
In retrospect, all this is eminently simple. But it did not seem so to fifteenth
century thinkers. Neither Alberti, Filarete nor Francesco di Giorgio Martini was
aware of the inverse size/distance law. Piero della Francesca considered the idea
but did not distinguish clearly between objects parallel with and objects at right
angles to the picture plane and therefore denied the existence of any simple inverse
proportion. Leonardo first discovered this principle around 1492. It took another
144 years before Desargues formulated this principle in mathematical terms and
another 20 years beyond that for Bosse to popularize them.
6. Angular, Conic and Cylindrical Planes
In the meantime thinkers explored the characteristics of various other types of
planes. The simplest of these was a concave V-shaped projection plane consisting
of two converging rectilinear planes (fig. 7.1). Marolois (1614), described this
possibility which was actually used in a peep show of a church interior now in the
National Gallery at Copenhagen. Bosse also considered the converse: a convex Vshaped projection plane again consisting of two rectilinear planes (fig. 7.2).
Corresponding cylindrical shapes both convex and concave were also explored by
the author of the Codex Huygens, Marolois, Nicéron and Schott (fig. 7.5-6, cf. pl.
67). Other variants, probably based on concepts of visual pyramids, involved
rectilinear and curvilinear pyramids or cones. Dubreuil (1649) considered frontal
projections onto both their exteriors and interiors (fig. 7.3-4, 7-8).
7. Spherical Planes and Surfaces
The practical projection of rectilinear surfaces onto spherical planes evolved in
Flemish painting practice of the fifteenth century when it became fashionable to
depict scenes reflected in convex spherical mirrors (fig. 8.1, cf. pl. 52.2). The
theory of spherical perspective (fig. 8.2), which has received much attention since
the 1870's due to the analogies with the retina of the eye, was not considered in the
fifteenth or sixteenth centuries. On the other hand, the reverse case of projecting
spherical surfaces onto rectilinear planes received much attention.
Ptolemy had considered this problem in the second century in his Planisphere
when he treated the South Pole as the position of a viewer and the equator as a
18
projection plane onto which he projected both the circles of Cancer and Capricorn.
This was essentially a first demonstration of the principles of linear perspective,
but under very limited conditions, where only scale was important and measured
distance played no role. Projections of the astrolabe involved a direct extension of
this principle: the lines of longitude and latitude corresponding to a particular place
on earth now also being projected onto the equatorial plane (fig. 8.3-6).
In the 1390's, Blasius of Parma, a professor of optics at Padua, wrote
commentaries on Euclid, Alhazen, Witelo and Peckham, confronting optical theory
with practical surveying methods. He also used Ptolemy's Planisphere as a
textbook. By way of demonstration he employed an armillary sphere, a threedimensional model of the earth reduced to circles of the poles and the circles of
Cancer, Equator and Capricorn along with the ecliptic (cf. pl. 75.3 and 49.3).
Using candles he projected these circles onto the walls of a darkened room.14
Biagio had two chief students. One was Paolo Nicoletto d'Udine (Paul of Venice),
who had studied at Oxford and thus brought an awareness of Bradwardine, the
Oxford calculators and the particular associations between theology, geometry and
optics developed by Grosseteste, Bacon and Peckham. The other was Prosdocimo
da Beldomandi, who had strong interests in mathematics and astronomy who in
turn taught Fontana, Toscanelli, Cusa and possibly the young Alberti.15 Hence
there were close links between those concerned with projection methods in
astronomy and the pioneers of linear perspective.
Through study of the planisphere and astrolabe, thinkers became aware that
perspective works in two directions: 1) to record images backwards onto the
picture plane as with the tropic of cancer or 2) to project images forwards onto the
picture plane as with the tropic of capricorn (fig. 8.3-4). The second of these
effects could be achieved using methods analogous to those of Blasius of Parma:
by substituting a candle for the viewpoint at the South pole and projecting the
circle of capricorn onto the equatorial plane in its enlarged form.
Systematic study of these possibilities came only gradually. It was not until the
sixteenth century that the rectilinear projection plane was shifted to a position at
right angles to the equator, which led to further developments in cartography. The
position of the (sometimes imaginary) candle varied. One alternative was to
position it at the centre of the earth, which resulted in a central or gnomonic
projection (fig. 9.1). Or it was positioned on the circumference of the equator at a
point opposite the hemisphere being projected, which resulted in a projection
known as horizontal, stereographical or Gemma Frisius (the teacher of Mercator)
(fig. 9.2). Subsequent thinkers chose positions slightly further removed: Clarke at
1.35 radii from the centre of the sphere (fig. 9.3); James at 1.367 radii (fig. 9.4)
and La Hire at 1.71 radii (fig. 9.5). Yet another alternative was to place the point
of projection at infinity which resulted in an orthographic, parallel or (Juan de)
Rojas projection (fig. 9.6), named after a Spanish contemporary of Gemma Frisius
and Mercator.
19
Not all projections were rectilinear. Mercator projected the sphere onto a cylinder
to arrive at his now famous grid system (fig. 11.1-2). Already in the second
century Ptolemy had explored another possibility: projecting the sphere onto the
inside of a cone (fig. 10.1-2) as well as a modified version thereof (fig. 10.3-4).
Recent discussions of his having had a third method, which was perspectival are
unfounded. It is true, however, that in his seventh book he described an eye
looking at the earth. The diagram associated with this, effectively a protoperspectival drawing of an armillary sphere (pl. 27.3), was clearly a source for
Dürer's perspectival drawings (pl. 27.4). In the case of another of Dürer's globes
(pl. 27.1) it has been suggested that he actually used a model of the earth tilted at
23« degrees (as in the angle of the ecliptic) and drew it with the help of a
perspectival window.16 A full analysis of cartographical methods is beyond the
scope of this essay, but is an area deserving much more attention (fig.12).
Notwithstanding interplay between astronomy, geography and perspective, it was
not until 1558 that Commandino published a formal study of correspondences
between planisphere projection and perspective, a problem which also interested
his student, Guidobaldo del Monte. Egnazio Danti in his commentary on Barozzi's
The two rules (1583) noted correspondences between perspective and geographical
projection--a topic obviously of interest to one who was cosmographer to the Duke
of Tuscany and author of the magnificent maps in the room of the globes in the
Palazzo Vecchio (pl. 24.5). The same Danti also studied sundials. This
combination of interests in perspective and dialling was subsequently pursued by
Desargues (1636) and Maignan (1648) (cf. pl. 48-49).
8. Perspective and Anamorphosis
We have already mentioned that perspective works in two directions: to record an
image backwards onto a picture plane and to project it forwards. In either case, as
long as the object and picture are in the same plane (fig. 6) the image remains
undistorted (or isometric), and varies in size only. When the object and picture
plane are parallel to one another, the perspectival image changes shape. In the
case of images recorded onto the picture plane these changes are usually unwanted
and are referred to as perspectival foreshortenings (fig. 13.1) or, in extreme cases,
as perspectival distortions (fig. 13.2). By contrast, anamorphosis involves
deliberate changes in shape produced in the case of images projected forward onto
a plane. The principle of anamorphosis is thus identical with that of projecting the
tropic of capricorn in the astrolabe17 (fig. 8.3), the sphere in various cartographic
projections (fig. 9) and of shadow projections in sundials. That those interested in
anamorphosis were often also concerned with projections in astronomy,
cartography and sundials is therefore no coincidence and of considerable
importance because it reminds us that the development of perspective and its
variants was considerably more than an artistic phenomenon: it was intimately
connected with the rise of the mathematical sciences in the Renaissance.
20
Although there exist a near infinite number of possible projections from a plane of
one shape onto a plane of another shape, sixteenth and seventeenth century
practitioners concentrated on a surprisingly small number of alternatives: a flat
projection plane at right angles to the original (fig. 13.3-4), a flat projection plane
at right angles to an original cylindrical (fig. 13.5-6), conic (fig. 13.7) or pyramidal
plane (fig. 13.8). In the cases of cylinders, cones and pyramids a mirror was
frequently positioned in the plane of the original object such that the anamorphic
forms could be transformed back to their original shape. Anamorphosis thus
demonstrated the principles of transformation and reversibility basic to linear
perspective.
The origins of anamorphosis can be traced with some precision. At an empirical
level problems of anamorphic distortion had arisen in trying to portray Christ, the
Pantokrator, in the rounded dome above the altar in mediaeval byzantine churches.
At the level of theory, Piero della Francesca, was the first to consider
anamorphosis in his On perspective of painting (c. 1480). Leonardo da Vinci
explored various aspects of anamorphosis.18 Jean-François Nicéron was the first
to devote an entire treatise to the subject (1638).
The origins of linear perspective are not so readily summarized. Guidobaldo del
Monte (1600), reminds us that there were twenty three competing methods at the
turn of the seventeenth century. Other sources including Benedetti (1580), Egnazio
Danti in his edition of Barozzi, il Vignola (1583) and Piero della Francesca (c.
1480) emphasize two principal methods: one based on geometry, the other on
practical demonstrations.
9. Geometry and the Distance Point Construction
In his Elements, Euclid had explored basic properties of ratios and proportions of
lines and surfaces as well as their equivalents and transformations. In the 13th
century interest in these problems was revived by Leonard of Pisa (Fibonacci),
who introduced them into the curriculum of the abaco school. In the 1430's Leon
Battista Alberti applied these geometrical principles to perspective in his Elements
of painting (pl. 28.1). Piero della Francesca (c.1480) developed this approach,
devoting the first two books of On perspective of painting to these geometrical
demonstrations based on proportional diminution (pl. 28.2). Later examples by
Serlio (pl. 28.3), Barbaro (pl. 28.4), P‚lerin (pl. 29.1-2), Androuet du Cerceau (pl.
29.3) or even Galli-Bibiena (pl. 29.4) are effectively logical extensions of this
approach.
In one of his propositions, Piero della Francesca mentioned the possibility of
confirming these principles with physical demonstrations. In the course of the
1480's and 1490's, individuals such as Francesco di Giorgio Martini sought to
carry this out by reconstructing the geometrical principles in terms of actual
surveying situations. In all likelihood it was Francesco who first explored the
principle of the distance-point.
21
In determining the distance point one begins by extending the converging sides of
a foreshortened square (fig. 14) until they meet at a central vanishing point.
Through this point a horizon line, parallel to the base is drawn. Through the
foreshortened square one also draws a diagonal which is extended until it meets
the horizon line at the distance point, so-called because the space from this point to
the central vanishing point marks in scale the original viewer's distance from the
picture plane which produced the foreshortening in question.
Fig. 14 Frontal and three dimensional diagram to illustrate the principle of the
distance point. ABC1D1 is the foreshortened version of ABCD as seen by a
viewer at F1. The viewer's distance from the picture plane F1E is equal to distance
FE. The distance point F can be found by simply extending diagonal BD1 until it
meets the horizon line.
This ability to work backwards from the foreshortened square to reconstruct the
original viewpoint which caused it has been termed the reversibility principle of
perspective. This only functions in the case of regular squares (or cubes)
positioned at right angles to the picture plane. That perspectival drawings tend to
feature regular geometrical and idealized architectural shapes is therefore no
coincidence.
Jean Pélerin gave the first published account of the distance point in 1505. In Italy
the method did not appear in print until Danti's edition of Barozzi's Two rules
(1583). As a result its Italian origins in geometrical principles were gradually
overlooked and modern scholars generally assumed that it stemmed from practical
workshop traditions in the North.19
22
10. Optics and the legitimate construction
The development of the second major method was closely tied with the history of
optics. Euclid's Optics had dealt primarily with what would today be termed
psychological optics, study of subjective aspects of vision. But the treatise also
contained four propositions devoted to surveying20 problems and thereby the
accurate perception and measurement of distance became part of the optical
heritage. By the ninth century thinkers in the Arabic tradition such as Al-Farabi
could define optics in terms of measuring the heights of mountains and even
distances of stars.21 Through this tradition there evolved an overlap between the
ideals of optics and those of surveying. In the optical treatises of Alhazen (early
11th c.) and Witelo (c. 1280) the concept of measured distance acquired new
significance.22 By the fourteenth century treatises on optics frequently appeared
together with those on surveying or practical geometry.
One important consequence of this interplay between optics and surveying was
that theoretical propositions in optics were increasingly tested in terms of practical
demonstrations. Euclid, for instance, had claimed that visual angles do not vary
inversely with distance.
Blasius of Parma, in the 1390's, tested this
experimentally, just as he used candles to test experimentally the projections of
armillary spheres. Brunelleschi's picture-plane or window (c. 1415-1425) was
probably a direct outgrowth of this tradition: a practical demonstration of the
visual pyramids and other principles of optical theory.
Alberti, in his On painting, described the principles of this method verbally, thus
providing a first theoretical formulation of what he termed the best method (modo
optimo), now remembered as the legitimate construction (costruzione legittima.
Even so, he saw the window, or veil (velo), as the practical equivalent of this
method and insisted on its fundamental importance:
Nor will I hear what some may say, that the painter should not use these
things...I do not believe that infinite pains should be demanded of the
painter, but paintings which appear in good relief and a good likeness of
the subject should be expected. This I do not believe can ever be done
without the use of the veil.23
Alberti assumed that optics provided the theory for both his verbal demonstration
of the legitimate construction, and for its practical equivalent, which used the
window. In the next generation, Francesco di Giorgio Martini and Luca Pacioli
also assumed this, although they classed perspective under practical geometry and
surveying. Even in the latter sixteenth century perspective continued to be seen in
terms of practice as is witnessed by titles such as Barbaro's Practice of perspective,
Barozzi's Two rules of practical perspective and Sirigatti's Practice of perspective.
Because authors continued to assume that Euclid's Optics and Elements provided
such theory as was necessary for their subject, there was no theory of perspective
as such at the time.
23
11. Practice and Theory
Indeed when we actually look at the fifteenth and sixteenth century treatises we
find that they are very different from what we might have imagined. The early
treatises are not repertories of elaborate spatial structures, which serve as
harbingers for a revolution in the treatment of space. The earliest extant
manuscripts of Alberti's On painting have no diagrams at all. Later versions have
only a few diagrams. By contrast, Piero della Francesca's On perspective of
painting may contain eighty diagrams, but these are only of isolated objects and
the most impressive of these shapes had already been mastered at least a century
earlier in painting practice.
Piero's diagram of an octagonal building (pl. 2.3) is a case in point. Duccio had
convincingly rendered a frontal view of this form in his Maestà (pl. 2.1-2).
Thereafter it had become a frequent theme in fourteenth century art and had served
as the subject of Brunelleschi's first perspectival picture. The interior of an apse in
Piero's treatise (pl. 3.2) provides another example. This shape had been mastered
by Giotto in the Scrovegni chapel in Padua at the beginning of the fourteenth
century (pl. 3.1).
The same holds true for diagrams in other treatises. The barrel vaults in Barozzi's
The Two Rules (pl. 3.4) also have a precedent in Giotto, this time in his
Sanctioning of the Rule in the Upper Church at Assisi (pl. 3.3). Even a much later
example such as the oblique building in Vaulezard's Abridgement (1631, pl. 3.6)
had been used in a simpler form in Pélerin's treatise and earlier still in painting
practice in Christ and the Apostles in the Temple attributed to Andrea di Giusto
(pl. 3.5).
Examination of Duccio's Maestà (pl. 2.1) offers some insight into the process that
took place. At first sight the altar consists of a bewildering complexity of spatial
scenes depicting the life of Christ. But on closer scrutiny it becomes apparent that
the nearly axonometric roof and the three columns shown in panel 7 recur in
panels 8, 14, 15, 23 and 28. Similarly a variant of this roof which appears in panel
13 recurs in panels 22 and 27. A further variant in panel 19, showing a type of
axial perspective in the beams of the ceiling, recurs in panels 24 and 25. These
shapes recur in Giotto, and indeed throughout the fourteenth century. The
Florentine hat or mazzocchio offers another case in point. Uccello painted it in his
frescoes long before it appeared in the treatises of Picro della Francesca, Leonardo
da Vinci, Daniele Barbaro and their successors. Even the perspectival lines
underlying Uccello's sinopia appeared in practice long before they appeared in
theoretical literature. Hence the spatial revolution, such as it was, lay in the
gradual mastery of a small number of these basic forms in practice. The early
treatises on perspective subsequently summarized these in mathematical terms.
Thus, rather than offering new visions of that which practice might explore, the
early treatises codified what practice had already achieved.
24
The development of perspective is too often associated specifically with painting.
It is important to emphasize that it affected all media of expression as is witnessed
by Donatello's use of proto-perspectival methods in his sculpture of St. George
(Florence, Or San Michele, 1417) or Ghiberti in his bronze doors of the Baptistery-particularly the Gates of Paradise (1435). In many cases perspective merely
served to represent spatially models available from classical Roman architecture.
The cassetted vault was, for instance, well known from the Roman temple of
Maxentius and other buildings. It became one of the great themes of humanistic
architecture. Masaccio used it in his Trinity (pl. 5.1), generally accepted as the first
extant work in perspective. Thereafter it occurs in literally hundreds of examples:
in paintings by the most famous artists, Mantegna and Raphael (pl. 11.5); less
famous such as, Foppa and even obscure artists such as the Ferrarese Master (pl.
6.3). It is used in drawings by Bellini (pl. 6.1-2) and a preparatory drawing by
Donatello (pl. 6.4). It is used equally in other media: in a marble alter by
Desiderio da Settignano (pl. 5.2); in a stone facade by Pietro Lombardo in Venice
(pl. 5.3), by Alberti in the facade of Sant'Andrea in Mantua and by Bramante in his
famous illusionistic choir (pl. 5.4). Borromini's use of a variant nearly two
centuries later in the Palazzo Spada (pl. 5.5) attests to the enduring fascination of
this illusionistic form.24
A cumulative process marks a next stage in development. Hence, Piero della
Francesca, having mastered the dome shape (pl. 3.2) and the cassetted vault,
produced an inverted dome in the form of a scallop and combined this with a
cassetted vault in his famous Brera Altar (pl. 7.1). Artists at all levels were
involved in this process. In his doors for the Baptistery at Florence, Ghiberti had
represented a cross vault (pl. 4.4). This form also appeared in the treatises of Piero
della Francesca (pl. 7.3) and Sebastiano Serlio (pl. 7.4). A derivative painter such
as Cima da Conegliano in turn combined a cross vault with a cassetted barrel vault
in his St. Peter Martyr and Saints (pl. 7.2).
Perspective, as thinkers such as Vredeman de Vries noted, involves looking into or
looking through objects.25 The number of objects which produce such an effect is
surprisingly limited. The vault is one. Another is the door or portal, which is
closely related to the vault. Fouquet used this perspectivally, for instance, in his
Hours of Etienne Chevalier (pl. 4.5).
The case of the portal is particularly interesting because, long before painters
represented it perspectivally, architects had begun to construct it spatially, as if
receding towards a vanishing point, as witnessed clearly in the Romanesque
example of St. Pierre, in Aulnaye La Santage in the South of France (pl. 4.1) and
later, more dramatically in Gothic examples such as Notre Dame (pl. 4.3). It is
noteworthy that trompe l'oeil versions of such portals also date back to the twelfth
century (pl. 4.2).
25
By the fifteenth century the portal had become a motif in Northern protoperspectival painting such as Vranck van der Stock's Altar of the Redemption (pl.
8.1), Rogier van der Weyden's Christ Appearing to his Mother (pl. 8.3) and his
Beheading of St. John (pl. 8.4). Another of Van der Weyden's paintings, The
Eucharist with Christ on the Cross (pl. 8.2) extended this effect of the portal until
it became flush with the nave of the church. Technically speaking the perspective
in these northern examples was not correct. In terms of details they were also very
different from Italian drawings of roughly the same period found in Jacopo
Bellini's Sketchbooks (9.3-4).
There were sharp contrasts between the Gothic architecture of the North and the
humanistic architecture of Italy with its emphasis on classical examples, on
measure and proportion. But in terms of general approach to space Bellini also
relied on portals to create perspectival effects in his drawings, a principle which
Domenico Veneziano (pl. 9.5) subsequently adopted for his own purposes, as did
Veronese (pl. 9.6) a century later. Bellini's portals, it will be noted, also involved
the, by now familiar, vault form, and moreover, had their parallels in actual
buildings of the time such as Brunelleschi's Pazzi Chapel (pl. 9.2), which in turn
bears comparison with an idealized ruin from Androuet du Cerceau (pl. 9.1) over a
century later. In this context, it is very tempting to see a logical progression from
the spatial effects in the entrance to the Romanesque church of St. Pierre (pl. 4.1),
and the Gothic cathedral of Notre Dame (pl. 4.3) to Brunelleschi's facade to the
Pazzi Chapel (pl. 9.2) and Benedetto da Maiano's Santa Maria delle Grazie in
Arezzo (pl. 15.1).
We have already noted Roger van der Weyden's extension of the portal principle to
produce a full view into a church, as if the entrance wall had been removed or
rather made into the equivalent of a window such that the entire nave functioned as
a cross section (pl. 8.1). Fouquet adapted it slightly in his Hours of Etienne
Chevalier (pl. 10.1). The Master of the Burgundy Hours used it more dramatically
in a miniature now in Vienna (pl. 10.2). In 1505 Jean Pélerin used it in his On
artificial perspective. Once again theory followed practice.
Meanwhile, the theme continued to develop in Italy as witnessed by Domenico
Ghirlandaio's Feast of Herod (pl. 11.4) and Raphael's School of Athens (pl. 11.5)
and, as the sixteenth century progressed, connections with Roman ruins also
became more apparent through engravings such as those of Androuet Du Cerceau
(pl. 11.1) and Cock (pl. 11.3). The logic of looking into involved in perspective
was such that it transcended regional differences. For all their stylistic variations
Rogier van der Weyden, Fouquet and Bellini in the early fifteenth century, and
Raphael, Du Cerceau and Cock in the sixteenth century, had a common approach
to space such that one can speak in a new way of a European phenomenon.
Indeed, it is probably no coincidence that the words Europe, Renaissance and
perspective have become so unconsciously linked in our minds. Perspective gave
to Europe a unifying logic of space, which pointed simultaneously to a diversity of
26
expressions, the opposite, as it were, of the later American ideal of making the
many into one (e pluribus unum).
That which occured with representations of sacred interiors happened equally to
visualizations of secular interiors. Here again it became customary to treat one
wall as if it were a transparent window permitting a clear view of the other walls.
One variant, favoured in the North, was to produce oblique views, emphasizing the
right walls or, as if in mirror versions of these, emphasizing the left walls (pl. 12,
7.1-4). More frequently there was a frontal view of an interior, the real wall of
which in turn contained a window or a larger opening such that one could see into
the distance. In Jan van Eyck's Madonna and the Chancellor Rolin the columns
served to frame a landscape in essentially the same way that they did in Piero del
Pollaiuolo's Annunciation (pl. 13). Again the details might differ, but North and
South share a common approach.
Such examples are particularly interesting because they show that the practice of
representing windows to frame spatial views had become customary (pl. 11.2-4) at
just about the time that the principle of the perspectival window, as an analytical
device, was establishing itself in practice in the 1430's: this time a case of practice
and theory developing almost simultaneously.
Meanwhile, the method of treating the front wall as a window (pl. 8.2) gained in
importance in the sixteenth century. Michael Pacher used it in his St. Wolfgang
Altar (pl. 16.1), as did Albrecht Altdorfer in his rendering of the Jewish Synagogue
at Regensburg (pl. 16.2) and other church interiors. The method was used in the
Luther Bible (pl. 16.3), and Rodler also employed it several times in his treatise on
perspective (pl. 16.4). The same method was frequently used in combination with
another basic perspectival form, the colonnade as in both Cesariano's Vitruvian
commentary (pl. 80.2, 82.1 cf. pl. 80-83), and his marquetry work in St.
Alessandro. Later sixteenth century examples include a drawing by Scamozzi (pl.
14.1) or, to take northern analogues, the engravings of Vredeman de Vries (pl.
14.2-3) and Cornelius Loos (pl. 14.4).
Already in the fifteenth century, Brunelleschi, one of the discoverers of
perspective, was almost certainly aware of the perspectival effects of actual
colonnades when he designed his Ospedale degl'Innocenti, as must have been the
case with the later designers of the new market in Florence and Benedetto de
Maiano when he designed Santa Maria delle Grazie in Arezzo (p.l5.2). By the end
of the century, artists such as Bramante realized that the representation of
colonnades was particularly suited for perspectival purposes because these
permitted one not only to look into but even look straight through a space. Later
sixteenth century examples included Vignola's plan for an open loggia (pl. 15.3) as
well as northern parallels, such as those in the treatises of Vredeman de Vries (pl.
15.4-5).
27
These developments did not, however, undermine the method of treating the front
wall as a window, which continued its popularity in the seventeenth century.
Hondius used it, for instance, in his engraving of a modern temple (pl. 17.1), as did
Steenwyck in his version of a Gothic Church (pl. 17.2) and Pieter Neefs in his
painting of Onze Lieve Vrouwe Kathedraal in Antwerp (pl. 20.1), which invites
comparison with actual photographs of the same building (pl. 20.2).
In the next generation, with Saenredam, this tendency towards what appears in
retrospect like photographic realism increased. But the actual process of arriving at
this result became considerably more complex.26 It became customary to make
preliminary drawings which were then adjusted in arriving at the finished painting
(pl. 20.3-6). The same process occured in the representation of exteriors (pl. 21.13). Physical models and printed engravings became increasingly important as
exemplars. Ironically as paintings truly came to look like windows to the natural
world, the number of versions or filters separating preliminary sketch and finished
work increased.
Something else also happened. There was no longer one obvious point of view
from which one represented a building or place. It is noteworthy that Saenredam's
preparatory drawing (pl. 21.1) shows us two views of the same building complex.
This tendency towards multiple viewpoints is even more obvious in treatments of
the central square at Haarlem where we have various views looking towards the
Grote Kerk (pl. 22.1-2, pl. 23.1) and others looking in the opposite direction (e.g.
pl. 23.2).
The spatial qualities of these paintings make them appear as epitomes of
perspective. In retrospect they seem and may even be a logical consequence of the
story in which perspective is linked with the conquest of realism. What needs to
be emphasized, however, is that the early treatises on perspective were not crucial
to this story. The basic texts by Alberti, Dürer, Barbaro, Barozzi (il Vignola), or
Accolti were sometimes too primitive, and invariably too abstract to serve as
models in this process. Even texts such as those by P‚lerin (pl. 10.3-4), Androuet
du Cerceau (pl. 11.3) or Vredeman de Vries (pl. 14.2-3, 15.4-5), which were
effectively albums of handy examples, codified images from painting practice. To
understand better this story of the conquest of realism we need a catalogue of basic
spatial forms in order to follow their gradual mastery within the practical tradition
and their subsequent integration into the theoretical treatises. Theatre also played
a role and will be discussed later (see below 2.4). Two other aspects of this story
deserve mention: architectural ruins and topographical surveying. Each of these
will be considered briefly in turn.
12. Architectural Ruins and Plans
It is well known that the key figures in the early development (both in terms of
practice and treatises) were architects, notably Brunelleschi, Alberti, Filarete,
Francesco di Giorgio Martini, Leonardo da Vinci, Bramante, Raphael, Baldassare
28
Peruzzi, Serlio and Palladio. Brunelleschi also spent considerable time studying
architectural ruins in Rome. Indeed his biographer, Manetti, credits him with new
methods in recording these (see below p. ). Hence, the same individual who was at
the frontiers of representing modern buildings, was also at the forefront of
measuring ancient ones, a combination of interests which we now think of as
typical to humanism. This combination of interests gains in significance when we
realize that it applies equally to Alberti. The author of On painting and Elements
of painting was also the author of Description of the city of Rome and On
architecture. It applied also to Francesco di Giorgio Martini whose treatises dealt
with practical perspective and the measurement of ruins and modern buildings
alike.
Rome was the centre of these activities, due in part to new patronage, which came
through the rise of papal power with Alexander VI and Leo X. In the early
sixteenth century Raphael, in his famous letter to Pope Leo X, examined the use of
ground plan and elevation with respect to both ruins and architectural
representation. He also wrote his own commentary on Vitruvius.27 Fra Giocondo
(1511) also played a role in this reinterpretation of Vitruvius, which was continued
by Cesariano (1521), Caporali (1536) and Ryff (1547). Serlio's Works of
architecture marked an obvious next step. It was the first published text in this
tradition: his treatise on perspective (Bk. 2) effectively serving as an introduction
to subsequent sections on both architectural ruins and contemporary architecture.
In the next generation, this combination of interests continued with Palladio, who
codified the uses of perspective in architectural design, in creating an artist's
conception of a projected work, and Androuet du Cerceau who, in one of his
books, added modern structures such as San Pietro in Montorio (pl. 96.6). At the
same time, a greater specialization also set in. Androuet du Cerceau wrote three
different kinds of books: one devoted to the principles of perspective, a second
applying it to ancient ruins, and a third to contemporary architecture.
Of these the third was the most interesting because it showed various French
chateaux in the context of their gardens and surrounding landscapes. Many of
these engravings, including Aret and Fontainebleau, were based on existing
structures, while others are idealized projections. Androuet's work nonetheless,
pointed the way to later books, such as Pérelle, and Decker (pl. 93.2) which
showed contemporary buildings in context as "perspectives."
Meanwhile, other modern artists were adding this element of context to what had
hitherto been studies of single columns, individual architectural elements or, at
best, isolated monuments. The sketchbooks of Maarten Heemskerck and
Francisco de Hollanda gave perspectival views, or vedute, of Roman ruins in their
original settings. Hieronymous Cock was another Northerner who probably visited
Rome in the period 1546-1548. His Some of the principal monuments of ruins
(1550) was one of the first of these collections of views (vedute) to be published.
A decade later they were reproduced, without acknowledgement, by Pittoni. In
1575, Etienne Du Pérac, who had been living in Rome, published the first work in
29
which these views were connected with perspective in the title: Vestiges of the
antiquity of Rome, collected and drawn in perspective. The same Du Pérac
subsequently went to France (1587) and introduced there the idea of perspectival
gardens which had been developed in Tuscany through Buontalenti and others (cf.
below 2.4) and which led ultimately to Le Nôtre's work at Versailles (pl. 93.1).
In Italy the tradition of perspectival views (vedute or prospettive) led on the one
hand to Piranesi's visionary scenes of terrifying dungeons and phantastic
cityscapes (cf. below 2.4), and on the other hand to Piranesi's remarkable
engravings in his Architectures and perspectives (1743 etc.) which, as Herschel
Levit has so effectively shown,28 bear careful comparison with modern
photographs of the sites. Hence, by the eighteenth century there existed those links
between perspective and, -- what we in retrospect--, see as a type of photographic
realism. In these developments, the fascination with ancient monuments, and the
tradition of measuring and surveying them, had played as much a role as formal
treatises on perspective.
As a focal point for Italian, Flemish and French practitioners and theoreticians,
Rome thus played a special role in the development of classicism in architecture,
but also in perspectival views and the so-called conquest of realism. It is important
to recall, however, that what occured in Rome was a manifestation of a deeper
trend that affected the whole of Europe.
13. Surveying and Topography
Ever since Vasari it has become customary to see Giotto as a key figure in the
reemergence of realism as a goal in Western art. Precisely why this happened
remains a matter of debate. Some have pointed to a new interest in the natural
world inspired by the Franciscan movement.29 Gombrich has connected this
interest, in turn, with a new emphasis on narrative, such that paintings were
involved with stories in cycles rather than isolated topics.30 Hence Giotto's
realism at Assisi, Padua and Florence was partly a function of his telling a story in
many episodes (see below 2.2).
In addition, it was almost certainly also a function of Giotto's other activities,
particularly his military concerns with surveying and topography which arose from
his position as superintendent of fortifications in Padua. Giotto's younger
contemporary, Simone Martini, who worked in Naples and Avignon as well as
Siena, had similar professional cross-appointments. As an artist he too had military
connections which makes us look afresh at the fortresses in the background of his
famous portrait of Guidoriccio de Fogliano (Siena, Palazzo pubblico, 1328). Our
concern here is not to enter into the lively debates whether these fortresses can be
identified specifically as Montemassi and Sassoforte; whether they are merely part
of a symbolic landscape or both, but simply to note that, notwithstanding
connections between art and the military, fourteenth century paintings contained
few stategic landmarks or recognizable buildings. Some would say that this was
30
because the concept of mimesis, in a new sense (see below 2.2) had not yet
reestablished itself. In the fifteenth century this changed. Brunelleschi in addition
to recording public sites such as the Piazza della Signoria perspectivally, was also
secretly engaged in military reconnaissance involving surveying and topographical
views.31 But the contexts of this new realism were not only military. Fra
Angelico included a clear view of Lake Trasimeno in his Cortona polyptych.
Meanwhile, the Limbourg brothers in the North were producing the Very rich
hours of the Duke of Berry with spatially convincing picture-postcard like
miniatures of St. Michael's Mount and a number of the duke's great chateaux.
Here patronage was almost certainly a factor. As artists began working for
individual potentates, it became politic and even necessary, to include
topographical views of their chateaux and other estates in the backgrounds.
In the case of the Limbourg brothers, this concern with topographical views or
exterior landscapes appeared in combination with interior churchscapes. A similar
combination of interests is found further north in the work of Roger Campin,
Roger van der Weyden and Jan van Eyck. Hence the same Van Eyck who did
interiors of churches and rooms which were perspectivally convincing, although
not yet completely accurate technically, includes the tower of a church at Utrecht
in the midst of the landscape in the central panel of his Ghent altarpiece. Indeed
an entire book has been written32 to show that landscapes such as those in the
Madonna with the Chancellor Rolin represent the area near Maastricht where he
spent his youth, although ambiguity remains about the extent to which these
landscapes are indeed real or imaginary.
In the next generation this ambiguity disappeared. Jean Fouquet, probably inspired
by his visit to Rome, produced landscapes in his Hours of Etienne Chevalier, in
which the cathedral of Notre Dame in Paris was clearly recognizable. In the same
book of hours, Fouquet also did a convincing perspectival interior of the same
church (pl. 10.1) and other rooms (pl. 53.3). Fouquet's contemporary, Konrad
Witz, also produced both perspectival interiors (pl. 53.4) and exteriors with fully
realistic landscapes as, for instance, in Christ walking on water (Geneva, Musée de
l'art), where he depicted the westernmost shores of Lake Geneva with the peaks of
the Moule and Mont Blanc in the background.
In Old and New Testament scenes, the inclusion of geographical features, with
local landscapes and townscapes in particular, soon became the fashion. The town
of Florence in the background of Pollaiuolo's Annunciation (pl. 13.2) was a typical
Italian example. But the phenomenon was by no means limited to Italy, as is
confirmed by Meckseper's excellent study of Renaissance German cities which
gives dozens of examples from Germany, Austria and Switzerland (pl. 26.1) in the
fifteenth and sixteenth centuries.33
There was a parallel development in secular landscapes. By the 1570's, with Braun
and Hohenberg, this had become systematic and included all the major cities of
31
Europe from Constantinople, Buda, Pest, Prague, Cracow, Moscow, Riga and
Stockholm at the peripheries to the familiar centres of Rome, Paris, London,
Ghent, Amsterdam and Zurich (pl. 26.2). In the next generation with Merian, this
systematic approach was further developed.
Hand in hand with this systematic approach was a new awareness of scale, a
consciousness that one could show the same view at different levels of abstraction
as is illustrated vividly in the sixteenth century hall of maps in the Vatican
showing regions in one scale with inserts for cities and fortresses in a larger scale
(pl. 26.3), much as modern highway maps do today. It is important to recall that
the same individuals were frequently involved in the mastery of these different
scales of reality. Hence the same Albrecht Dürer who wrote on perspective and
did interiors of rooms showing Saint Jerome, also did townscapes (pl. 60.1-2),
views of earth from a nearby viewpoint (pl. 27.1), a viewpoint further away (pl.
27.4) and even maps of the stars (pl. 27.6). Similarly, the same Egnazio Danti who
wrote the commentary to Giacomo Barozzi, il Vignola's Two rules of practical
Biagio Pelacani da Parma
Giovanni Fontana
Jacopo Bellini
Leon Battista Alberti
Filippo Brunelleschi Paolo Uccello
Domenico Veneziano
Filarete
Piero della Francesca
Francesco di Giorgio Martini
Luca Pacioli
Leonardo da Vinci
Fig. 14. Lines of influence among the chief theoreticians (1390-1500).
32
perspective (1583), was cosmographer to the Medici, produced the systematic
series of maps in the hall of the globes in the Palazzo Vecchio and also produced
star maps in the form of astrolabes (cf.pl. 27.5).
In the course of the sixteenth and seventeenth centuries it became possible not only
to compare different views of a scene in one scale (pl. 22-23), but also different
views of a scene in different scales, as for instance, the bridge in Zurich (pl. 26.12), or the orphanage34 in Amsterdam (pl. 24.3-4). For the latter of these there
exist also detailed pictures of the gate to the inner courtyard (pl. 24.2) and front
gables of the house to the left in front of it (pl. 24.1). Atlases of the time by
Mercator (pl. 25.1-4) and Ortelius invite a similar comparison of a given land in
different scales.
Theoretician
L. B. Alberti
Jacopo Bellini
Filarete
Piero della Francesca
F. di Giorgio Martini
Leonardo da Vinci
Luca Pacioli
Name of Treatise
On painting
Elements of painting
Louvre Sketchbook
London Sketchbook
Treatise on architecture
On painters' perspective
Book of abacus
Book of 5 regular solids
Practice of geometry
Codex Atlantico
Manuscript A
Compendium of Arithmetic
Divine Proportion
Mss
9
6
1
1
8
6
1
1
6
1
1
0
2
Written
Published
1434
143_
1430-1450
1430-1450
1460-1470
c. 1480
c. 1480
c. 1480
c.1480-1490
1480-1519
1492
c. 1493
c.1496-1499
1540
1890
1910-1012
1910-1012
1880
1880
1972
1916
1841
1894-1904
1881
1494
1508
Fig. 15. Fifteenth century theoreticians and their works. Excluded from this list are
possible works by Fontana, Mantegna ,Bramante, Bramiantino,Foppa, Butinone
and Zenale.
In this context we are able to look afresh at Vermeer's Allegory of Painting
(Vienna, Kunsthistorisches). On the surface, it is an epitome of perspectival
realism applied to an interior scene. On closer inspection, however, the map on the
wall (pl. 25.5) reveals that we are looking at the Netherlands in a scale very similar
to that found in Mercator. The left and right borders of the map show us cityscapes
at another scale. The painter's easel records a third scale. The model in the
background stands for the original scale and, at the same time, because she is
painted, again represents another scale. Hence Vermeer's Allegory is a testament
of a systematic integration of various scales of abstraction within a single painting.
The sources of this achievement lie much more in the tradition of perspectival
practice than in the so-called theoretical literature on perspective.
33
What then were the themes and functions of these theoretical texts? These are
questions to which we shall return in the third and fourth chapters of our survey.
Here it is important to note, by way of introduction, that the very question of what
constitutes a theoretical text on perspective is itself problematic.
14. Problems of Definition
We have already mentioned that sixteenth century authors such as Barbaro,
Barozzi and Sirigatti saw themselves as authors of books on practical perspective
on the assumption that Euclid's Elements and particularly his Optics, provided
them with a theoretical basis. But the problem goes deeper. Alberti is regularly
cited as author of the first extant treatise on perspective. Yet the title of that work
is On Painting and it contains only a few paragraphs devoted to technical aspects
of perspective. Dürer is another case. His work is entitled Instruction in
measurement and again contains only a few pages on perspective.
The truth is that we know far too little about early perspectival theory. We know
that a number of works have been lost. Giovanni Fontana, may have written the
earliest treatise on perspective (see below p. ), although it is likely that he only
dealt generally with effects relating to colour and aerial perspective. Paolo Uccello
was certainly much concerned with perspectival principles. We have his famous
sinopia for the Nativity (Florence, San Martino alla Scala), but we have no clear
record of his having written a treatise. The same is true of Mantegna although, in
this case, Lomazzo35 alludes to perspectival drawings he did. Both Lomazzo36
and Cellini37 refer to a now lost book by Leonardo da Vinci. Lomazzo also refers
to treatises by Bramante, Bramantino and Foppa of which no trace remains.38
Looking at the fifteenth century as a whole we find there were only seven authors
whose works are extant (fig. 15). All their fifteenth century manuscripts together
amount to 34. Published material was limited to seven pages in Luca Pacioli's
Compendium of arithmetic, geometry, proportions, and proportionality (1494).
Only one treatise, Piero della Francesca's On perspective of painting actually had
perspective in its title. All the authors were Italian. There were four main centres:
Florence, Venice, Milan and Rome. Connected with these were other cities:
Padua, Mantua, Bologna, Pisa, Siena, Urbino, Perugia and Naples. The
theoreticians moved with surprising freedom. Alberti worked in Venice, Mantua,
Bologna, Florence and Rome. Luca Pacioli sojourned in Venice, Urbino, Milan,
Perugia, Florence, Rome and Naples. Leonardo worked in Florence, Milan, the
Romagna, Rome and Amboise.
This applied equally to practitioners. Masolino, for instance, worked in Florence,
Prato, Rome, Castiglione d'Olona from whence he accompanied Cardinal Branda
Castilione to Hungary and worked for King Matthias Corvinus. All this helps to
explain the lack of manuscripts. Artists invariably worked together in workshops
(botteghe) and generally would have learned their theory by word of mouth from
the travelling experts. So, although perspective was technically limited to a dozen
34
theoreticians moving between as many cities, the impact was larger. In retrospect,
however, it is necessary to keep reminding ourselves just how small was the scale
of the phenomenon if we are to appreciate, for instance, Luca Pacioli's complaint
that after Leonardo left Milan in 1499 he was unable to find anyone who could
draw the semi-regular solids for his Divine proportion in proper perspective.39
North of the Alps, technical knowledge of perspective was restricted to rare
individuals with Italian contacts such as Jean Fouquet and Petrus Christus. In this
context Dürer's letter to Pirckheimer, in which he wrote that he hoped to learn the
secret of perspective, makes sense. Knowledge of the laws of perspective evolved
gradually and secretively during the fifteenth century in what was effectively a
closed shop. Yet, as we have shown, the topics with which it dealt were part of a
much larger phenomenon involving both the construction and representation of
basic spatial forms which affected the Low Countries, France and Germany as well
as Italy such that can properly speak of a European phenomenon.
In the sixteenth century, this evolution gathered momentum. Between 1500 and
1600 there were thirty further authors who produced approximately 140 printed
texts on perspective. Of these 70% were published North of the Alps. What had
begun in Italy, spread to the major cities of Europe. Nevertheless, basic problems
of definition remained, partly because perspective continued to be classified under
other topics such as painting (Alberti), sculpture (Gauricus), optics
(Ringelbergius), geometry (Hirschvogel), measurement (Dürer), and architecture
(Serlio) or simply included in encyclopaedic works (Reisch, Ringelbergius, Ryff)
rather than as an independent topic of its own (see below 1.4)
Jean Pélerin's On artificial perspective (1505) in Toul was the first published text
dedicated specifically to perspective. In Germany, Rodler's A beautiful, useful
booklet (1531) was the first such treatise. In the Low Countries, it was Vredeman
de Vries' Scenography or perspective (1560). In Italy, Barbaro's Practice of
perspective (1568) was the first published treatise to deal specifically with
perspective.
The problem of definition became complicated in the mid-sixteenth century with
the appearance of texts designed mainly for architects, which were primarily
collections of perspectival images, serving as practical model books with no
theoretical explanation. The case of Androuet du Cerceau is particularly interesting
in this regard. One of his books, Contains optics which they call perspective
(1551) alludes directly to perspective in its title (pl. 86.3-4). However, many of
the engravings in this work are based directly on his Fragments of old structures
(1550), in which perspective is not included in the title. Does this mean that
Fragments is not a perspectival text whereas Contains optics which they call
perspective is? At the risk of offending purists, I have included both.
Indeed, I have consciously chosen to err on the side of including too much rather
than too little for reasons which should by now be obvious. A search for books on
35
perspective in the narrow technical sense described at the outset would have
excluded Alberti, Filarete, Francesco di Giorgio Martini, Leonardo da Vinci, Luca
Pacioli and even Albrecht Dürer on the grounds that they dealt primarily with
other subjects. In addition it would have excluded Jacopo Bellini, Androuet du
Cerceau and Vredeman de Vries on the grounds that they contained only examples
and no theory. For this reason another strategy was taken. All titles found in the
35 standard bibliographies thus far (Index I.A.) were included, as were a number
of borderline works overlapping with architecture, optics, surveying and roman
ruins.
15. Conclusions
This chapter opened with careful modern definitions to serve as tools in analyzing
the texts and closes with a plea that they not be used too directly in determining the
boundaries of the field. For to do so would be to miss the whole phenomenon of
historical development, of the ambiguities that existed before a new term had
found its own place in an established system of classification; of the changes in
meaning that came as thinkers slowly turned from the practical effects to the
theoretical foundations of the method and gradually recognized that the basis
thereof lay in geometry and not in optics.
36
2. CENTRES
1. Introduction. 2. Europe. 3. Greater Europe. 4. Britain. 5. America. 6. Far East
and Elsewhere. 7. Conclusions.
1. Introduction
The importance of centres in the development and diffusion of Renaissance
culture, assumed by Vasari (1550),1 and discussed by Burckhardt (1860),2 became
the topic of an important book by Chastel (1965),3 who acknowledged that there
were problems with the approach. For while Florence, Lombardy, Rome, Naples,
Venice and Padua were of enormous significance, smaller cities such as Lodi and
Prato were also important. In a subsequent book on Italy's workshops (1969)4
Chastel gave greater emphasis to these smaller cities surrounding the larger ones,
as, for example, Bergamo, Brescia, Como, Vigevano and Pavia in the case of
Milan. Since then there has been increasing attention in the relation between
centre and periphery. Ginzburg and Castelnuovo,5 in a fundamental study, have
challenged the very notion of a centre.
A detailed study would need to confront these problems of method, and might
draw parallels between criticism of great centres and the fashion to criticize great
individuals. Our concern is more modest: to outline the development of the major
centres of publication regarding perspective and to trace how these shift with time.
Centres in cities were usually due to the presence of a court, university and/or a
workshop. They could be centres in at least three different senses: as places of
production, as places which attracted painters to meet, or as places of transit. Nor
was it just a question of painters. As Settis has shown, humanist counselors played
an important part in these developments.
We shall concentrate on the published treatises, aware that there is a further story
to be told in terms of printed engravings and the spread of images through loose
drawings, which were occasionally collected in sketchbooks. For our purposes the
world as a whole may conveniently be divided into five areas: Europe, greater
Europe, Britain, America and the Far East (including India and Australia). The
publication of texts on perspective began in Italy in the late fifteenth century. In
the sixteenth century it spread to France, Belgium, the Netherlands, Germany and
Switzerland. These core European countries are responsible for about 37% of all
publications.
Directly adjacent to these core countries are a number of others, which may be
termed greater Europe. These include Spain, Portugal, Denmark, Sweden, Finland,
Norway, Austria, Czechoslovakia, Poland, Roumania and the U.S.S.R.
Publication in these usually began sporadically in the sixteenth, seventeenth or
eighteenth century, with actual centres emerging only in the nineteenth and
twentieth centuries. A third area in Britain, in which England, responsible for
nearly 15% of all publications, plays a dominant role. In the late sixteenth and
37
throughout the seventeenth centuries it remained very much in the shadow of
Europe, relying largely on translations of continental texts. But by the eighteenth
century London emerged as the leading centre in the world.
A fourth area, America, did not emerge until the nineteenth century, when the
United States, and New York in particular, became a major centre. Canada, by
contrast, has developed no centres. As for South America, Rio di Janeiro has been
the only city with more than a few publications. Finally, in the case of the Far East,
although perspective was introduced to China by the Jesuits in the early eighteenth
century, centres of publication have only emerged in the twentieth century. In
Japan, it did not begin until the 1960's, and in Taiwan, not until the 1970's.
Publications in India go back to the nineteenth century, but they have remained too
sporadic to speak of centres. In Australia the same has been true in the twentieth
century. In the Middle East and throughout the whole of Africa no centres of
publication have emerged.
From the above it is clear that although perspective is an international phenomenon
the extent of its impact varies enormously. Of the 48 countries involved, three
published over eleven hundred treatises each: Germany (1480), England (1187)
and France (1185). Three others produced between 400 and 1000, namely, Italy
(851), the United States (828) and the Netherlands (425). Five countries produced
betwen 100 and 200 texts (Austria, Belgium, Spain, Switzerland and the U.S.S.R.);
seven produced between 25 and 100 (China, Czechoslovakia, Denmark, Japan,
Poland, Scotland and Sweden), while 31 countries produced less than 25 texts
each. In terms of continents, this means that approximately 85% of all
publications occurred in Europe, 13% in North America, and 2% in the rest of the
world. To understand better how these patterns emerged it will be useful to
consider developments in each of the major areas in turn, beginning with Europe,
and specifically Italy where it all began.
2. EUROPE ITALY Padua
We have already suggested (above p. ), that the perspectival principles which
Brunelleschi and Alberti applied to paintings, may well have been inspired by
Biagio Pelacani's lectures on optics in Padua in which he used Ptolemy's
Planisphere as a point of departure in comparing theoretical and practical
projection methods. In any case, Padua certainly played a role in the early history
of perspective. Here Giotto produced his famous examples of proto-perspectival
space in the Scrovegni Chapel (1305-1307), and here, in the fifteenth century,
Alberti worked, while Squarcione and Mantegna painted famous early examples of
perspective. In the seventeenth century there were also a few publications,
including instruments connected with perspective: Galileo's proportional compass
(1606) and Scheiner's pantograph (1637) and a treatise by Viola-Zanini (1629,
1677, 1678, 1698). The eighteenth century brought work on conic sections by
Rocchius (1756) and a general text on linear perspective by Stellini (1778-1782).
38
PADUA
Biagio Pelacani da Parma
Paolo Nicolotto d'Udine
(Paul of Venice)
Prosdocimo da Beldomandi
Giovanni Fontana Nicholas of Cusa Paolo dal Pozzo Toscanelli
L. B. Alberti
Fig. 12. Theoreticians in Padua (1390-1420). In this and the following charts,
underlined names indicate authors of texts on perspective and related topics.
Names underscored with a broken line indicate authors to whom texts on
perspective are attributed. Those not underlined are practitioners.
The nineteenth century brought a reprint of Barozzi (1808) and two moderately
interesting texts by Tabacchi (1844) and Bellavitis (1851). Our century has seen
two further such texts by Severi (1918, 1919) and Martinetti (1926) plus one
popular work by Campedelli (1945, 1948, 1950, 1960, 1970).
But to return to the fifteenth century: from Padua the ideas spread north to Venice
and south to Florence (fig. 12). Giovanni Fontana returned to Venice and wrote
what may have been the first treatise on perspective--no longer extant--which he
dedicated to Jacopo Bellini, author of the famous Sketchbooks (pl. 6.1-2; 9.3-4,
11.2) who, in turn probably influenced Domenico Veneziano. Meanwhile Paolo
dal Pozzo Toscanelli and Leon Battista Alberti returned to Florence where both
were friends with Filippo Brunelleschi, reputed to have made the first
demonstration of perspective sometime between 1415 and 1425. Toscanelli's
interest in projection methods is shown by the sundial he constructed by means of
an aperture in the cupola of the cathedral at Florence. He may also have been the
author of an anonymous treatise on optics entitled On perspective 6 (Florence,
Riccardiana ms. 2110). Alberti wrote the first extant treatise on perspective, the
Italian version of which he dedicated to Brunelleschi, and also discussed
perspective in the context of transformational geometry in his Elements of
painting.
Soon there were direct connections between Florence and Venice. Paolo Uccello,
who studied with Donatello in the workshop of Ghiberti (1404), and knew Alberti,
worked in Venice on the perspectival mosaics at San Marco (c. 1425-1430) and
later also in Urbino (1465). In 1439, Domenico Veneziano moved from Venice to
Florence, where he became a teacher of Piero della Francesca, who later also went
to Urbino. There, in the atmosphere of the court, Piero became involved in the
39
traditions of classical mathematics, which led to his writing treatises on the
subject. Piero's insights became a starting point for two other individuals active in
Urbino: the architect-engineer, Francesco di Giorgio Martini and the
mathematician, Luca Pacioli. In the early 1490's, Francesco di Giorgio Martini
was together with Leonardo da Vinci at Pavia, and from 1496 to 1499 Pacioli and
Leonardo worked together at the court of Ludovico il Moro in Milan. Leonardo
drafted a treatise on perspective7 in the Manuscript A (36v-42v, 1492), and also
wrote a famous treatise which is no longer extant. What emerges therefore is a
fascinating network of individuals spreading ideas from Padua to centres such as
Venice, Florence, Urbino and Milan. The complexity of this network will emerge
more clearly as we examine these centres in turn.
Venice
There were important links between Florence and Venice. In 1424 Paolo Uccello
went from Florence to Venice. He returned to Florence in 1431. In 1423 Jacopo
Bellini travelled from Venice to Florence, became a student of Gentile da
Fabriano, and came under the influence of Ghiberti, Donatello, Brunelleschi and
later perhaps of Masaccio. This has led a modern author, Joost Gaugier, to speak
of the tuscanization of Bellini's art.8 Bellini's Sketchbooks, produced mainly in the
1430's and 40's, were, however, much more than simple reflections of Florentine
conventions. They emphasized the visual aspects of perspectival space, and
introduced a new monumentality that was pioneering at the time. Bellini's two
manuscripts, now in the Louvre and British Library, included no discussion of
theory and contained instead brilliant examples of imaginary architectural views in
perspective (pl. 9.3-4). In so doing, he initiated in tradition, which continued in
Rome (see p.
), and which Androuet du Cerceau and Vredeman de Vries
popularized in the North during the latter sixteenth century. Bellini's Sketchbooks
had a more profound impact on Venetian culture than is usually appreciated. As
Corboz (1986)9 has astutely shown, Bellini's visionary drawings functioned in an
extraordinary way as an architect's conception of what in the next generation
became the Doge's Palace and St. Mark's Square as we know them today.
In the realm of painting, Vasari tells us10 of Jacopo Bellini's influence on
Domenico Veneziano,(figs. 13 and 17), who subsequently went to Florence. Not
mentioned by Vasari is Bellini's influence on Carlo Crivelli, which becomes
obvious on comparison of two of Bellini's preparatory sketches for an
Annunciation (pl. 83.1-2) with Crivelli's famous version of the same subject now
in the National Gallery, London (pl. 83.3). Jacopo Bellini's influence is, of course,
most directly evident through his children. His eldest son, Gentile, taught Vittore
Carpaccio. Vasari tells us11 that Jacopo Bellini's second son, Giovanni (cf. pl.
7.2), taught both Montagna and Cima da Conegliano. The elder Bellini's daughter,
Nicolosia, in turn, married Andrea Mantegna, and thus drew him into the inner
circle of Venetian perspectivists, Mantegna influencing them, as much as they did
him.
40
VENICE I
Giovanni Fontana
Jacopo Bellini
Squarcione
Vivarini
Domenico
Veneziano
Nicolosia Bellini
+
Mantegna
Antonello da Messina Gentile Bellini Giovanni Bellini
Carlo Crivelli
Vittore Carpaccio
Montagna Cima da Conigliano
Fig. 13. Venetian theoreticians and practitioners (1400-1500).
In the last two decades of the fifteenth century the monk, Luca Pacioli, became
fascinated with the theological dimensions of perspective. During one of his many
stays in Venice he even gave a sermon on the subject of proportion and
perspective12 in the church of of San Bartolomeo on 11 August 1506, which he
later published in the 1509 edition of Euclid's Elements. But Pacioli's tendencies as
a publicist went well beyond sermons. With the appearance of his Compendium in
1494, Venice became the first city in Italy to publish a work on perspective (fig.
14). The next decades saw the publication there of his Divine proportion (1509),
and a second edition of the Summa (1523). By the 1540's, Venice had become the
most important publishing centre in Italy for texts on perspective, with 64 titles
prior to 1600. Some were classical texts considered important for perspective such
as Euclid (1505, 1510), Ptolemy (1511, 1548, 1561, 1562, 1564, 1574) and
Vitruvius (1511). Some were architectural treatises: e.g. Cataneo (1554, 1567),
Palladio (1570, 1581) and Scamozzi (1582, 1583).
In some cases, as with Cristoforo Sorte (1580), who had worked with Giulio
Romano, only passing comments on perspective were involved. Others, such as
Giovanni Battista Benedetti (1586), were highly technical. More important was
Daniele Barbaro who, as Patriarch of Aquileia, played an important role as a gobetween for new ideas, especially among instrument makers with interests in
perspective, such as Baldassare Lanci, Cosimo Bartoli, Silvio Belli and Fabrizio
Mordente (fig. 39, see below 2.1). Barbaro alluded to a number of these
innovations in his Practice of perspective (1568, 1569), in which he consciously
set out to popularize the subject, drawing on both Piero della Francesca and
41
VENICE II
Piero della
Francesca
Luca Pacioli Bramiantino
...........
Bramante
Giovanni Zamberti
Baldassare Peruzzi
..................
Giulio Romano
Christoforo
Sorte
Albrecht Dürer
Sebastiano Serlio - Pieter Coecke
Jacopo Sansovino Jacopo Meleghino Hieronymus Cock
Daniele Barbaro
Andrea Palladio
Giacomo Barozzi G.B. Pittoni
Egnazio Danti
Vincenzo Scamozzi
Fig. 14. Venetian theoreticians and practitioners (1500-1600).
Albrecht Dürer, thus bringing together ideas from both central Italy and Nürnberg.
Also important was Sirigatti's treatise (1596), which was based largely on Giorgio
Vasari Jr.'s unpublished manuscript, and introduced a number of semi-regular
solids (e.g. pl. 37.2) into the printed repertory.
Indeed, Venice itself increasingly functioned as a clearing-house in exporting ideas
North of the Alps, as witnessed by the most popular of all sixteenth century
publications on perspective by Serlio. While still in Rome, Serlio had inherited the
writings and work of Baldassare Peruzzi on the subject. This he collected as a
treatise which he published separately (1542) and subsequently as book two of his
works on architecture (1544-1568). By 1545, a French translation by Jean Martin
42
appeared in Paris. Two years later, a German (partial) translation by Walther Ryff
appeared in Nürnberg, and it is claimed that a Dutch translation by Pieter Coecke
van Aelst followed in 1549.
Among the individuals directly influenced by Coecke's translation of Serlio, was
Hieronymus Cock who went on the produce a work on roman ruins with
perspectival views (Antwerp, 1550). This was republished a decade later in
Venice, in a pirate edition by Giovanni Battista Pittoni (1560, 1575), which then
became the basis for a treatise by Scamozzi (1582). Paolo Gallucci also published
his Italian translations of Dürer (1591, 1954), and Pélerin (1599), in Venice.
Hence, in addition to exporting local ideas, Venice served as one of the only Italian
centres, which publicized work done North of the Alps.
In the seventeenth century, the significance of Venice as a centre for publishing
texts on perspective dwindled considerably with 13 titles in the first three decades
and only 5 in the seventy years that followed. The majority of these were reprints.
Among the new authors, the best known were Contino (1645, 1660), followed by
Diano da Diano (1628) and Raverta (1603) whose work on surveying and
perspective also appeared in a German translation in Nürnberg (1726). The
eighteenth century brought thirteen further titles, of which only Visentini's (1742)
book of Venetian views bears mention. The nineteenth century added only three
titles.
Florence
Florence was never a particularly important place for the publishing of texts on
perspective. In the fifteenth century there were none. Its significance for the early
history of perspective (cf. fig.
XVI) was nonetheless enormous. Here
Brunelleschi, who was being referred to as a perspectivist (prospettivo), as early as
1410, performed his historic demonstrations involving the Baptistry and the
Piazza Signoria (1415-1425) and even before this, according to Vasari, Lorenzo
Ghiberti was exploring proto-perspectival methods which influenced Maso di
Christofano, Paolo Uccello,13 Donatello and Antonio Pollaiuolo. In addition,
although modern criticism doubts the heritage, Vasari also reports on14
Donatello's significance for both Masolino and Squarcione who in turn taught
Mantegna the rudiments of perspective in Padua and influenced the Ferrara school
through Cosme Tura and his pupil, Ercole de Roberti (fig.15).
The perspectival treatises of Alberti and the optical manuscript ascribed to
Toscanelli written in Florence have already been mentioned. It is noteworthy that
the painter Vasari omits mention of their possible debt to Biagio Pelacani and the
Paduan tradition of optics and astronomy, emphasizing instead their association
with Brunelleschi and that painter's influence on Masaccio and Filarete.15
In the second generation (1440-1470), with the exception of a few pages on the
subject by Filarete,--who, although Florentine by birth, was much more influenced
43
by the Roman and Milanese tradition--, the field was dominated by practitioners
(fig. 16). From the North, Domenico Veneziano brought with him a Venetian
sense of space which inspired Fra Angelico and, as Vasari tells us,16 the lineage of
painters including Andrea del Castagno, Piero Pollaiuolo, Filippo Lippi and
Sandro Botticelli, as well as Andrea del Verrocchio, whose workshops included
Sandro Botticelli, Botticini, Fiorenzo di Lorenzo, Leonardo da Vinci, and
Perugino. Piero della Francesca was another key figure, who also had a large
number of followers, including, as Vasari reports, the maker of intarsia, Cristoforo
da Lendinara; the painter Melozzo da Forli,17 the architect-engineer Francesco di
Giorgio Martini and the mathematician, Luca Pacioli.
In the period 1470-1500 (cf. fig. XVIII), four individuals with Florentine
connections wrote on perspective, namely, Piero della Francesca, Francesco di
Giorgio Martini, Luca Pacioli and Leonardo da Vinci. But of these, Piero and
Francesco di Giorgio had Urbino as the chief base for their theoretical work,
Leonardo da Vinci did his most significant writing in Milan, while Pacioli's
writing occurred in Milan, Venice and Rome.
Nor did the situation change drastically in the sixteenth century which saw the
publication of one important work by Gauricus (1504), a work by Dosio inspired
by Roman ruins (1589) and three classical authors believed relevant to perspective,
namely, Lucretius (1512), Euclid (1573) and Heliodorus of Larissa (1573). There
was also Giorgio Vasari, Jr.'s manuscript of 1595 (pl. 36.3), which served as a
basis for Sirigatti's treatise (1596, cf. p. 37.2). If Florence was never really a major
centre in terms of theory, it was nonetheless of crucial importance in terms of
paintings, gardens (see below II.3), object (e.g. what the Italians call
bicchierographia), and architecture.
FLORENCE I
Paolo dal Pozzo Toscanelli
Leon Battista Alberti Lorenzo Ghiberti
Taccola - Filippo Brunelleschi
Pollaiuolo
Paolo Uccello Donatello
Antonio
Maso di Christoforo
Masaccio
Antonio di Tuccio Manetti
Squarcione
Masolino
Filarete
44
Cosme Tura
Mantegna
Cosme Tura
Ercole di Roberti
Fig. 15. Florentine practitioners and theoreticians (1400-1440).
FLORENCE II
Domenico Veneziano
Fouquet
Andrea del Castagno
Filarete
Fra Angelico
Piero Pollaiuolo
Alesso Baldovinetti
Filippo Lippi
Andrea del Verrocchio
--
Jean
Piero della Francesca
Sandro Botticelli Ghirlandaio Botticini Fiorenzo di Lorenzo Perugino
Fig. 16. Florentine practitioners and theoreticians (1440-1470).
FLORENCE III
Francesco di Lauranna
Piero della Francesca
45
C. da Lendinara Melozzo da Forli F. di Giorgio Martini Luca Pacioli
Andrea del Verrocchio
Luca Signorelli
Fra Giovanni da Verona
Leonardo da Vinci
Perugino
Cennino Cennini Baccio Bandinelli
Raphael G.B. Caporali G. Genga
Benedetto
da
Maiano
Sebastiano Serlio Diaceto Bugiardino Francesco de Salviati
Fra
Bartolommeo
Benedetto Salviati della Porta
Giulio Romano
Baldassare
Lanci
Martino Bassi
B.Genga
Ammanati
Giorgio Vasari
Giorgio Vasari Jr.
46
Fig. 17. Florentine practitioners and theoreticians (1470-1600).
Curiously enough it played the same role with respect to universal measuring
instruments and the sector which came to be intimately connected with perspective
(cf.pp.
). This story involves a complex heritage of techniques and ideas which
can be traced (fig. 41) from Nürnberg in the latter fifteenth and early sixteenth
centuries (Peurbach, Regiomontanus, Apian), via Antwerp in the 1530's and 40's
(Gemma Frisius, Mercator), and Paris in the 1540's - 1560's (Orone Finé, Pierre de
la Ramée and Abel Foullon), south (fig. 39) to Venice in the 1560's (Silvio Belli,
Daniele Barbaro, Fabrizio Mordente, Latino Orsini), and finally to Florence
(Cosimo Bartoli, Egnazio Danti, Francesco Pifferi) where in 1594, the same
Giorgio Vasari, Jr. who wrote on perspective, prepared a compendium of all
universal measuring instruments in the grand duke of Tuscany's collection. In
terms of practical examples, this manuscript was undoubtedly of interest to Galileo
Galilei who, by 1596, was developing his sector in Padua.
The seventeenth century saw no basic change in this Florentine pattern. There was
a book on Roman ruins by Maggi (1600), and on views of Jerusalem by Amico
(1620); a manuscript by Galileo's friend Lodovico Cardi (il Cigoli, c. 1612), which
was never published; one important textbook by Accolti (1526, cf. 1627, 1628); a
significant treatise by Malombra (1630) and a mathematical one by Torricelli
(1644). The eighteenth century saw one classical text by Apollonius (1722) and
two modern works by Lorenzini (1721) and Grandi (1744, 1750, 1764) on conic
sections, plus a significant edition of Leonardo's Treatise of painting (1792). The
nineteenth century brought a half dozen new authors: Rossi Melocchi (1805),
Benvenuti (1817), Castagnoli (1830), Sanquirico (1840), Cucchi (1862) and
Bellotti (1892) plus a new interest in Renaissance authors particularly Ghiberti
(1839), Alberti (1843, 1849, 1890) and Barozzi da Vignola (1831). The twentieth
century has seen a development of this trend with editions of Toscanelli (1964),
Alberti (1950, 1972), Bellini (1908), Francesco di Giorgio Martini (1970), Piero
della Francesca (1942, 1974, 1984), Leonardo (1973) and Lomazzo (1975) plus at
least ten modern authors, notably Saccardi (1961, 1970, 1975), Monticolo (1965,
1975) and more recently Aterini (1978, 1980). The interest in reprints is a
reflection of a larger pattern, for Florence has become one of the leading centres in
terms of secondary literature about the history of perspective.
Urbino
At Urbino interest in perspective was more closely connected with mathematics.
As Rose (1975),18 has so elegantly shown, by the 1470's Urbino had become a
major centre for the collection of mathematical texts, largely due to duke
Guidobaldo da Montefeltro's personal interests. The duke had his own copies of
Piero della Francesca's Book of the abacus, Booklet of the five regular solids, and
47
On the perspective of painting, all three of which--as Egnazio Danti (1583) noted-were considered as texts on perspective and served, as Daly Davis (1977)19 has
demonstrated, as sources for Luca Pacioli's Summa (1494) and Divine proportion
(written 1496-1499) and published 1509). In the latter decades of the fifteenth
century, Francesco di Giorgio Martini, who20 was one of the chief architects of
the ducal palace, and responsible for the striking perspectival intarsia in the library
(pl. 79.1), also wrote on perspective there.
In the mid-sixteenth century, the collection of mathematical manuscripts was given
new impetus by Federico Commandino who launched a programme to edit and
publish major Greek and Latin classics. His initiatives attracted a wide circle of
scholars and scientists (fig. 38), which included Nicolo Tartaglia, John Dee and
Giovanni Battista Benedetti.Of particular interest for our purposes, is
Commandino's edition of Ptolemy's Planisphere (1558), in which he related the
projections of planispheres with those of linear perspective. This recognition, that
perspective involved a special case of projections that occured also in planispheres
and astrolabes, brought to light a need for a more general theory of projections,
which Commandino's student, Guidobaldo del Monte, attempted to fulfill in his
classic text (1600), in which he demonstrated that a single universal principle
underlay 23 practical methods then in use.
In the revival of the Greek mathematical tradition, the texts of Apollonius and
Pappus played a special role because they focussed on the theme of conic sections.
Already in the 1540's, Nicolo Tartaglia in Venice had drawn attention to them.
Francesco Maurolyco had gone further. But again it was Commandino who set
about editing them. Both Maurolyco and Commandino were in touch with
Christopher Clavius who was, in turn, a mentor of both Paul Guldin and Gregorius
Saint Vincent. In the next generation Galileo, a direct descendent of the Urbino
tradition, became the teacher of Bonaventura Cavalieri, Italy's foremost expert on
conic sections in the early seventeenth century. These same individuals were
involved with projection problems in astrolabes (Commandino, Clavius), sundials
(Maurolyco, Clavius) and perspective (Commandino, Guidobaldo del Monte), and
became aware that such practical interests were related to the projections involved
in conic sections.
The study of conic sections also brought a philosophical problem into focus. A
cone at its base is a continuous surface bounded by lines. At its apex it is a discrete
point. Ancient philosophers had treated continuous and discrete quantitities,
(geometry and arithmetic) as independent worlds. Renaissance thinkers began to
explore how the two related to one another: whence Galileo's long introduction in
his Dialogue concerning the two chief world systems, devoted to line and point,
involving cones as examples, or Cavalieri and Saint-Vincent's preoccupation with
indivisibles, or Fermat's concerns with maxima and minima. But in a sense,
Urbino merely prepared the way. As will be shown below (pp.
), it was in
Paris that these new connections between conic sections and perspective came to
fruition.
48
In Urbino, this same small circle of Commandino and Guidobaldo del Monte, in
touch with Clavius, Mordente and Galileo, were equally involved with the
development of universal measuring devices and principles of statics and
dynamics. Hence, the search for general principles of perspective in Urbino, was
part of a larger trend towards quantification, which made possible the universal
claims of early modern science (cf. below 2.1). However after the collapse of
Urbino's political power at the end of the sixteenth century, its significance quickly
vanished and did not return. Paris soon took its place as the chief centre for
mathematics. Meanwhile Rome remained the chief city in Italy.
Rome
In terms of perspectival practice, Rome was important from the outset, as
witnessed by the Annunciation in San Clemente by Masolino and his pupil
Masaccio in the late 1420's, and Fra Angelico's work in the Vatican Stanze (c.
1455). With the return of the papal court from Avignon back to Rome, there was
renewed papal patronage. Beginning with Sixtus IV in 1482 and continuing until
1527 there emerged in Rome a vision of Italian national art. Sixtus IV saw Rome
as a twin capital: through the church it was the capital of Italy, but it was also the
capital of the Roman empire.
The rebuilding of the Vatican complex provided a major incentive for perspectival
practice beginning with isolated paintings such as Melozzo da Forli's Inauguration
of the Vatican Library (c. 1475), Mantegna's decorations in the chapel of Innocent
VIII (1490), and the friezes in the map room of the Palazzo Venezia attributed to
him (c. 1490); series by Botticelli, Ghirlandaio and Perugino on the walls of the
Sistine Chapel, Michelangelo's trompe l'oeil effects on the ceiling of this same
chapel (1506-1508), and finally Raphael's monumental cycles in the Stanze, with
the School of Athens (pl. 11.5), which remains one of the most famous
perspectival interiors, although the details of its construction may be inaccurate.
ROME I
Foppa Mantegna
Melozzo da Forli
Leonardo da Vinci
Perugino
Bramante
Antonio da Sangallo
Raphael
Giulio Romano
49
Baldassare Peruzzi Antonio da Sangallo, Jr. Cristoforo Sorte
Sebastiano Serlio
Fig. 20. Practitioners and theoreticians in Rome (1450-1550).
ROME II
Antonio da Sangallo
Heemskerck
Martin
Hieronymus
Cock
Antonio Labacco
Giovanni
Battista Pittoni
Etienne du Perac
Antoine Lafreri - Antonio Salamanca
Vincenzo Scamozzi
Mario Kartarus
J. Sadeler
Pieter II. Stevens
Hendrik II Hondius
Samuel Marolois
Fig. 21. Artists and publishers of perspective and Roman ruins (1550-1620).
The numerous artists' conceptions for the new St. Peter's, by Raphael, Bramante,
Antonio da Sangallo, Baldassare Peruzzi (cf. pl. 84.5) and Michelangelo, were a
further incentive to perspectival drawings21 (fig.20). In some cases, as with the
50
Farnesina, a commission from within papal circles, led to a remarkable trompe
l'oeil interior by Baldassare Peruzzi.
Meanwhile, there were also the ruins of the ancient city, which made Rome a
centre for those concerned with surveying and perspectival representation. This
had begun in the early fifteenth century as a type of artistic pilgrimage with
architects and painters such as Brunelleschi and Donatello. Alberti's Description of
the city of Rome, was part of that tradition, as were Filarete's sketches of isolated
buildings--which influenced Fouquet when he visited Rome. Lotz (1967),22 has
outlined some of the more important steps in these developments, which continued
through the sixteenth century with Agostino Veneziano, Sebastiano Serlio and
others producing individual engravings, which were later collected in albums such
as the Wolfenbüttel book of engravings (c. 1540).
From the 1460's onwards, however, others such as Francesco di Giorgio Martini
had begun gathering their sketches together in manuscript treatises on architecture
and geometry. Bramantino's Antiquity of Rome (c.1500) marked a next step.
Meanwhile, another tradition was coming into play. Pope Julius II took particular
interest in Rome's antiquity, to study which he brought in Bramante (1501) and
Raphael (1508), whom he subsequently (1510) appointed as director of antiquities.
Raphael introduced both a new scale in construction and an archaeological
dimension. He had his own manuscript translation of Vitruvius, was concerned
with how the principles of perspective related to architectural representation
(involving ground plan and elevation). As a result, the Roman monuments came to
be seen increasingly in the context of contemporary architectural theory and
practice. The illustrated editions of Vitruvius, by Fra Giocondo (1511) and
Cesariano (1521), heralded this new interest and led to new architectual treatises
by Palladio (1570) and Scamozzi (1582).
At a more practical level, Francesco di Giorgio Martini's student, Baldassare
Peruzzi, developed the ordinary rule, a short cut method of finding diagonals, later
discussed by Danti in his edition of Vignola's Two rules of practical perspective
(1583). Peruzzi also developed a new kind of illustrated architectural book, which
included both roman ruins and modern edifices. Serlio systematized this, and
began publishing his work in the 1540's. Northerners, such as Francisco de
Hollanda, Martin van Heemskerck, Hieronymus Cock and Jacques Androuet du
Cerceau developed their own type of sketchbook, specializing in idealized
perspectival ruins, which were sometimes a conscious combination of real and
phantastic elements. By 1550, Androuet du Cerceau (pl. 86.3-5) in Orl‚ans (and
later in Paris), and Hieronymus Cock in Antwerp began publishing these.
In the 1560's, Antonio Labacco, a student of Antonio da Sangallo, began
publishing his own versions of the ruins in Rome (fig. 21). This was followed, in
1575, by Etienne du Pérac's treatise. His acquaintance, Antoine Lafréry, who was
both cartographer and publisher, collected together a number of isolated
engravings by Antonio Salamanca and others in producing his great Topography of
51
the city of Rome (1575-1602). Cartaro (1578), produced his own collection on a
smaller scale. In the seventeenth century, ruins, sometimes in combination with
modern buildings, dominated publications in Rome, including Lauro (1612, 1625,
1637, 1641), Orlandi (1612), Maggi (1618, 1649), Montano (1624, 1638, 1691),
Bramante (1647), Rossi (1647), Falda (1655, 1663, 1665, 1666, 1667, 1670, 1675,
1680, 1683) and Ferrario (1655, 1665). There were several editions of Barozzi
(1602, 1642, 1644, 1684), while the scientific side was dominated by Jesuits,
beginning with Scheiner's work on the pantograph (1631), Kircher's encyclopaedia
of light and shade (1646), Maignan's great treatise on sundials and perspective
(1648, 1698), and at the end of the century, Pozzo's Perspective of painters and
architects (1693, 1694).
In the eighteenth century, two authors dominated the scene: Pozzo (1700, 1702,
1707, 1717, 1723, 1737, 1741, 1758, 1764, 1793) and Piranesi (1740, 1743, 1748,
1750, 1752, 1761, 1770, 1781, 1797, 1798). There were a number of reprints of
earlier works by Maignan (1725), Le Clerc (1746), Barozzi (1770), Du Perac
(1773), Falda (1773), Labacco (1773). There was an Italian translation of Taylor's
fundamental work (1755, 1756) and there were at least three new treatises by
Campiglia (1739), Antonini (1770) and Orsini (1771).
The nineteenth century added only 25 new titles, as compared to 52 in the
eighteenth. There were again reprints such as Leonardo (1817, 1890), and Pozzo
(1810, 1828, 1840), plus at least seven new authors including Sereni (1826),
Lanciani (1849), Gilli (1887), Fiorini (1889), Garneri (1895), Borgogelli (1897)
and Bechetti (1899). Of these Borgogelli remained popular in the twentieth
century with at least seven new editions (1905, 1908, 1909, 1915, 1919, 1920,
1937). There have also been at thirty-six other books, notably Fausto Vagnetti's
classic textbook (1947), and works by Lazzaroni (1908), Nico (1920, 1923),
Simoni (1973, 1976), and Sinisgalli (1978). Rome, which was the world centre of
perspective at the turn of the sixteenth century, has thus retained a significant role
to this day.
Milan
The role of Milan in the development of perspective is frequently underestimated.
The marriage of Francesco I Sforza with ** Gonzaga (1451), issued in a new era.
Vincenzo Foppa went to Mantua, where Mantegna served as an exemplar. By
1468, he was back in Milan working in Sant Eustorgio. In the decades that
followed, Bramante produced his great illusionistic Choir in Santa Maria presso
San Sepolcro (pl. 5.4) and Leonardo painted the Last Supper (1495-1497). In
terms of perspectival practice, these two works could be seen as the greatest
examples of the entire Renaissance.
Milan was also of some importance in terms of theory (fig.18). Vasari reports23
that Filarete taught Vincenzo Foppa, who in turn taught the painter Butinone,
Zenale and Bergognone. If credence can be given to the testimony of Lomazzo,24
52
Foppa, Butinone, Bramante, Zenale and Leonardo da Vinci all wrote treatises.
Unfortunately no trace of the originals survives. Even so the scattered evidence in
Leonardo's notebooks provides some impression of what was happening in the
1480's and 1490's. Leonardo recognized that perspective involved more than
copying the physical world, that it applied equally to different levels of abstraction
and served as a bridge between the concreteness of nature and abstractions of
mathematics. In addition, while his elder contemporary Piero della Francesca was
content to rely on Euclid for theory, Leonardo insisted on systematic experimental
demonstrations of the principles of perspective. He also became convinced that
these principles could be applied equally to the physics of heat and light, indeed to
the whole of nature25 (cf. below 2.1).
MILAN
Fouquet
Pisanello Mantegna
Bramante
Filarete
Jacopo Bellini
Leonardo da Vinci
Vincenzo Foppa
Zenale
Butinone
Luca Pacioli
Bergognone
Bramiantino
...........
Lomazzo
Jacopo Sansovino Luca Signorelli
Fig. 18. Milanese theoreticians and practitioners (1450-1500).
In terms of published works during the fifteenth century there was only Fazio
Cardan's edition of Peckham's optical textbook, Common perspective (1482). The
French invasion of 1499, and the dispersal of the Sforza court temporarily
obliterated Milan's importance as a centre.
And yet it continued to have some importance as is witnessed by the work of Carlo
Urbino. Martino Bassi's diatribe against Pellegrino Tebaldi, concerning the relief
of the Annunication for the choir of Milan cathedral, remained primarily of
academic interest. (This work published in Brescia in 1571, 1572 was reprinted in
Milan in 1771.) In the latter sixteenth century, in nearby Cremona, Carlo Urbino is
believed26 to have composed the Codex Huygens, based on Leonardo da Vinci's
studies of proportion and foreshortening applied to the human body (pl. 68.5).
53
Lomazzo's treatise, published in Milan (1584, 1585), was largely a review of
earlier glory. The seventeenth century brought only two new works: Raverta's
treatise on surveying and perspective (1602), and Barca (1620), as well as a
possible edition of Bramantino (1612). The eighteenth century brought nothing.
The nineteenth century, by contrast, brought 52 books published in Milan. A
dozen of these were reprints of Renaissance texts, notably Alberti (1803, 1804,
1840), Barozzi (1814, 1819, 1830, 1832, 1840, 1850, 1869) and Leonardo (1804,
1859, 1894). There were at least four original authors: Zanotti (1804, 1825),
Taccani (1813, 1825), Bordoni (1816) and Landriani (1815, 1818, 1824, 1827,
1833), plus others such as Sella (1861), Suini (1880, 1896), Aschieri (1883, 1888,
1895) and Vegetti (1894, 1895).
The twentieth century brought 78 further books, including reprints of five
Renaissance authors, Ghiberti (1965), Filarete (1972), Martini (1967), Pacioli
(1956, 1973) and Dürer (1973) and one baroque author, Guarini (1968). Thanks to
firms such as Hoepli, Milan has become the chief Italian centre for primary texts
on perspective in the twentieth century. It has published the two authors who have
dominated the scene: Claudi (1896, 1897, 1903, 1910, 1915, 1920, 1924, 1929,
1935, 1938, 1940, 1942, 1951) and Chiesa (1931, 1938, 1943, 1944, 1947, 1951,
1956, 1961, 1967, 1969, 1975, 1980). It has also published three other popular
authors: Seller (1942, 1944, 1946, 1949, 1960); Roversi (1945, 1948, 1949, 1952)
and Bonfigli (1960, 1962, 1968, 1975, 1976, 1979). Smaller companies such as
Bertolini have published Elias (1973) on spherical perspective.
Bologna
Bologna with its university, the Bentivoglio family, who created a court-like
atmosphere, and--after 1500-its connections with the papacy, was another
important centre, the history of which sadly needs study. We are told that Albrecht
Dürer learned the secret of perspective there. In Bologna, Bramante was
responsible for the cloisters of the catholic university. During the sixteenth
century, the works of Apollonius and Serenus were published there (1566) as was
Ptolemy's study of the planisphere (1572). In the seventeenth century, other than
two editions of Vignola (1662, 1682), the main works were by Jesuits: Mario
Bettini's monumental Beehive of the universe of philosophy (1642, 1645, 1654,
1660), and Scheiner's work on the pantograph (1653). Giulio Troili also published
his important textbook in Bologna (1672, 1683).
The eighteenth century saw 26 publications which included two new editions of
Scheiner (1726, 1749), a series of editions of Galli da Bibiena (1703, 1725, 1731,
1732, 1745, 1749, 1753, 1764, 1777) and some original work by Quadri (1744),
Tesi (1787) and Zanotti (1755, 1766, 1767, 1782). The nineteenth century saw a
reprint of Troili (1863), plus a half dozen new authors: Basoli (1810, 1812),
Marconi (1811), Magistrini (1816), Fagnoli (1840), Cocchi (1851, 1855), and
Fiorini (1892). This pattern remained unchanged in the twentieth century, with
one reprint of Barozzi (il Vignola) (1974), and seven new authors: Tagliavini
54
(1904), Severi (1906), Chisini (1960), Boccaleone (1963), Speranza 91963),
Lorgna (1971) and Nannoni (1978) none of whom has changed the field.
Naples
Naples is another centre, which deserves more attention. Under the patronage of
Alfonse of Aragon, it was here that Pisanello produced his proto-perspectival
frescoes. The city's historical connections with Anjou brought important visitors
from the North such as Jean Fouquet and Ren‚ d'Anjou. In Naples, Fra Giocondo
worked on his famous edition of Vitruvius (Rome 1511). Publications did not
begin until the latter half of the sixteenth century, with Porta's work on natural
magic, which discussed the use of camera obscuras in painting (1558, 1569, 1593)
and Romano's treatise on military uses of perspective (1595). The seventeenth
century brought new editions of Porta (1611, 1726) and Maurolico's (1611) work
on optics. The eighteenth century saw reprints of two Renaissance authors, Alberti
and Leonardo (1733), plus three new ones: Januariis (1714), Martino (1727, 1734),
Grandi (1737). The nineteenth century brought one popular author, Flauti (1815,
1820, 1827, 1841, 1842, 1846) and five further authors of whom Capobianco
(1960, 1966), Fusco (1968) and Tenta (1968) may be mentioned in passing.
Other Italian Cities
There were a number of Italian cities, which published only one title on
perspective in the period 1500-1700. Frequently these were in the orbit of a nearby
court. Connected with Milan for example were Como, where Cesariano published
his edition of Vitruvius (1521); Brescia where Bassi's Various matters (1571)
appeared, Vigevano, as well as the court at Mantua, where both Alberti and
Mantegna were active. Linked with Urbino, was Pesaro, which saw the first
edition of Guidobaldo del Monte's landmark Six books of perspective (1600).
Linked with the court of Ferrara was Ravenna.
Siena offers an interesting case of a city, which began with an independent
tradition. Ambrogio Lorenzetti's Annunciation (Siena, Gallery, 1348), is reported
to have been the first painting in which all the lines of the floor tiles converge to a
single vanishing point.27 But by the fifteenth century, as the Florentines developed
demonstrations of perspective, Donatello and Ghiberti influenced the Sienese Il
Vecchietta (fig. 19). He, along with another Florentine, Verrocchio, became the
teacher of Francesco di Giorgio Martini, who went on to do his main work in
Urbino and Rome.
SIENA
Il Sassetta
Ghiberti Donatello
Verrocchio
Il Vecchietta
55
Francesco di Giorgio Martini
Agostino Chigi
Leonardo da Vinci
Pintoricchio
Sodoma
Baldassare Peruzzi
Fig. 19. Sienese practitioners and theoreticians (1400-1550).
Some smaller cities, which published treaties on perspective, maintained their
independence, notably Cesena, Livorno, Monte Regale, Perugia and Pisa. In the
case of Palermo, there were no publications until the eighteenth century, which
brought four interesting authors: Spuccez-Lanza (1701-1711), Aidoni (1706),
Amato (1714, 1733, 1736) and Amico (1750). Then for almost 150 years there was
nothing until Basile (1898), with seven further authors in the twentieth century of
which Filosto (1964, 1979) and Santapa (1968) may be mentioned.
It is important to note, however, that these patterns of publication do not tell the
whole story. Some cities had no publications yet owed their significance to an
artist who left his mark there. Piero della Francesca in Arezzo is the classic case.
Masolino in Castiglione Olona or Filippo Lippi, with his great Annunciation in the
cathedral at Spoleto, are other examples. Moreover, as Vasari reminds us, oral
communication played a much greater role than is sometimes imagined. This took
place at three distinct levels. In rare cases, a thinker would communicate with an
author as in the case of Malatini when he advised Daniele Barbaro. Sometimes, a
practitioner would counsel a theoretician, as Giulio Romano did with Cristoforo
Sorte. More often, the master of a workshop would simply instruct his apprentices
directly. This is almost certainly how Masaccio, Fra Angelico, Botticelli,
Ghirlandaio, Michelangelo and a number of their contemporaries learned
perspective. There was yet another factor. Even after the invention of printing,
manuscripts continued to have precedence over books in some humanist libraries
which helps explain why none of the major fifteenth century authors on
perspective was published at the time (figure 15).
In the North, the relative emphasis on oral, manuscript and printed communication
was different. From the prefaces of Pélerin (1505) in France, and Vredeman de
Vries (1604) in the low countries, we know that this oral tradition existed also in
the North, but to a lesser degree, and in Germany, Pfintzing (1598) reports only
one individual, Hans Haiden, who communicated his ideas by word of mouth. As
for manuscripts, we know of isolated instances such as the copy of Alberti made in
1476, but no cases where an author on perspective relied on manuscripts for the
spread of his ideas. There was much more emphasis on printing. Indeed authors
were sometimes publishers of their own works as with Jacques Androuet Du
56
Cerceau. Others such as Hieronymous Cock, Philippe Galle, Melchior Tavernier
and Francois Langlois published their own and other writings. This is also true of
Theodore Galle who, in addition, had close contacts with another publisher
through his marriage to Christoph Plantin's sister. It is not surprising therefore, that
already in the sixteenth century approximately 56% of titles on perspective were
published in the North. By the seventeenth century this had risen to 77%. Paris
played a special role in this trend. Indeed between 1500 and 1700, 150 books were
published there, as many as in the whole of Italy combined. It will be useful
therefore to consider this city in some detail before turning to other northern
centres.
FRANCE
Paris
It is generally agreed that Fouquet was the first in France to practice linear
perspective, as is evidenced by his rendering of Notre Dame in Paris, in his Hours
of Etienne Chevalier (pl. 11.1). He is thought to have learned the principles from
Filarete in Rome, sometime between 1445 and 1450 (fig. 22). Around 1476, a
French canon, Jean P‚lerin, Le Viator, is also believed to have made a visit to Italy,
where he too learned perspective.28 This became the basis for his treatise (Toul,
1505), which was based partly on Parisian scenes (pl. 11.3) and must have been
known in the city as it formed the basis of Ringelbergius' treatise (Paris 1521).
Francis I provided an important catalyst for perspective in France by inviting
Italian artists to his courts at Amboise, Romorantin and Fontainebleau, first
Leonardo de Vinci (1515-1519), then Rosso Fiorentino, whose students included
Jean Cousin, author of a Book of perspective (1560), and Sebastiano Serlio, from
1541 until his death in 1551, who worked on plans for reconstruction of the
Louvre, and whose writings were translated by Jean Martin and published in Paris
(1545-1547, 1587, 1590).
Also engaged in these plans for the new Louvre, was Jacques Androuet du
Cerceau, a native of Orléans, who published a posthumous treatise of Leonard
Thiry from Antwerp, as well as his own writings about architecture and
perspective. When religious wars forced Androuet du Cerceau to leave Paris, his
architectural projects were inherited by Etienne Du Pérac, of roman ruins fame,
who taught Claude Mollet about perspective in gardening and whose son, André
Mollet, in turn became a teacher of Andr‚ Le Nôtre, who constructed the great
illusionistic gardens at Vaux le Vicomte and Versailles (see below 2.3).
During the sixteenth century, seventeen books on perspective were published in
Paris: approximately 14% of the total in Europe. Even so, only four authors were
involved: Androuet Du Cerceau, Cousin, Dürer and Serlio: two French, one
German, one Italian. Hence, as late as 1600 Paris was surprisingly limited in its
horizon. In the next century this changed radically: a third of all books on the
subject were published there. Indeed with 133 books in the seventeenth century
Paris became the world's leading centre. This did not involve a complete break
57
with the past. There were reprints of foreign Renaissance authors: Alberti (1651),
Barozzi (1620), Leonardo (1651) and Cardi (1663), as well as earlier French
authors, particularly Androuet Du Cerceau (1607, 1611, 1615, 1648, 1676) and
Cousin, le jeune (1600, 1603, 1612, 1618, 1625, 1635, 1642, 1647, 1656, 1671,
1676). There was a continued interest in both military architecture (e.g. Perret
1601, Bourdin 1655, and Bourgoing 1661) and civil architecture (e.g. Blondel
1675, 1698, Bullet 1675, Rohault, 1682, Deis 1698 and Aviler 1691). But there
was a shift in the context of discussions. What had been a topic for painters in the
fifteenth, and architects in the sixteenth centuries, now also became a concern for
mathematicians.
The reasons were several. One involved conic sections. As in Urbino (cf. pp. ),
the Parisian thinkers were stimulated by problems arising out of the classical texts
of Apollonius and Pappus, the difference being that in Paris, the connections
between conic sections and perspective were explored much more intensely. Here
Jean, le Sieur de Vaulezard (1631) played a role. But it was mainly due to an
extraordinary circle of the 1630's known as the Académie Parisienne which
included Roberval, Etienne Pascal, Marin Mersenne, Blaise Pascal, Claude
Mydorge and Girard Desargues, the latter three of which were at the centre of
studies concerning both conic sections and perspective. The questions they raised
later directly influenced Philippe de la Hire, Leibniz and Newton.
In Urbino, thinkers had recognized that this nexus of problems raised philosophical
questions concerning the relation of geometry (continuous quantities or lines) to
arithmetic (discrete quantities or points). In Paris, these questions became much
more acute. In 1600, Henri de Monantheuil, a student of Pierre de la Ramée had
written a treatise on the relationship between point and line. His claims were
challenged
PARIS I
Filarete
Jean Fouquet
Leonardo da Vinci
Jean Pélerin
Rosso
Fiorentino
Jean Cousin
58
Leonard Thiry
Sebastiano Serlio
Hieronymus Cock
Jacques Androuet du Cerceau
Daniele Barbaro
Hans
Lencker
Etienne Du P‚rac
Jean Cousin le jeune (?)
Jacques Boyceau
Claude Mollet
Andr‚ Mollet
Olivier
de
Serres
Andr‚ le Nostre
Fig 22. The emergence of Paris as a centre for perspectival theory (1450-1600).
by the mathematician, Jacques Aléaume, also the author of a treatise on
perspective, edited by Etienne Migon, which influenced both Claude Mydorge and
Girard Desargues.
There were other developments, which gave an unexpected urgency to these
debates concerning points, lines, perspective and conic sections. During the
sixteenth century, the leading German experts on cossist algebra, notably Michael
Stifel, Peter Rothe and Johann Faulhaber, had concentrated on numerical problems
and their symbols. French thinkers such as Pierre de La Ramée‚ had suggested
that cossist algebra was a vulgar form of the analytical method of Greek
mathematics. François Viète developed this idea. He distinguished clearly
between a purely numerical approach (logistique numérique), and his more general
method (logistique spécieuse or calcul des symbols), whereby he resolved
geometrical questions by means of algebraic analysis. Pierre de Fermat further
developed Viète's idea of symbolic algebra as a tool by means
PARIS II
Philippe Danfrie Pierre de la Ram‚e Franc ois ViŠte
59
Salomon de Caus Henry de Suberville
Henri de Monantheuil
Johann Faulhaber
Jacques Aléaume
Denis Henrion
Etienne Migon
Jean,le Sieur Vaulezard
Pierre Hérigone
Descartes Mersenne Pascal Desargues Mydorge E. Pascal Roberval P. de
Fermat
Jean Francois Nicéron
Nicolas Poussin
Abraham Bosse
Melchior Tavernier
Laurent de la Hire
Jean Dubreuil
Jean Curabelle
Philippe de Champaigne
Jean le Bicheur
Gr‚goire Huret
Philippe de la Hire
60
Leibniz
Isaac Newton
Fig. 23. Paris as the world centre for mathematics and perspective.(1600-1700).
of which one could unite the realms of arithmetic and geometry. Fermat's study of
Apollonius' Conics, led him to perceive in the cone and its sections, a standard
geometrical framework through which he could establish correspondences between
equations and curves. The result was an analytic geometry, which concentrated on
the geometrical construction of curves.
His contemporary, René Descartes, another of the founders of analytic geometry,
slighted Fermat's manner of construction, and focussed his own energies on a new
and more advanced theory of equations. As he explained in a letter to Beeckman
on 26 March 1619, Descartes was consciously searching for a new science "by
which all questions can be reduced that can be proposed for any sort of quantity
either continuous or discrete."29 In arriving at this new science, whereby geometry
and arithmetic were reconciled, and numbers could be plotted as lines on
coordinates, Descartes also relied on the construction theorems of Apollonius'
Conics. This helps to explain both the tremendous fascination with conic sections
from the 1630's onwards, and the preoccupation with perspective, which offered a
scientific means of visualizing the complex intersections involved (fig.23).
Yet another factor went hand in hand with these developments. As in other
European centres (cf. 2.1), Paris witnessed a great interest in universal measuring
instruments in the latter sixteenth century: Abel Foullon's holomètre, Jacques
Besson's cosmolabe, Philippe Danfrie's graphomètre and Henry de Suberville's
henrymètre. By about 1609, Jacques Aléaume, who also wrote on perspective, had
developed his own version of a sector. Denis Henrion improved upon it. Pierre
Hérigone further developed it, and mentioned its application to perspective, a topic
which Jean, le Sieur de Vaulezard took further, showing the sector's uses in
determining various anamorphic projections in conic mirrors. In his letter to
Beeckman about his new science, Descartes had specifically referred to the need
for "new kinds of compasses"30 to demonstrate the new method. Was this what
Hérigone and Vaulezard were doing? In any case we find thereafter, especially in
the French tradition, an ongoing link between sectors and perspective (e.g. Bosse,
Huret, Chales, Lambert).
There was also a religious and magical context to these studies. As early as the
1450's, Giovanni Fontana, a student of optics and author of what may have been
the first treatise on perspective, had used his knowledge in these fields to project
images of devils onto the walls of buildings presumably to demonstrate that effects
claimed to be supernatural by followers of black magic could be accounted for by
purely natural causes. In the sixteenth century, Giovanni Battista della Porta,
working in the tradition of artist-engineers, pursued this approach to natural magic.
61
Meanwhile, Fontana's contemporary, Taccola had explored other aspects of these
natural wonders, particularly those involving hydraulics. Francesco di Giorgio
Martini and Leonardo developed these demonstrations and the latter's sojourn in
France probably explains the particular attention given this topic in the second half
of the sixteenth century by Abel Foullon, Jacques Besson and Agostino Ramelli.
In the seventeenth century, Salomon de Caus, developing techniques introduced by
the Florentine, Buontalenti, effectively combined these two traditions of natural
magic and hydraulics in creating his remarkable mechanical automats in grottoes
with fountains and optical effects (pl. 98.1). If we, in retrospect, are tempted to
dismiss such projects as superficial examples of baroque playfulness, it is
instructive to recall that when Descartes, in his Treatise on man, was trying to
establish the credibility of his mechanistic model of the nervous system he
appealed to "those hydraulically controlled puppets and mechanical statues found
in the grottoes and fountains in the gardens of our kings".31 In this context,
Baltrusaitis (1956) concerns with both automats and perspective,32 take on greater
importance, as does his quote from Jean François Niçéron, where he cites both
automats and perspective as instances of natural magic, adding "the true magic or
perfection of the sciences consists of perspective which makes us understand and
discern more perfectly the beautiful works of nature and art."33
The small circle of thinkers in the 1630's, who were concerned with automats and
used mechanical sectors to demonstrate principles of perspective by means of
conic sections, were therefore more than the forerunners of Popular Mechanics.
They were stimulating Descartes to articulate a new mechanistic model of reality
(cf. below 2.1). Of course, other mechanical devices such as clocks,34 were also
important in this context.
Not all the reactions were so profound. Melchior Tavernier, in a book now lost
(1639), sought to popularize these ideas, an aim that was taken up in an
anonymous three volume work by Jean Dubreuil entitled, Practical perspective
(1642-1649), which emphasized the recreational value of these anamorphic
demonstrations, and at the same time misrepresented Girard Desargues' original
ideas. Desargues and Dubreuil exchanged pamphlets filled with diatribe. Others
followed between Desargues and Curabelle.
Subsequently Abraham Bosse, first professor of the Royal Academy and a friend
of both Poussin and Desargues, continued the debates on Desargues' behalf, and as
mentioned earlier (pp.
) brought into focus the dichotomy between projection
planes of linear perspective, based on geometry, and the visual angles principles of
Euclid's optics. This inspired the further opposition of Jean Le Brun and more
writings against him by Jean Le Bicheur and Grégoire Huret, leading eventually to
Bosse's expulsion as the academy's professor of perspective. And ironically,
Dubreuil's text, with its various faults, went on to become one of the most popular
texts with nine issues by the end of the century and another dozen in the eighteenth
century, including translations into English and German. Dubreuil was a Jesuit. So
62
too were Leurechon (1630), Nicéron (1638, 1646, 1651, 1652, 1663, 1669, 1673)
and Derand (1643). Their wish to popularize perspective was guided by a desire to
stress its moral and didactic potentials. Others were more concerned with
popularization for its own sake. Le Clerc's work, for instance, went through five
editions in the seventeenth (1679, 1682, 1690, 1691, 1694) and at least seven in the
eighteenth century (1712, 1716, 1719, 1744, 1754, 1764, 1774). Even more
popular was Ozanam with seven editions before 1700 (1684, 1689, 1693, 1694,
1696, 1697, 1699) and fourteen more in the century that followed (1711, 1720,
1734, 1724, 1725, 1735, 1741, 1749, 1750, 1769, 1770, 1778, 1781, 1790).
The eighteenth century again brought a few reprints of Renaissance classics,
notably Leonardo (1716), Serlio (1745), Barozzi (1786) and Cousin, le jeune
(1750) and a number of new works relating to architecture. Chief among these
were Bretez (1706, 1746, 1751), Courtonne (1725), Jeaurat (1750) and Roy (1756,
1757). New books specifically devoted to perspective were few: e.g. Lamy (1701),
Saurin (1720), Lanselles (1767), Saint Morien (1779, 1788) and Sabro (1790).
There were also three new trends. One was the publication in Paris of
contemporary foreign works including Wolff (1747), Galli da Bibiena (174 ),
Palomino (1749), Gravesande (1755), Muller (1760), Piranesi (1762), Mengs
(1788) and Lairesse (1787). A second trend was an increasing emphasis on conic
sections with authors such as La Hire (1701, 1757, 1776), L'Hôpital (1707, 1720,
1776), Chapelle (1750), Gallimard (1752), Mauduit (1757, 1761), Rivard (1757),
Mazens (1758, 1761, 1765, 1768, 1774, 1775, 1777) and Muller (1760). A third
trend linked mathematics, engineering and perspective through Bouchotte (1721,
1722, 1743, 1754, 1755), Dupain de Montesson (1750, 1760, 1763, 1774, 1775,
1786, 1789, 1792) and Monge (1785, 1795, 1798, 1799).
During the eighteenth century Paris, with 144 books, had fallen behind London as
the leading centre of publication. In the nineteenth century, with 528 publications,
Paris once more took the lead as chief centre. In some respects the patterns of the
eighteenth century were maintained. There was no dramatic change in the reprints
of Renaissance authors: Alberti, Androuet, Barozzi, Leonardo and Pélerin. The
number of editions of contemporary foreign authors remained almost constant
although most of the names changed: Piranesi (1804), Smith (1824, 1843), Amici
(1823), Burnet (1835), Hughes (1864), Helmholtz (1870), Brucke (1878, 1881,
1885) and Salmon (1870). With respect to architecture and perspective, four
authors dominated the scene, each of whom went through a number of editions:
Lagardette, Normand, Robinet and Etex. In terms of mechanical drawing and
perspective, there were a series of works on new instruments, among them,
Ph‚lippeaux, Burnier, Jump, Mauduit, Le Blanc and Petit.
Other factors led Paris to be the most prolific centre of publication in this field
during the nineteenth century. Chief amongst these was the link with descriptive
geometry, forged by Monge in the latter eighteenth century, which was spread by
further editions of his work (1811, 1820, 1827, 1838, 1847), and a series of
followers notably Hachette (1815, 1817, 1818, 1822, 1828), Olivier (1831, 1837,
63
1839, 1840, etc.), Lefebure (1834, 1837, 1842, 1847, 1864, 1870), Leroy (1834,
1837, 1842, 1846, 1850, 1851, 1855, 1859, 1862, 35c.), and Dufailly (1869, 1873,
1875, 1878, 1880, 1882, 1884, 1886, 1892, 1894). Some individuals, such as La
Gournerie, wrote important works on both descriptive geometry (1851, 1853,
1855, 1860) and perspective (1859, 1884, 1898). Pillet was another, who wrote on
both descriptive geometry (1876, 1887, 19291), and perspective (1885, 1886,
1888, 1901, 1921, 1953). Meanwhile, another strand, through Poncelet (1822,
1863) and his followers explored an alternative using projective geometry.
In terms of artistic perspective, there were a number of popular authors including
Adhémar, Bouillon, Delaistre, Jaunez-Spauville, Cassagne and Henriet. But the
most significant single development in nineteenth century Paris was a new link
between drawing (dessin) and perspective which included authors such as
Boniface (1823, 1832, 1847), Choquet (1823, 1832, 1847), Francoeur (1827),
Paillot de Montabert (1832), Thibault (1837), Trélis (1840), Daix (1842), Lahure
(1847), Rouillet (1857, 1863), Grimblot (1869, 1877), Bracquemond (1885),
Valtron (1888), Watelet (1893) and Forel (1893). Among the most popular authors
were Henry des Vosges, who went through twelve editions and Lamotte, who went
through fourteen editions. Underlying this development were basic issues
concerning the role of perspective in education, inspired by philosophers such as
Locke and Rousseau (see below 1.4).
The combined result of these developments was to convince thinkers that
descriptive geometry, and the principles of perspective, must (somehow)
correspond to both objective reality and the laws of vision. Vallée played a
considerable role in establishing these suppositions, and accordingly, the second
half of the century saw a series of works relating perspective to sight (e.g.
Malaval), or to observation (e.g., Babinet, Devinat, Watelet), a theme which
continued into the twentieth century (e.g. Bocquillon, Legrand), although new
evidence concerning discrepancies between vision and representation had arisen in
the meantime (see pp. ).
In addition, there were a number of works devoted to specialized topics including
carpentry (Biston), colour (Roux de Valdonne), landscape (Robert, DemarquetCrauk), photography (Colson) and even war (Philebert) and many works by minor
authors.
Although the twentieth century has seen 160 further publications, few of these
have been innovative. Indeed, in the first decade, many were simply reprints of
nineteenth century authors including Breithof, Cassagne, Delaistre, DemarquetCrauk, Laurent, Lebon, Olagnon, Pillet, Planat, Robert and Tubeuf. Cloquet was
one of the few new works to go through several editions (1905, 1912, 1913, 1919,
1927). The period 1910-1960 marked a definite slump, with only a handful of
authors rising to prominence, namely: Grosclaude (1919, 1946, 1947), Boll (1921,
1932, 1934), Boucher (1921, 1931, 1934), Gromort (1932, 1945, 1944, 1953) and
Olmer (1932, 1943). In the period since 1960, three popularizing authors have
64
dominated the scene: Parrens, Raynaud and Bonbon, their work being almost
simplistic when compared to nineteenth century classics such as La Gournerie.
The period since 1960, has also seen a revival of interest in Renaissance texts, with
reprints of Androuet du Cerceau, Bracelli, Dürer, Jamnitzer and Vredeman de
Vries. New trends in recent literature include attention to spherical perspective
(Barre et Flocon, cf. pp. ), and the use of models and photography in architectural
design (Jantzen).
In the context of France as a whole, it is striking to note how completely Paris has
dominated the scene. Indeed, there are only four other cities worthy of mention:
Orléans, Lyon, Rouen and Strasbourg. Orléans had a brief period of importance in
the sixteenth century through publications by Androuet Du Cerceau, before he
moved to Paris. Lyon, in the sixteenth century produced no original works of its
own, but saw the publication of Ringelbergius (1556) and Porta (1571, 1579,
1591), with its description of the camera obscura in respect to painting. The
seventeenth century brought three French authors (Binet, Cousin and Chales), and
three foreign ones (Caramuel de Lobkowicz, Fabri, Porta). The next century
brought one important work in instruments by Grollier de Servière (1719), and a
French edition of Brook Taylor (1758). The nineteenth century saw only minor
works by Girardon (1850, 1859) and Fournet (1859).
In Rouen, by contrast, almost all the activity was limited to the seventeenth
century with ten editions of Binet, and seven of Porta, with only one minor work
by Trénard (1913) in our century. The fourth city, Strasbourg, has felt the
influence of Germany more than France. During the sixteenth century there were
pirate editions of Pélerin (1508, 512, 1515) and treatises by Specklin (1589) and
Dietterlin (1593). A reprint of Specklin (1608) was the only contribution of the
next century. The eighteenth century brought Herttenstein (1736, 1737), Frézier's
classic work on stereotomy (1737) and a treatise by Curel (1766). The nineteenth
century added a technical work by Rätz (1879, 1883, 1894) and a reprint of Piero
(1899). The twentieth century brought a reprint of Dürer (1905), and treatises by
Adam-Leonard (1905) and Opitz (1907). Of all these publications outside of Paris,
only Frézier's was of fundamental importance, and its conclusions were soon
integrated within the Parisian mainstream by thinkers such as Monge. So, in a very
real sense, there was only one centre in France. In countries such as the Lowlands
and Germany the situation was very different.
BELGIUM
We have already noted that a fascination with pseudo-perspectival space
developed in Flanders in the early fifteenth century at the same time that
Brunelleschi and Alberti were exploring the principles of perspective in Florence
(pl. 8-11). No evidence has been found to confirm a claim (Fielding 1835), that
Jan van Eyck also wrote a treatise on the subject. Instead, it is now generally
accepted35 that Petrus Christus brought the principles of perspective to the
Lowlands around 1457, probably after a journey to Italy, where he may well have
65
learned them from Antonello da Messina. Over seventy years passed before there
were publications in Antwerp. By the early seventeenth century some works also
appeared in Brussels, but by then activities had shifted northward with Amsterdam
as a new centre, and with Arnhem, the Hague and Leiden as satellites. Each of
these will be considered in turn.
Antwerp
The first publications were foreign books: Gauricus (1528) and Pieter Coecke van
Aelst's translations of Serlio (1539, 1542, 1545, 1549, 1550, 1553). Coecke, who
was also a translator of Vitruvius, became the teacher of both the painter, Pieter
Breughel, the Elder and Hieronymus Cock, who became an artist, engraver and
publisher. By the 1550's, Cock's publishing house, At the four winds, played an
important role in the spread of perspectival texts: his own Roman views, those of
Gerard de Jode and, a decade later, those of Jan Vredeman de Vries--a series of
picture books, usually with about twenty perspectival views each of fountains,
gardens, tombs, ruins and idealized architectural scenes. When Philippe Galle took
over Cock's press there were reissues, frequently with new plates of the
perspectival views, of Cock, Jan Vredeman de Vries and his son Paul. Philippe
Galle's son, Theodore, continued in his footsteps for another
ANTWERP
Martin Heemskerck
Serlio
Vitruvius
Peter Flötner
Hans Blum
Pieter Coecke van Aelst
G. Ghisi
Pieter Breughel the Elder
Hieronymus Cock
Gerard de Jode
Hendrick III Cleve
Philippe Galle
Jan Vredeman de Vries
Theodore Galle
Paul Vredeman de Vries
66
Hendrik Hondius, II
Samuel Marolois
Joseph Moxon
Fig. 24. Authors and publishers on perspective in Antwerp (1450-1600).
generation (fig. 24). In all some 30 publications of Vredeman de Vries appeared
before Janson began publishing his works in Arnhem and Amsterdam.
In the seventeenth century this flurry of activity ended as suddenly as it had begun.
Aside from reissues of Vredeman de Vries (1606,1673), Blum (1640), and Serlio
(1653), there were only a handful of new publications: a collection of ruins and
views by Nieulandt (1610, 1628), an optical treatise by Aguilonius (1613), a work
on conic sections by Saint Vincent (1647) and a technical treatment of perspective
by Tacquet (1669). The eighteenth century saw a reissue of Tacquet (1707), the
nineteenth, a new work by Neetsonne (1883) and the twentieth, one by Farcy
(1943). Meanwhile Brussels had acquired some significance.
Brussels
Hondius, one of the students of Vredeman de Vries, is said to have published the
first edition of his work on perspective in Brussels (1617, cf. Amsterdam 1623).
The latter seventeen century saw a work on military perspective in Spanish by
Lepeda (1661). The eighteenth century brought only an edition of Pozzo (1708).
The nineteenth century brought sixteen publications: a popular textbook by
Smachtens (1820, 1825, 1827); treatises by Brisson (1827), the editor of Monge,
and three other mathematicians: Leroy (1837), Charles (1839, 1870) and Schmidt
(1869), as well as minor works by Bossuet, Gratry, Mols, Morena and Pierre.
Since nineteen hundred there have been six publications of which perhaps only
Barre's (1904) discussion of alternative methods of perspective bears mention.
THE NETHERLANDS
Amsterdam
Aside from ancient texts such as Euclid and Ptolemy, the first perspectival treatise
published in Amsterdam was a translation of Blum (1598, 1612, 1619, 1623,
1647). Italian authors published in the first half of the seventeenth century
included Serlio (1606, 1616), Alberti (1649) and Gauricus (1649). Of German
authors, there was only Jamnitzer (1608, 1618, 1626), who appeared in three
anonymous pirate editions. In the latter seventeenth century there were editions of
three French authors, Desargues (1686), Ozanam (1683, 1693, 1698) and Le Clerc
(1692), as well as one English author, Wren (1671).
67
As of 1550, Jan Vredeman de Vries had published a series of perspectival views in
Antwerp. In 1604, together with his student, Hendrik II Hondius, he issued a more
ambitious work with some mention of theoretical principles. This appeared in
Leiden. In the next decade, Marolois, another student of Vredeman de Vries,
developed a lengthy theoretical section to which he added engravings by Jan and
Paul Vredeman de Vries, Hendrik II Hondius, and Pieter Stevens. This work in
turn formed part of a massive tome in four sections dealing with geometry,
perspective, architecture and fortification respectively, which had its first edition in
Leiden (1614) and subsequent editions mainly in Amsterdam. For a generation this
remained a standard work appearing in Latin, French, Dutch and German,
sometimes complete, frequently in combinations or abridged versions.
In the mathematical realm, van Schooten's (1659, 1660) treatise on conic sections
was the only noteworthy publication in Amsterdam during the seventeenth
century. In terms of artistic perspective there were texts by Bosboom (1686) and
Hartsoeker (1699), and more general treatises by van de Passe (1643, 1644, 1664),
de Graaf (1662, 1679) and de Bisschop (1670). Towards the end of the century
there appeared also Lairesse (1694, 1695) who became popular in the next century
(1701, 1706, 1707, 1712, 1713, 1719, 1727, 1729, 1766). Foreign publications in
Amsterdam during the eighteenth century were limited to Ozanam, Lamy, Le
Clerc and a translation of Brook Taylor. There were further editions of Bosboom,
Graaf and Hondius. New works ranged from minor texts by Schenk (1705) and
Ypey (1764), to significant contributions by Houten (1705), Vlaming (1773) and
Gravesande (1774). By far the most influential eighteenth century author was
Philips Jacobszoon, with a series of publications (1765, 1767, 1775, 1780, 1781,
1785, 1786, 1788, 1803, 1823, 1827), notable for his use of mirrors and other
instruments in connection with perspective.
In the seventeenth century, 114 books were published in Amsterdam. In the
eighteenth, there were 38, and in the nineteenth this dropped to 26, of which only
two were translations of foreign works: Lagardette (1833) and Thénot (1859).
Most were single publications of local interest including Apol, Bes, Bilderdijk,
Bing, Campen, Ferrers, Groenevelt Meerwaldt, Rinkes and Schoone. The one
dramatic exception was Versluys, whose textbooks for schools went through a
series of editions (1881, 1884, 1887, 1889, 1890, 1891, 1896). The twentieth
century has seen at least 35 further publications, the majority of which were again
of local interest only, including Albert, Hana, Kumminga, Muyak, Mayens and
Ozinga. Only two authors have enjoyed more than one edition, namely, Mialaret
(1910, 1922) and Arendzen (1934, 1942, 1950). There was also one translation
from the German, Stark (1930).
Arnhem and the Hague
Intimately connected with publications in Amsterdam in the early seventeenth
century, were two other cities: Arnhem and the Hague, due to Jan Jansson's
publishing firm. In Arnhem, he published Dürer (1603, 1605, 1613, 1614, 1617),
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Ptolemy (1617) and Marolois (1621). Since that time, Arnhem has seen only one
further treatise by Graaf Hermanszoon (1870). Meanwhile, as mentioned above,
Jansson had published a first edition of Marolois (1614) in the Hague. He also
published Hondius, but in the 1620's the firm's activities were centred increasingly
in Amsterdam. Thereafter, the Hague saw only sporadic publications. In the latter
seventeenth century, Rohault (1690) and Ozanam (1691) were published there.
The eighteenth century brought an important work by Gravesande (1711, 1771), a
treatise by Eckhardt (1778), and an edition of Pascal's Conics (1779). The
nineteenth century brought a translation of Lagardette (1821), an anonymous text
(1846), and one by a local author, Aken (1891). The twentieth century has added
works by three new authors, Sakkers, Schmidt and Woude, but little innovation.
Leiden
During the sixteenth century, the only work connected with perspective published
in Leiden was Porta (1561, 1569), further editions of which appeared in the next
century (1644, 1651, 1657). At the turn of the seventeenth century, the Hondius
family published Vredeman de Vries (1604-1605, cf. 1664) in Leiden, thus
involving that city in a nexus of relations with Amsterdam, Arnhem and the
Hague. On the mathematical side, Leiden saw an edition of Stevin's (1634)
important work, editions of Van Schooten (1646, 1656, 1657) on conic sections
and Huygen's (1690) Treatise on light. Foreign publications included the Jesuit,
Milliet de Chales' (1674) compendium. The eighteenth century brought only new
editions of Gauricus (1701, 1732), while the nineteenth century added a half dozen
authors of books on artistic perspective: Brag, Bregmann, Campen, FokkeSimonszoon, Richard and Schaap, and a manuscript by Humbert de Superville
(1830). The twentieth century has seen a new edition of Ptolemy (1932).
Other Netherlandish Cities
Three other cities in the Netherlands, which have emerged in the nineteenth and
twentieth centuries deserve brief mention: Groningen, Tiel and Deventer. In
Groningen, the earliest text on perspective dates back to Frederik (1853, 1935).
The decades that followed saw four authors of local interest: Berghuis, Gravelaar,
Groneman and Soeren. The two popular authors, Versluys (1877, 1887, 1924) and
Bes (1890, 1893, 1900, 1901, 1903) were also published in Amsterdam. The
twentieth century has added ten further authors including Alders, Gestel, Jansen,
Luinge, Nuyens, Steenderen and Wijdens, who have added nothing fundamental.
In the nineteenth century, Tiel produced one textbook for schools by Berghuis,
which went through at least six editions (1887, 1891, 1894, 1898, 1902, 1907).
The twentieth century has brought Jansma's introduction to conic sections which
went through eight editions and textbooks by de Vries de Hecklingen (1908), who
published other works in Zwolle, Goslinski (1911, 1930) and Scholten (1915).
Deventer is of interest mainly due to one individual active in the early twentieth
century, namely, Ridderhof, whose textbook on perspective went through eight
69
editions (e.g. 1906, 1949) and who also wrote on parallel perspective and
perspective sketching for schools. Texts by Wijdens (1904), Reynders (1945,
1951) and Twijnstra (1948) were also published there.
GERMANY
Dürer's famous comment, in his letter to Pirckheimer in 1504, that he was hoping
to learn the secret of perspective,36 reminds us that perspective reached Germany
later than either France or the Lowlands. And unlike France, where everything
was centralized, developments in Germany were scattered throughout a number of
cities. The earliest of these was Nürnberg, which had a seminal influence on
Augsburg and Frankfurt. Cologne developed separately. The seventeenth century
saw publications in a few more cities: Hamburg, Stuttgart, Hanover, Freiburg and
Munich. The eighteenth century added Berlin, Göttingen and Karlsruhe, followed
by Braunschweig, Darmstadt and Wiesbaden in the nineteenth century.
Meanwhile, in East Germany, only one real centre emerged at Leipzig, although
some works were published at Weimar. Each of these will be considered in turn.
Nürnberg
Nürnberg was an important trade centre already in mediaeval times. Because it
was the leading European city for the production of mathematical instruments (cf.
fig. 41), Regiomontanus moved there in the 1470's to pursue his own scientific
interests, and to become the world's first publisher specializing in scientific texts.
Martin Behaim produced one of the first globes there in 1492. This context
accounts for both the fascination with perspectival instruments, which developed
later in the century, and the appearance of scientific and mathematical texts,
including Ptolemy's Geography (1514), Werner's work on conic sections (1522),
Witelo's great optical treatise edited by Apianus (1535), and Peckham's Common
perspective (1542).
On his second Italian journey, Dürer may have obtained a manuscript copy of
Alberti's On painting, (possibly the one now in the Bavarian state library?), which
could have served as the basis for the alledged 1511 edition (mentioned in earlier
bibliographies). But all this is conjecture. The first published text was Dürer's
Instruction in measurement (1525) with fourteen pages devoted to the topic.
In 1531, the author of A beautiful, useful booklet, set out to write a more popular
book with numerous perspectival illustrations, including church interiors (pl. 16.4),
building construction scenes (pl. 60.3-4) and even demonstrated the use of the
perspective window in drawing landscapes (cf. pl. 58.1-2). In the full title of the
treatise we read that it is about “the art of measurement called perspectiva in
Latin”.37 Here the link between perspective and measurement was unequivocal.
This treatise, edited by Dürer's student, Hieronymus Rodler, combined serious
theoretical discussion and picture-book type practical example in a new way. John
Dee made a partial manuscript copy of the work (now British Library Cotton
70
Vitellius VII). Augustin Hirschvogel pursued this approach, explicitly setting out
to relate theoretical geometry with practical perspective in a work fittingly entitled:
Geometry. The book geometry is my name. Originally all liberal art from me came.
I bring architecture and perspective together. Hirschvogel also wrote an
unpublished treatise on surveying (now Vienna, Stadtmuseum).
Dürer had entitled his book Instruction in measurement...with the compass and
ruler (1525), and had emphasized the general problem of practical geogetry.
Heinrich Lautensack's text (1564) echoed Dürer's title, adding also of perspective.
Following a brief introduction on geometry, Lautensack focussed on theoretical
and practical aspects of perspective, including anatomical proportion and
symmetry, themes which had been explored independently by two of Durer's other
students: Hans Beham and Erhard Schön.
Meanwhile, Hans Lencker and Wenzel Jamnitzer had developed a great interest in
the perspectival representation of regular and semi-regular solids (pl. 36.3-37.1).
Did they perhaps see therein shapes into which to cut their jewels? They also
improved upon the mechanical aids for perspective, which Dürer had developed.
When Pierre de La Ramée and Frederick Risner from Paris, visited them in 1568,
they were so impressed by their work that they persuaded Jamnitzer and Lencker
to publish.38
The next significant publication was a little known treatise by Paul Pfintzing
(1599), originally intended for private distribution among friends. Conscious of the
continuity within the Nürnberg tradition (fig.40), Pfintzing traced the development
of mechanical devices from Dürer and the anonymous author of A beautiful useful
booklet, through Lautensack, Lencker (pl. 54.2), Jamnitzer (pl. 54.4), and the
otherwise obscure Hans Haiden (1590), (pl. 54.5). Pfintzing was also aware of
both traditional authorities in optics: Euclid, Alhazen and Witelo, as well as
foreign authors on perspective, including, Luca Pacioli, Androuet du Cerceau and
Lorenzo Sirigatti.
This awareness of the cumulative nature of knowledge was even more manifest in
Levinus Hulsius' four treatises on mathematical instruments (1603-1605), which
included mechanical aids for perspective, a description of Jost Bürgi's proportional
compass and a similar device (by Michel Coignet) from Belgium. By way of
introduction, he provided one of the earliest bibliographies containing dates of
publication of the books consulted. The list included works from Germany, France,
Italy and the Netherlands (fig.42). The same Hulsius also studied with Galileo in
Padua, and subsequently published a first Latin translation (1612) of Galileo's
Geometrical and military compass (1606). Hulsius also worked with Jobst Bürgi's
brother in law, Benjamin Bramer, active in the construction of the compass, sector
and perspectival aids.
An unexpected pattern thus emerges. The key centres for scientific instruments
were also important in the development of perspective: Padua, Florence, Nürnberg,
71
Antwerp and later Paris and London. Moreover, the key figures were often directly
in touch with one another or at least indirectly influenced by one another. A more
systematic approach to studying the world scientifically brought with it a more
systematic network of contacts and a greater awareness of the cumulative effect of
knowledge (see below 2.1).
Meanwhile there had also been publications of foreign authors of perspective in
Nürnberg beginning with Gauricus (1542). Of considerable importance was a
compendium by Walther Ryff which provided partial translations of Alberti,
Gauricus and Serlio (1547, 1558)--a third edition of which later appeared in Basel
(1582). The seventeenth century saw new editions of Pfintzing, Dietterlin and
Porta; treatises by Krammer (16--) and Brunn (1614), Schwenter's work on
perspectival instruments (1616) and his compendium of basic principles (1651).
Most popular were two treatises by Albrecht, which may have gone through as
many as nine issues (e.g. 1620, 1671, 1677). Erasmus (1667, 1672, 1687), not the
humanist, edited an updated version of Blum's work on the five columns, while the
famous antiquarian, Sandrart, reported briefly on Italian developments in
perspective in his German Academy (1675). In terms of foreign literature
published in Nürnberg in the seventeenth century, Daniel Schwenter edited a
German translation of Raverta's treatise on surveying and perspective (1627, cf.
1602). There were two editions of Falda (1685, 1695) and a translation of
Desargues (1692).
The eighteenth century saw translations of two Dutch authors, Witgeest (1702) and
Lairesse (1727, 1728, 1780) and two French ones, Dupain de Montesson (1759,
1762, 1790) and Bosse (1767). Among the German authors, there were Zahn
(1702), of interest concerning camera obscuras and other instruments, Sturm
(1704, 1714), who wrote a handy compendium; Pressler (1774), important for his
theories of drawing and Mayer (1785). The one major new author was Schubler
(1719, 1732, 1734, 1735, 1749, 1758, 1763).
The nineteenth century saw only one translation from the French: an important
book on drawing theory by Thibault (1833, 1834, 1841). German authors included
Heidelhoff (e.g. 1827, 1892), whose work on shadow construction for architects
went through five editions; Eberlein (1859, 1876, 1878), Gugler, Klingenfeld and
Wenz. The twentieth century has brought only two textbooks by Fürst (1908) and
Pechwitz (1950).
Augsburg
In Augsburg, the first publication was a collection of examples for use in
marquetry by Stoer (1567, cf. 1617), of particular interest because the motifs
therein appear to have inspired some of the woodwork at the Escorial done that
very year.39 Like Nürnberg, Augsburg was famous for its instrument makers,40-notably Christoph Schissler and his son41--, which helps to explain a trend in
Augsburg during the early seventeenth century to reprint Nürnberg authors who
72
emphasized the use of instruments in perspective, namely, Lencker (1615, 1617),
Lautensack (1616), and Pfintzing (1617). The two new works published in
Augsburg at the time also mentioned the use of instruments, although Halt (1625)
was mainly concerned with polyhedra, while Furttenbach (1640) focussed on
perspective as applied to scenography.
The eighteenth century saw a small number of significant publications. Three
were translation of foreign authors: Dubreuil (1710), Le Clerc (1756) and Pozzo
(e.g. 1706, 1800), who went through seven issues. With respect to artistic
perspective, Heinecken produced an influential textbook with examples showing
church interiors, landscapes and other complex perspectival scenes (1727, 1732,
1743, 1753). On the mathematical and technical side, there were important
publications by Lambert (1760, 1768, 1770, 1772) and Brander (1764, 1767, 1769,
1771), which contained new combinations of camera obscuras with surveying
instruments, telescopes and microscopes. Augsburg's only contributions to the
field since have been two treatises by Voch (1780, 1817).
Frankfurt
As an important publishing centre, Frankfurt served mainly to make known work
done elsewhere. The first treatise on perspective published there, attributed to
Rodler (1546), had appeared earlier in Simmeren. The next works were by
N rnberg artists: Beham (1552), 1557, 1587, 1594) and Lautensack (1564, 1565,
1567). There followed Italian authors, Serlio and Porta, and the Frenchman,
Boissard (1597, 1603). The seventeenth century saw further works by foreign
authors: two French, Perret (1602) and De Caus (1516); two English, Roger
Bacon's work on optics entitled, Perspective (1614), and Fludd (1624), and later
the Italian, Serlio (1672). German works included an alledged edition of Krammer
(1600), editions by the Nürnberg artists Beham (1605) and Lautensack (1618);
technical treatises on perspectival instruments by Hulsius (1603, 1605, 1615) and
Faulhaber (1610); an encyclopaedic treatment by Schott (1677) and a further
discussion of instruments, particularly camera obscuras by Zahn (1686).
The eighteenth century brought compendia by Sturm (1710) and Wolff (1725,
1750, 1775) and a French treatise by Curel (1768). As in Nürnberg, the nineteenth
century brought translations of Thibault's theories of drawing (1800, 1835, 1840).
It also brought an anonymous work in drawing and perspective translated by
Becker (1815, 1817, 1818) and a text by Ritter (1884). The twentieth century
added reprints of Bacon, Jamnitzer, Lencker and Sch”n as well as two new
authors: Eith (1940) and Meyers (1951).
Cologne
Not unlike Frankfurt, but on a smaller scale, Cologne was mainly important for
what it published from elsewhere, rather than for its original contributions. Indeed
in the sixteenth century it produced only foreign works relating to perspective
73
including Porta (1562, 1563), Peckham's (1580, 1592) optical textbook,
Guidobaldo del Monte's (1581) work on the planisphere and Ptolemy's Geography
(1584, 1597). This pattern continued in the seventeenth century, with new editions
of Ptolemy and Peckham, the Swiss, Blum (1600), the Dutch, Vredeman de Vries
(1615, 1655) and the Italian, Bettini (1642). German authors included Krammer
(1611) and Kaessmann (1630), based on Blum. Since then there have only been
two minor works by Janke (1900) and Boehmler (1969) and a reprint of Ens
(1951).
A different pattern prevailed in the cities which began publishing works on
perspective in the seventeenth century (Hamburg, Stuttgart, Hanover, Freiburg and
Munich). Although they frequently began with foreign works, they soon relied
almost entirely on local authors.
Hamburg
In the seventeenth century, Hamburg saw only an edition of the optical treatise by
Heliodorus of Larissa (1610). The eighteenth century brought works on
perspectival instruments by Norberg (1762) and Steinholz (1775) and the
nineteenth century brought another by Stuhlmann (1869, 1974, 1876, cf. 1914) as
well as a text on descriptive geometry by Schlotke (1867) and optical treatises by
the famous physiologist Helmholtz. Apart from one further treatise on perspectival
aids, Peter (1911), the twentieth century has brought only textbooks of local
interest by Beimföhr, Heinsohn, Kröger, Reichelt, Schaub and Vorwerk.
Stuttgart
In Stuttgart there has been a consistent emphasis on the mathematical and technical
side of perspective. The earliest publication was a new edition of Hirschvogel
(1611 cf. 1543). Over two hundred years passed before publication resumed with a
translation of Lamotte (1835), on linear drawing. There followed translations of
Leroy's influential texts on stereotomy (1846, 1850, 1861, 1876, 1883) and
descriptive geometry (1853, 1873), as well as Green's (1892) textbook, which had
gone through fourteen editions in England. In terms of German authors, there were
mathematical works on conic sections by Riecke (1842) and Zech (1857); on
descriptive geometry by Gugler (1844, 1851, 1874, 1875) and Riess (1871);
geometrical drawing by Vogel (1874) and Müller (1891); projective drawing by
Kleiber (1888) and Vonderlinn (1888, 1889, 1892, 1893) as well as Böckler's
popular treatise on construction drawing (1866, 1876, 1878, 1886). With respect to
textbooks on artistic perspective there were Vollweider (1862), Niemann (1882,
1902, 1907), Steindorff (1884), Conz (1882, 1902, 1909, 1920) and Söllner (1891).
There were at least 52 books published on the subject in the nineteenth century,
and 41 in the twentieth including Bernhard's popular text on descriptive geometry
(1901, 1904, 1909, 1920, 1923). In 1934 there was a debate concerning the role of
perspective in art education between Gahlbeck and Klauss. The most significant
74
development has, however, been with respect to architecture. Reile (1922, 1923,
1941, 1949, 1951) developed a new device for architectural perspective, and more
recently there have been several books on architectural drawing by Coulin (1966,
with later English editions), Jacoby (1971, with later English and Japanese
translations), Thomae (1976) and Prenzel (1978).
Hanover
The seventeenth century saw two editions of Porta (1619, 1644). The next
publications in the second half of the nineteenth century were on mathematical
perspective, Koutny (1868, 1869) and descriptive geometry, Gerke (1881, 1889),
as well as one treatise on artistic perspective, Jantzen (1872). The twentieth
century has seen a continued emphasis on the technical and mathematical side of
perspective with works on isometrical drawing by Grimshaw (1902) and Vogel
(1912); a text on descriptive geometry by Pohl (1951) and a popular work on
architectural perspective by Dahmlos (1966, 1970, 1977). There have also been
texts on perspective drawing by Zehnder (1907), on perspective and shadow by
Heubach (1908) and a reprint of the German translation of Dubreuil (1977 cf.
1710).
Freiburg
Publications in Freiburg followed a similar pattern. In the seventeenth century
there was an edition of Scheiner (1621), of interest regarding camera obscuras,
then nothing until the nineteenth century which was dominated by mathematical
and technical texts including Ladomus (1812) on geometrical construction
drawing, Weisbach (1857) on axonometrical perspective, and Flinch on
geometrical perspective. More important was Delabar with no less than ten
publications (from 1866 through 1893) relating to linear drawing, descriptive
geometry, shades and shadows and parallel perspective. The twentieth century has
seen only a work on perspectival instruments by Routschek (1963).
Munich
As might be expected, there was somewhat more variety in Munich, although the
seventeenth century again saw only one technical work on telescopes by
Hercynianus (1625)--included under perspective in some in some early
bibliographies,--while the eighteenth century saw three further mathematical
works: Karsten (1768, 1773) on spherical projections in astronomy, as well as
Danzer (1780) and Rauch (1790) on conic sections. The nineteenth century
brought Quaglio (1811, 1822, 1823) and Adamo (1899) on architectural
perspective; Schrank (1812) on blue shadows, and three authors on linear drawing:
Haindl (1835, 1843), Weishaupt, whose influential work went through at least nine
issues between 1856 and 1882, and Edelmann (1871). In terms of textbooks on
artistic perspective, there were Gottgetreu (1851), Seeberger, whose principles of
perspective went through at least ten issues between 1860 and 1904, Kleiber
75
(1885) and Lübenau (1898). The twentieth century has brought at least 29 further
publications of which the most original is Klee's (1925) discussion of perspective
with respect to modern art. Also worthy of mention are practical textbooks by
Pabst (1918, 1921, 1922), Fürstweger (1928) and Fischer (1937, 1943) plus a more
recent work on technical drawing by Fäustle (1969, 1971).
Berlin
In Berlin, the first publication was near the middle of the eighteenth century with
Jügel (1744), who wrote on architectural perspective, followed by a general
textbook, Segner (1799). However, mathematical texts predominated, including
Lambert's (1776) article on aerial perspective, Lagrange (1781) on cartographical
perspective, Hildebrandt (1783) on conic sections, Mönnich (1794) and Burja's
(1795) textbook addressed specifically to the mathematical painter. The nineteenth
century saw 101 further publications. Some ten authors wrote on artistic
perspective, namely, Benteli, Berger, Eytelwein, Frangenheim, Gennerich,
Kolbenheyer, Lobedan, Rätz, Schmid and Schreiber. There was some work on
architectural drawing, Burg, Schmidt; perspective drawing, Francke, Schwedler
and drawing generally, Meyer. But the emphasis continued to be on mathematical
aspects of perspective, with seven authors on conic sections; Bauer, Grüson,
Hamilton, Martus, Pofelger, Schellbach and Schneider. There were works on
descriptive geometry by Busch, Flohr, Ohm and Wolff (1835, 1840, 1847, 1861);
on more general mathematical topics by Arndt, Caspary, Peschka, Ravoth,
Rosanes and Steiner, on instruments by Brauer and Hauck,--also famous for his
work on subjective curvatures and curvilinear perspective,--as well as on
geometrical drawing by Burg, Heimpl, Hertzsprung and Hoffmann.
In the twentieth century, there have again been works on artistic perspective by
Doehlemann (1912, 1918, 1922), Freyberger (1913, 1918, 1923), Kurth and
Tuckermann; reprints of classics including Chippendale, Ghiberti and Lambert;
architectural perspective, Danielowski (1968, 1969, 1976, 1982) and gardening
perspective, Wilczek (1929, 1941). But the earlier pattern continues and
mathematical treatises dominate with writings on descriptive geometry, e.g.
Fischer, Kramer, Ludwig (1919, 1922, 1924); Rehbock (1957, 1964, 1969),
Scheffers (1919, 1920, 1922, 1927) and Schmid (1912, 1919, 1922); projective
geometry, Doehlemann (1924); instruments including Brauer, Edler, Griesinger,
Haeder, Traenkle, and geometrical perspective, e.g. Rehbock (1978, 1979, 1980).
In addition to linear perspective there has been work on cartographic perspective,
Greef (1922), Sievke (1934); axonometric perspective, Papperitz (1916); parallel
perspective, Vonderlinn (1914, 1920, 1925) and Meyer Sidd (1970), as well as
spherical perspective, Birken (1923) and Barre (1963).
76
Other West German Cities Since 1700
In the eighteenth century, there were two further cities with publications on
perspective, Göttingen and Karlsruhe, and since the nineteenth century three
further cities have emerged, namely, Braunschweig, Darmstadt and Wiesbaden.
Here too mathematical and technical aspects of perspective were predominant, as
will become clear as each is considered in turn.
Göttingen
In the eighteenth century, publications at Göttingen included a work on
scenography, Meister (1753), a treatise on conic sections, Hube (1759), and a
reprint of Werner's important work on drawing with geometry and perspective
(1796). The chief author at the time, however, was Kästner whose interests ranged
from conic sections to mathematical perspective in general (1758, 1759, 1764,
1771, 1774, 1786, 1790, 1792, 1796, 1800). Since the eighteenth century there has
only been a German translation of Fuller's Perspective to scale (1955, 1956, 1958,
cf. 1952).
Karlsruhe
In the eighteenth century, there was an important work on conic sections by de la
Chapelle (1770, 1771, 1791) followed by two others in the early nineteenth
century, by Hofmann (1815) and Ladomus (1817). These were followed by
publications by Schreiber on descriptive geometry, technical drawing and
perspective (1822, 1828, 1833, 1839, 1854); by Doll (1867) on drawing and
geometrical plans, and Riess (1872) on geometrical perspective. The twentieth
century has seen a further textbook on descriptive geometry by Reutter (1948,
1958).
Braunschweig
In Braunschweig, during the nineteenth century, there were works on conic
sections by de la Chapelle (1801) and Beyssel (1862); construction drawing using
parallel perspective, Müller (1865, 1874), freehand drawing, Fürstenberg (1854,
1863); perspectival drawing, Klette (1867, 1869, 1870, 1873, 1887) and free
perspective, Balmer-Rinck (1887). In addition there were at least two works
specifically intended for artists by Frangenheim (1880) and Ehrhardt (1885, 1895).
The twentieth century saw a new edition of Haeder's instrument (1949, cf. 1914)
and a general textbook by Bärtschi (1982).
77
Darmstadt
In the nineteenth century, Darmstadt saw a series on publications on descriptive
geometry, geometrical drawing and technical drawing by Rössler (1839, 1845,
1847, 1852, 1853, 1861). The twentieth century added Getrost (1913) on free
perspective for schools, and a dissertation by Stoll (1971) on projective geometry,
as well as new editions of Vitruvius (1964, 1976).
Wiesbaden
Wiesbaden, also had some mathematical publications during the nineteenth
century including Hildenbrand (1867) on conic sections; Gut (1888), and Bouffier
(1893) with respect to perspectival shadows. There were also works on artistic
perspective, namely, Eberhard (1824) and Bouffier (1892, 1905). In the twentieth
century there was a greater emphasis on the technical side with works on
perspectival instruments, Haeder (1914), Ranke (1955); engineering perspective,
Ranke and Niebler (1956, 1957, 1960); parallel perspective, Schumacher (1951)
and architectural perspective, Bonbon (1977), König (1978, 1979). There was also
one popular textbook on artistic perspective, Schmidt (1972, 1976, 1978).
EAST GERMANY
Leipzig
In East Germany, Leipzig was slow in becoming a major publishing centre for
perspective. During the sixteenth century, there was only an edition of Peckham's
optical textbook (1504), and an alledged edition of Brunn (1595). The seventeenth
century was almost as sparse, with optical treatises by Euclid (1607) and Kohlhans
(1663, 1777). The eighteenth century brought fifteen books of which only two
dealt with artistic perspective, namely, Lairesse (1745) and Horstig (1979). All the
rest dealt with mathematical aspects including general principles, Kästner (1752),
Schönberg (1770, 1771, 1773); map projection, Hasius (1717, 1719), Lambert
(1763); instruments, Wilke (1772), Leupold (1774), Adams (1795) and
encyclopaedic summaries, Adelung (1781), Karsten (1782).
But it was only in the nineteenth century that Leipzig emerged as a major centre,
with some 170 books in the field, of which no less than 43 were due to the
emergence of Teubner, which published classics such as Euclid, Hero of
Alexandria, Ptolemy, Proclus and Serenus as well as books in mathematics and
science. These subjects dominated the field in Leipzig. There were some general
works, including those of Beck, Bünau, Holzmüller and Schubert. On conic
sections there was little in the first half of the century other than Grunert (1824)
and Jahn (1836), whose work had the remarkable title, Introduction to more than
50 million primarily new geometrical projections as a result of conic sections. But
when Salmon's work was translated into German it went thorugh at least ten issues
from 1860 to 1918, cf. 1848. Dietzel, a younger contemporary went through five
editions from 1864 to 1902; Fiedler, went through four, while Erler went through
78
eleven from 1877 to 1911. Other publications on conic sections appeared by
Drach, Eckhardt, Meyer, Schröter and Zeuthen.
With respect to descriptive geometry there were important texts by Stoevesandt
(1869), Wiener (1884), Disteli (1888) and a new edition of Monge (1900). In terms
of projective geometry there were contributions by Bünau, Hänkel, Hoch and
Sturm. Cartographical projections were treated by Reusch (19881) and Wangerin
(1884). Drawing books ranged from general works such as Ehrenberg (1868) to
various kinds, including axonometric drawing, Mayer (1855), Schmidt (1859);
cavalier drawing, Neigebaur (1836); construction drawing, Steiner (1861);
geometrical drawing, Schmidt (1859) and technical drawing, Schmidt (1886).
Versatile individuals such as Schreiber wrote on linear, projective and technical
drawing as well as perspective, descriptive geometry and shadow projection.
In terms of artistic perspective, three individuals dominated the field: Berger, who
went through twelve editions from 1855 to 1898, Kleiber with six editions and
Freyberger whose works went through six and four issues respectively. Fliesen's
three textbooks went through two editions each. Other authors included Burmester,
Gehler, Hetsch, Heyn, Krause and Morstadt. The twentieth century has brought
two significant textbooks by Doehlemann (1916, 1928) and Baier (1955, 1957,
1957) and a half dozen more general works by Albert, Beuhne, Meise, Riegel,
Schulze and Weiner.
The most important contributions have again been in terms of mathematical and
technical aspects. With respect to general theory, Von Öttingen (1901, 1905, 1906,
1907), has made important contributions. In descriptive geometry the chief
authors have been Müller, with five editions, and Papperitz, with three editions.
Other authors included Geyger, Gercken, Hessenberg, Opitz, Salkowski, Schlotke
and Timerding. In projective geometry there was Doehlemann (1898, 1901, 1905).
With respect to shadow projection there was Vonderlinn (1904, 1904) who also
wrote on parallel perspective (1905, 1910, 1914, 1920). With respect to drawing
there were general works such as Ebner (1924), and specific studies in
axonometric drawing, Papperitz (1906), Haase (1907); perspective drawing, with
three significant authors, Gründling, Severin; Weishaupt, and projective drawing,
Geissler (1911).
Other East German Cities
Four other East German cities deserve brief mention. Weimar, with 21
publications, was dominated by the works of four authors concerned mainly with
perspective in relation to drawing: Hertel, Steiner, Thon, Weishaupt. Greifswald
was essentially a one author town, responsible for the encyclopaedic works of
Karsten. Halle played a similar role with respect to Wolff's compendia, while
Dresden published mainly the works of Schlotke on descriptive geometry and
perspective.
79
SWITZERLAND
Basel
In Switzerland, there were three centres in Basel, Zürich and Geneva. In the
sixteenth century, Basel's role lay in the dissemination of texts, rather than in
original contributions. At the outset, there were classical texts, which the
Renaissance associated with perspective, namely, Galen (1533), Ptolemy, in six
editions, and Euclid (1537, 1546, 1558). Later, the chief mediaeval authors on
optics, Alhazen and Witelo (1572), appeared there. In terms of artistic perspective,
there were editions of Pélerin (1535, 1583), the acknowledged first edition of
Alberti (1540 cf. 1582, although there was alledged to have been an earlier 1511
edition in Nürnberg), Ringelbergius (1541), Serlio (1582) and Gauricus (1582).
The seventeenth century brought only editions of Serlio (1608, 1609) and Meyer
(1676); the eighteenth century, nothing, and the nineteenth century general
textbooks, Merian (1832) and Balmer-Rinck (1884). The twentieth century has
brought two new textbooks by Billeter (1904) and Artaria (1947).
Zürich
In the sixteenth century, Zürich had one significant author, Blum,--the so called
Swiss Serlio--, whose works on ruins and the five orders of columns went through
numerous editions. The eighteenth century brought a more original author,
Lambert (1759, 1774, 1789), concerned mainly with the mathematical and
technical side of perspective. Interest in this dimension dominated nineteenth
century publications by Largiader (1858), Kronauer (1861), Geiser (1866),
Graberg (1868), Ott (1868) and Möllinger (1882). The twentieth century brought a
new interest in artistic perspective, with textbooks by Gull (1839, 1941),
Brunschwiler (1941, 1958, cf. 1939), Artaria (1945), Meier (1945) and Schedegger
(1963).
Geneva
Geneva's role was more restricted. In the eighteenth century publications were
limited to a compendium by Wolff (1732, 1740, 1741, 1743, 1773, 1783). The
nineteenth century brought a textbook by Prader (1897) and a new perspectival
instrument, Ziegler (1889). The twentieth century has seen another instrument,
Odier (1934); a textbook, Leone (1962) and reprints of earlier works: Gauricus
(1969), Bosse (1973) and Valenciennes (1973).
3. GREATER EUROPE
Adjacent to the half dozen core European countries discussed above, were a series
of other countries: Spain, Portugal, Denmark, Sweden, Norway, Finland, Austria,
Czechoslovakia, Poland, Roumania and Russia. Almost all of these were in some
way directly affected by the Renaissance. Some even played a significant role in
its development. In rare cases isolated books on perspective were published in the
sixteenth or seventeenth centuries. And yet it was not until the eighteenth and
80
usually only in the nineteenth or twentieth centuries that centres of publication
emerged in these countries, as will become apparent as each is considered in turn.
SPAIN
Madrid
Spain has had three centres: Madrid, Barcelona and Valencia. During the sixteenth
century Madrid saw only a translation of Euclid's Optics (1585) and in the
seventeenth century, a general textbook, Hidalgo (1693). The eighteenth century
saw editions of Renaissance treatises by Alberti (1784, cf. 1827) and Barozzi
(1792) and texts on artistic perspective by Palomino de Castro y Velasco (1715,
1724, 1795, 1947), Tosca (1721) and Casanova (1794). This genre developed in
the nineteenth century with authors such as Brambila (1817), Rodriguez (1834),
Herñaez de Perea (1875), Aranaz y Izaguirre (1891), Muñoz Morillejo (1893) and
Salvador y Rodrianez (1897, 1898). On the mathematical and technical side, there
was a Spanish translation of Vallée's (1838) Manual of the science of drawing; a
work on descriptive geometry by Lavina Blasco (1859); on shades and shadows by
Pereda y Lopez (1866) and on axonometry by Torroja y Caball‚ (1879).
The twentieth century brought further works on artistic perspective, a compendium
by Muñoz Morrilejo (1914, 1923), and texts by Arola y Sala (1920, 1921), Marin
Magallon (1924), Martines Sanz (1936) and Iniguez (1962). But the mathematical
and technical side has continued also, with texts on cavalier and axonometric
perspective by Alonso Misol (1911), shades and shadows by Fernandez Casanova
(1917) and Arola y Sala (1921). Since 1950 this dimension has dominated the
scene, with texts on descriptive geometry, Soto Hidalgo (1960, 1967); cavalier and
axonometric perspective, Cano de la Torre (1966, 1970) and Garcia Gutierrez
(1978, 1979).
There has also been a surprising amount of attention to alternative forms, namely,
spherical perspective, Flocon (1966) and conic perspective, Adroer (1953),
Sandoval Guerra (1967), Corbella Barrios (1968), Martinez la Madrid (1968) and
Fuentes Alonso (1973, 1975).
Barcelona
In Barcelona, publications began much later, with only four textbooks on artistic
perspective during the nineteenth century: Planella y Corominas (1840), Alsamora
(1842) and Castelucho (1892, 1896) as well as one text on descriptive geometry,
Cardona y Escarrabil (1896). Nevertheless, in the twentieth century, Barcelona
became the leading centre in Spain, with 65 publications. Of these 15 were
translations of Italian, German and English texts, namely, Claudi (1914, 1965,
1971), Raneletti (1921), Reile (1928, 1972), Gull (1948, 1965), Schaarw„chter
(1970, 1974), Norden (1954), Morehead (1956), Lawson (1959, 1975) and Brown
(1982).
81
There has been some attention to mathematical and technical aspects, namely,
descriptive geometry, Ranelletti (1921); shades and shadows, Arola y Sala (1923)
and Rovira y Rabassa (1956); and conic perspective, Robira y Rabassa (1910), and
Perez Asensio (1964). Even so the major emphasis has been on artistic perspective
including authors such as Calvo y Verdonces (1912, 1924), Salat y Ferrando
(1919), Vidal y Vidal (1935), Anasagasti y Algan (1945), Daming (1954), Basilio
Gomez (1961, 1964) and Mestres Cabanez (1964). Four authors have stood out in
terms of popularity: an individual known only by his initials F. T. D. (1933, 1942,
1958, 1964, 1969, 1973); Freixas Arangaren (1944, 1960, 1968, 1978); Parramon
Vilasalo (1966, 1972, 1974, 1977) and particularly Rovira Sumalla, whose text
went through 12 editions between 1966 and 1977.
Valencia
In the sixteenth century, there was an early edition of Peckham's optical treatise,
Common perspective (1504), in Valencia. The eighteenth century saw editions of
Tosca's compendium (1707, 1712, 1757). The nineteenth century brought texts on
descriptive geometry, Alix (1767) and artistic perspective, Salva (1880). The
twentieth century has added works by Bonuet Minguet on different branches of
perspective: axonometric (1944), conic (1968, 1979) as well as linear (1969).
Conic perspective has also been treated by Grajales Carbonell (1977).
DENMARK
Copenhagen
In Scandinavia, publication has been centred in the capitals, quantity varying
considerably with 38 books in Copenhagen, 61 in Stockholm, 2 in Oslo and 16 in
Helsinki. In Copenhagen publications began near the mid-eighteenth century with
Horrebow's (1748) text on conic sections. There followed a textbook on artistic
perspective by Jardin (1758), a compendium by Kästner (1788) and a
mathematical treatise by Krebs (1799). In the nineteenth century, the field was
dominated by three individuals: Hetsch, who wrote textbooks on both geometrical
drawing (1822, 1828, 1840, 1844), and perspective (1839, 1851, 1868, 1881);
Eckersberg (1833, 1841, 1978) and Nielsen (1869, 1878, 1884, 1894, 1899, 1907),
also famous as a pioneer in the history of perspective. Less prolific authors
included Fabris (1860), Klein (1879), Kranys-Hansen (1879, 1880) and Blom
(1899). On the mathematical and technical side there were Schjödte (1864),
Seidelin (1890), Janniche (1891, 1897) and Christensen (1896) on stereometric
drawing and Petersen (1897) on descriptive geometry. The twentieth century
brought further works on this subject by Hjelmslev (1943) and Pihl (1955) as well
as texts on artistic perspective by Riberholt (1956), Schiellerup (1964) and Baro
(1979).
SWEDEN
Stockholm
Publications in Stockholm began just over a century later than in Copenhagen,
with isolated works on geometrical drawing by Mandelgren (1849) and Hetsch
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(1852). Since the latter nineteenth century, the field has been dominated by a
handful of individuals, the most influential of which was Henriques. His textbook
on geometrical and projection drawing went through 24 editions between 1896 and
1953, while his textbook on perspective for technical schools went through six
editions. Indeed, technical works have been predominant, notably, Segerborg,
with six editions, Werner, with five and more recently, Lagerquist, with five. In
terms of artistic perspective, the major author has been Johansson, whose textbook
has enjoyed seven issues.
NORWAY
Oslo
Oslo's publications have been limited to a text on artistic perspective by Guldberg
(1880), and a technical treatment by Bergh (1872), with an appendix on
axonometric perspective.
FINLAND
Helsinki
During the nineteenth century there were only two general texts in Helsinki:
Neovius (1869) and Nikkanen (1890). The twentieth century added 14 further
publications of which a handful dealt with artistic perspective: Hetsch (1906),
Nordström (1912), Stromberg (1912), Asp (1915) and Somerniemi (1955).
Meanwhile, the two most influential authors, Nyström (1943, 1944, 1947, 1948)
and Kauppinen (1978, 1978), as well as Asp (1915), Leanto (1916) and Markeno
(1975) wrote technical treatises.
AUSTRIA
Vienna
There was but one publication in Vienna during the sixteenth century, Has (1583),
with seventy-five engravings of ceilings intended to be seen from below (disotto in
su, quadratura), based on Italian models, with no explanatory text. The next
publication, nearly a century and a half later, Fischer von Erlach (1721) was again
a collection of engravings: imaginary perspectival reconstructions of famous
architectural monuments. There followed editions of a general textbook by La
Caille (1757, 1767), and works on perspectival instruments, including an
anonymous author (1752), Scherffer (1781) and Vorgtlanderl (1785).
It was not until the nineteenth century that Vienna emerged as a major centre with
70 publications. Even so, only a small number of these were devoted to artistic
perspective including works by Rittinger (1839), Schoen (1863), Staudigl (1868),
Burmester (1884) and Kajetan (1884). There was a translation of Philips
Jacobszoon (1803) and in the latter quarter of the century, with Eitelberger von
Edelberg's sources of art history, there were new editions of Renaissance treatises
by Alberti (1877, 1888), Leonardo (1888), Pacioli (1889, 1896) and Filarete (1890,
1896).
83
The majority of publications concerned mathematical and technical aspects. There
were works on conic sections, by Binder, Blank, Grünert, Jesser, Koutny and
Salomon; textbooks on descriptive geometry by Stieser, Heissig, Peschka,
Schlesinger and Stampfl, and on instruments by Corbin, Dietmann, Fialkowski and
Hillardt. There were also more specialized works on cartographical projection by
Steinhauser and Laffauk; axonometric projection by Pelz, and Stäudigl and
photographic perspective by Schiffner. As in Paris, London and elsewhere in
Europe, connections between perspective and drawing inspired the most new
work. In Vienna two authors were particularly influential: Heissig (1852, 1854,
1855, 1858, 1863, 1868, 1875, 1888) and Fialkowski (1879, 1880, 1882, 1893).
But there were at least seven others active in the field, namely, Arbesser, Hieser,
Hillardt, Jelinck, Kajetan, Limpoth and Wernigk.
The twentieth century has added twenty further books, of which four have dealt
with artistic perspective: Barenyi, Deininger, Goldstein, Meyer. Mathematical and
technical works have continued to dominate the scene. Of these, new perspectival
instruments by Sitte (1907, 1980) and Mack (1918, 1923), are perhaps the only
ones worthy of note.
CZECHOSLOVAKIA
Prague
When Prague was the centre of the Holy Roman Empire, and seat of the Emperor,
Rudolph II, there were editions of Krammer (1602, 1606) and Sadeler (1606).
Over a century and a half later there appeared a work on conic sections, Tesanek
(1764). The nineteenth century brought several contributions on mathematical and
technical aspects including geometrical drawing, Paulus (1818); instruments,
Hillardt (1840) and parallel perspective, Skuhersky (1858). The latter nineteenth
century added three authors with respect to artistic perspective: Tilscher (1865,
1867), Smolik (1874) and Pelisek (1890), and the twentieth century has seen
another two: Chalupnicek (1913) and Crhak 91978). But the focus of attention
has remained on mathematical and technical aspects, including Ebert (1910),
Jer bek (1912), Mack (1924), Salner (1954) and Setzer (1955). The most
significant contributions have been made by Kader vek (1822, 1929, 1954, 1954),
who has also made important contributions to the history of the subject.
POLAND
Warsaw
The first publication in Warsaw, Bartel (1928, 1955, 1958, 1960), was one of the
best textbooks on artistic perspective of the twentieth century, replete with
historical background and subtle examples. Since then there have been further
texts by Kurzynski (1957, 1960) and Sheybal (1958, 1963), as well as Witwicki
(1954) and Rolinski (1962). On the mathematical and technical side there have
been contributions by Appia, Domsta and Strasburger, texts on axonometric
perspective by Lange, Lewandowski and Piotrowski and architectural perspective
by Sizin.
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Elsewhere in Poland publications have been too sporadic to speak of centres,
although since 1960 there have been three texts published at Cracow, namely,
Gomoliszewski (1966), Bruzda (1971) and Palasinsky (1971).
ROUMANIA
Bucharest
Publications in Bucharest only began in the 1950s and have focussed on
mathematical and technical aspects with authors including Defour, Gheorghiu,
Mayer and Mihailescu. Even so two authors have been active with respect to
artistic perspective: Tanasescu (1963, 1971), and Teodoru (1964).
RUSSIA
Leningrad
In Russia, Leningrad and Moscow have been the two centres. In Leningrad, the
first publication is said to have been a translation of Pozzo (1737), arranged by the
Jesuits. In the latter eighteenth century, the academy at Leningrad, which had close
links with its sister institution at Göttingen, became a vehicle for a series of
important mathematical articles on cartographical and spherical projection by
Euler (1778, 1778, 1778) and Schubert (1784, 1788, 1790), as well as on conic
sections, Fuss (1805). The first clearly documented book on artistic perspective
was a remarkable trilingual (Italian, French and Russian) textbook by Petitot di
Lione (1789), the year of the French Revolution.
In the nineteenth century, Potier (1816, 1817) introduced descriptive geometry in
relation to drawing, a theme pursued by Sevastianov (1830) and subsequently by
Rynin (1918). Leve (1858) also wrote on perspective in relation to shades and
shadows. Even so, the majority of nineteenth century authors in Leningrad
focussed on artistic perspective, including Lavit (1834), Shparvart (1862), Markov
(1875) and Russet (1893) and continued into the twentieth century with Makovskii
(1911). The chief author in this domain at the turn of the century was Makarov
(1892, 1896, 1899, 1902, 1908, 1914). The revolution brought a complete break in
this tradition which was not resumed until 1959. Since then the focus has been
entirely on artistic perspective with at least seven new authors: Evteev,
Kolokol'nikov, Novikov, Pavlov, Shimanskaia, Turro and Zmetnyi.
Moscow
The pattern in Moscow has been quite different for at least three reasons.
Publications did not begin until the last decade of the nineteenth century,
Martynov (1891). There was then a break for over 35 years until Chernetsov
(1927). Since then there have been at least 60 further titles dealing with various
aspects. On the mathematical and technical side there has been significant interest
in descriptive geometry involving a translation of Monge (1944), and since then,
works by at least seven authors: Debrjakov, Evdokimov, Glagolev, Gordon,
Kuznetsov, Ostrovskii and Rudaev. Shades and shadows have been treated by
Klimukhin (1967), and Filina (1975). There have been studies of cartographical
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projection by Berdljant, Evdokimov, Ginzburg, Polovinkhin and Tolstoukhov;
architectural perspective by Federov, Krinskii, and Mashkov; technical drawing by
Solov'ev and Nepomnjaschchii, and drawing by Aksenov and Federov.
With respect to artistic perspective the earliest authors were Rerberg (1933, 1937)
and Shcherbakov (1939, 1969). Since then, there have been over a dozen authors
including Buinov, Danilijuk, Kuznetsov, Mochalov, Peterson and Solov'ev. The
two most influential writers have been Baryshnikov (1948, 1949, 1955, cf. 1952)
and Vladimirskii (1950, 1952, 1958, 1969). An interest in childrens' drawings in
relation to perspective developed in the 1960's with Labunskaya (1965), Sakulina
(1965), Levin (1979), as well as in the teaching thereof, e.g. Alekseeva (1968),
Dembinskii (1970). Alternative forms of perspective, notably inverted and
spherical perspective, have been considered by Rauschenbakh (1975, 1980).
4. ENGLAND
London
London became by far the most important centre in England. But it was slow to
develop. In the sixteenth century there were no publications relating to perspective.
During the seventeenth century foreign publications dominated the field. The
earliest of these was a treatise on the five orders of architecture by the Swiss
author, Blum (1608, 1635, 1660, 1674). There was also a French edition of De
Caus (1612), who came to England in 1608, as tutor to Henry, prince of Wales.
Translations of Italian authors included Serlio (1611, 1657), Porta (1658, 1669)
and Pozzo (1693). Translations of French authors included Desargues (1659), Le
Clerc (1671, 1672), and Dubreuil (1672, 1673, 1698). A work by the Dutch author,
Hondius, became the basis for a treatise by Moxon (1670, 1672, 1673). There was
also an anonymous work by a learned stranger. English works as such were limited
to a treatise on dialling and shadow projection by Wells (1635); on camera
obscuras by Hooke, (1669) and an anonymous (1690) work on the geometry of
landscapes.
In the course of the eighteenth century, with 210 publications, London emerged as
one of the most important centres of the world. Foreign translations continued to
play a significant role. The most popular among these were the French authors,
Dubreuil, with 11 editions, and Le Clerc, with seven editions, and the Dutch
author, Lairesse, with five editions. Other French authors included Blondel, La
Hire, Lamy, Le Blon, Le Clerc, L'Hospital and Ozanam. Translations from the
Italian included Alberti, Buonamici, Piranesi, Pozzo and Sirigatti. Other foreign
authors included the Dutch, Gravesande and, the Spanish, Palomino. Altogether,
these translations of foreign works amounted to under a fifth of all publications.
At the level of theory, one English author, Brook Taylor, had a seminal influence.
This came less through actual editions of his linear perspective (1715, 1719, 1742,
1815, 1835), than through a series of more popular works that it inspired, by
Kirby, with ten issues; Fournier, with five issues, as well as, Cowley, Highmore,
and the Maltons, senior and junior. These popularizations continued into the
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nineteenth century through Blacker, Edwards and Jopling. In terms of theory,
during the eighteenth century there were at least four other, more independent
authors, notably, Hamilton (1734, 1738, 1748, 1749), Hodgson (1734, 1743, 1765,
1782, etc.), Martin (1745, 1770, 1790) who, not unlike Brander in Germany, also
wrote on perspective in relation to microscopes (1771) and telescopes (1775,
1780); as well as Bradberry (1795, cf. 1789). By contrast, Ditton (1712) and Noble
(1771) stressed practical perspective, an approach shared by numerous more
popular authors including, Bardwell, Bowles, Dodsley, Ferguson, Peele and Smith,
whose combined works amounted to over 45 issues and editions.
Strictly mathematical works relating to perspective were fewer in London than in
France or Germany and were limited primarily to conic sections, including Muller
(1736, 1765), Jack (1742, 1769), Campbell (1755), Emerson, Hutton and Walker
who also wrote on other mathematical topics. There were also specialized works
on curved shadows, Murdoch (1746), and geometrical drawing, Adams (1791,
1797, 1803, 1813). Architectural works relating to perspective were also fewer
than on the continent, notwithstanding authors such as Pain with six issues;
Nicholson with no less than 18 issues by the mid-nineteenth century, and others
including Longley (1726, 1730), Carwitham (1739) and Miller (1759).
Meanwhile, publications in London emphasized new areas. One was the use of
perspective in cabinet making and furniture, inspired largely by the classic texts of
Chippendale, which eventually went through at least ten editions, and Sheraton,
which went through at least nine editions. There were other publications by Ince
(1762) on household furniture and by the London Society of Cabinet Makers
(1788). Since then there have been further works by Brown (1820, 1822, 1835),
Smith (1826), Newlands (1880), Bell (1930) and Emory (1955).
On the continent, there had been a preoccupation with views of monumental
architecture, notably of Rome (see above p. ), of French palaces, e.g. Androuet Du
Cerceau, P‚relle and idealized German palaces, e.g. Decker. London developed its
own variant of this type of literature with views of small towns, Buck (1724, 1729,
1736, 1745); local churches and buildings, West (1736, 1739); houses of
individuals, Serle (1745); views, Chatelain (1753); gardens, Chambers (1763) and
even a voyage from Gibraltar to Malaga, Carter (1777). In the nineteenth century,
this led to a literature on perspective applied to landscapes and nature, with authors
including Orme (1801, 1802), Clark and Noble (1805, 1809, cf. 1840), Wood
(1814), Rider (1836, 1849), Prout (1836, 1848, 1876), Green (1840) and Chapman
(1858).
In the nineteenth century, with 515 publications relating to perspective, London
was second only to Paris and here only a very summary description can be given
of the complex developments they entailed. In terms of foreign works, with the
exception of Lairesse and Leonardo, translations were of French authors. Two, Le
Clerc and Ozanam, were familiar from the eighteenth century. The remainder,
Armengaud, Dupin, Francoeur, Thénot and Thibault were all concerned with
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perspective in relation to (technical) drawing, a theme which also acquired
considerable significance among English authors.
Early in the century Hodson and Dougall produced a universal drawing book
(1804, 1805, 1821). Although the first work on isometric drawing appeared in
Cambridge, Farish (1820), publications in London soon followed. Two of the most
popular authors were Jopling (1833, 1834, 1835, 1839, 1842) and Binns (1857,
1861, 1865, 1871, 1874, 1876, 1878). Important also was Davidson who
published works on isometrical drawing (1868, 1873, 1897), model drawing,
building construction and a textbook on practical perspective, which went through
eight editions. There was also Burns, who wrote on isometrical drawing (1835,
1855), a work on mechanical drawing which went through ten editions, and
drawing generally. Other authors on isometric drawing included Atkinson,
Heather, Sopwith and Spanton. At the same time there were books on other
branches of drawing including engineering drawing, Clarke, Spooner, Wells;
geometrical drawing, Bradley, Winter; industrial drawing, Spooner; mechanical
drawing, Blunt, Foster, Mangall, Pease and particularly Rose; model drawing,
Armstrong, Williams and notably Trobridge as well as technical drawing, Mast.
With respect to mathematical aspects, considerable attention was devoted to conic
sections, the most influential authors being Drew, Durell, Hunter, Puckle and
Taylor, followed by others such as Bridge, Narrien, Pasley, Placock and
Robertson. Together, they produced at least 47 publications on the subject. Unlike
continental centres, such as Paris or Berlin, there was little emphasis in London on
descriptive geometry, notwithstanding textbooks by Heather (1851), Bradley
(1860), Pierce (1873) and Miller (1878). As concerns technical instruments, there
was Wollaston's camera lucida (1807, 1812), also discussed by Dollond (1830).
Stanley (1866 etc.), described various drawing instruments in a standard work
which saw seven editions by 1900. There was also Hulme (1879), on this topic,
and Milles (1895) on pinhole photography. Meanwhile, there was some interest in
shades and shadows, both in terms of mathematical principles and applications to
architecture, with works by Barnes, Gwilt, Puckett, Pratt and Ribbans. With
respect to architecture there were important works by Spiers (1887, 1888, 1892,
1902, 1905) on architectural drawing and Ferguson (1891, 1895, 1907, 1915) on
architectural perspective, as well as lesser works by Domschke, Longfellow, Reid
and Rimmer.
One of the most striking developments in nineteenth century London, was the
emergence of popular textbooks which went through many editions. At the head of
this list were Penley, whose Elements of perspective had 34 editions; Knight,
whose Practical guide to perspective had 29 editions, while Lewis', Principles of
perspective, and Pyne's, Perspective for beginners, both went through 17 editions
each. There were followed by Green, with 14 editions, Davidson with eight,
Burnett with seven, and Burgess, Hayter and Jewitt, each with six editions. The
emergence of these textbooks went hand in hand both with developments in
drawing, and the new interest in perspective as a part of education in schools (cf.
88
below chapter 4 below). Some works were specifically aimed at this market. Most
popular were Dennis', Elementary school grade perspective, with 17 editions, and
Burchett, Linear perspective for schools of art, with at least 10 issues. As the
century progressed, this educational dimension was increasingly reflected in titles
such as Allen's Short treatise of perspective for the use of schools (1886, 1887) and
Spencer's Practical perspective for the use of students (1890).
Less popular, but frequently more important in terms of substance, was another
class of authors, whose works had three or four editions such as Wood (1804,
1809, 1844), Varley (1815, 1820, 1888), Garry (1820, 1821, 1826), Whittock
(1825, 1840, 1849), Fielding (1829, 1836, 1843), Duffin (1852, 1853, 1864),
Cartlidge (1883, 1884, 1889), Miller (1887, 1892, 1895, 1914), Polak (1895, 1897,
1907) and Swinstead (1896, 1901, 1907). There were also at least ten authors
whose works went through two editions including Crossley, Deacon, Dicksee,
Hadfield, Howard, Moore, Nicholls, Parsey, Ryan and Symns and at least as many
who had only one edition, notably, Abbatt, Baker, Boyle, Clapin, Collins,
Delmont, Emerson, Jolly, Locock and Taylor. Among these were authors
concerned with unusual aspects of the subject, such as Bayliss (1856), who wrote
on aerial perspective, or Herdman (1853), who was among the first to devote a
treatise to curvilinear perspective.
In the twentieth century, with 265 publications, London has remained one of the
leading centres of the world, although there have been significant shifts in focus.
For instance, in terms of foreign works, the French influence which dominated
nineteenth century publications has gone. Instead, there have been new editions of
Renaissance texts, Alberti, Leonardo and Dürer; a general textbook by Parramon
(1973) and German architectural texts by Schaarwächter (1967) and Jacoby
(1977).
On the mathematical side, there has been little on conic sections and perspective,
other than Askwith (1908) and Somerville (1929). On the other hand, there have
been various developments with respect to map projection including Arden-Close,
Jameson, Kellaway, Merriman and Morrison. With respect to architecture, the
most popular author has been Holmes, with a work specifically on architectural
shadow projection, and a general textbook (1937, 1938, 1946, 1948, 1954, 1957,
1962, 1967). Other authors have included Barnes, Farcy, Forman, Hobbis and
Roberts. In terms of perspective for draughtsmen, there was one popular work by
Seller (1925, 1926, 1930, 1931), followed by others by Manktelow (1957), Harvey
(1959), Skelton (1966) and Ordon (1971).
As for general textbooks on perspective, there have been no new works which
have enjoyed twenty or thirty editions as in the nineteenth century. Indeed, only
half a dozen authors have gone through four to six issues or editions, namely,
Hatton (1903, 1910, 1919, 1924, 1929), Storey (1910, 1911, 1915, 1972), White
(1954, 1968, 1969, 1974), who has also been translated into German and Japanese,
Hollis (1955, 1956, 1960, 1962, 1968, 1974), Bromham (1970, 1974, 1975, 1978)
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and Walters (1970, 1974, 1975, 1976, 1978). Only slightly less popular have been
authors such as Cole, Lubschez, Warren and more recently, Gill. One of the most
original contributions to the field was made by Gordon (1922) who related the
reversibility principle of perspective to practical problems in photogrammetry
which has had consequences for many disciplines, including architectural design.
Abbott (1957, cf. 1950) remains a standard textbook. There have also been
numerous authors with only a single publication, including Barne, Brown,
Coombes, Last, Lyndon, Myerscough-Walker, Percival, Warnes and Wylie.
Perhaps the most striking development has been with respect to various types of
technical drawing. During the first half of the twentieth century there were some
works on this subject by Mayock (1915), Draycott (1927) and Evans (1949) as
well as works on engineering drawing, Richards (1913) and Maxton (1928) and
mechanical drawing, Jagger (1910). The field was dominated by two individuals,
Giesecke, whose works were published simultaneously in America, and Parkinson,
whose textbooks went through at least 25 issues. Since 1950, there have been a
handful of authors with more than one publication, namely, Forbes, Glenister,
Hewitt, Lewis and Marriott. In addition, there have been at least 50 new authors
with books on some aspect of engineering or technical drawing including, to name
but a few, Bathe, Cook, Davies, Freeburg, Harris, Kale, Kelsey, and Woolven.
Two other centres in England bear mention, Oxford and Cambridge.
Oxford
At Oxford, Haydocke's translation of Lomazzo (1598), became the first English
publication related to perspective. The seventeenth century saw only an edition of
Ryff's (1655) summary of Witelo's optical compendium. The eighteenth century
brought editions of classical texts by Apollonius, Euclid, and Serenus; works on
conic sections by Milnes (1702, 1712) and Robertson (1793), of which there were
further editions in the nineteenth (1818, 1825), along with a mathematical text by
Cremona (1885, 1893) and a handbook of pictorial art by Tyrwhitt (1868, 1975).
The twentieth century added a textbook by Storey (1910), works on engineering
and technical drawing by Cousins, Dunne, Hails and Hicks as well as a standard
work on polyhedra by Cundy and Rollett which has gone through at least 14
issues.
Cambridge
The first publication relating to perspective was on conic sections, Frevigar (1731),
a topic which dominated publications in the nineteenth century, with authors such
as Vince (1800, 1805, 1810, 1817), Hustler (1820, 1843, 1845), Hamilton (1830,
1834, 1838, 1843), Puckle (1854, 1856), Taylor (1872, 1873, 1883, 1888, 1889,
1891, 1903), and Besant (1884). Other contributions included an important paper
by Farish (1821) on isometrical perspective, mentioned earlier, as well as texts by
Hamilton (1828) on descriptive geometry, and Carhart (1883) on artistic
perspective. The twentieth century has added works on various types of drawing,
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Kennedy (1905), Dales (1914), Rudd (1916), Walsh (1944, 1945); map projection,
Hinks (1921), Melhuish (1931) and a work on architectural perspective, Lawrence
(1931, 1945). Hence at Cambridge, as at Oxford, concern has been focussed on
mathematical and technical dimensions of perspective.
SCOTLAND
Edinburgh
In Scotland there were two centres: Edinburgh and Glasgow. In Edinburgh during
the eighteenth century, with the exception of two texts on the principles of
perspective by Bradberry (1789), and Martin (1790), the focus was on conic
sections, with works by Simson (1735, 1750, 1775, 1792), Jack (1742) and Wright
(1772). The nineteenth century brought several basic texts on perspective, most of
which were, however, also published elsewhere, particularly London: Wood
(1801), Fergus (1802, 1803, 1823), Douglass (1803), an anonymous Catechism of
perspective (1821), Clark (1840), Chambers (1851), Burn (1855) and Yule (1873).
The twentieth century has seen only a text on technical drawing, Malcolm (1966).
Glasgow
In Glasgow, the first publications were editions of a work on conic sections by
Simson (1804, 1814, 1817), which had appeared previously in Edinburgh. The first
textbook on artistic perspective in Glasgow, Hodge (1876), was also published
previously in both Edinburgh and London. Even so, Glasgow developed an
independent approach in a way that Edinburgh, or Dublin, did not. The latter
nineteenth century saw textbooks by Forsyth (1883, 1885). Even earlier, Blackie
and Son (Glasgow, New York), had published a translation of Armengaud's,
Engineer and machinists drawing book, which proved so influential in America.
In the twentieth century, the same publisher has issued works of William Abbott,
including textbooks on technical drawing (e.g. 1929, 1930, 1957), a standard
textbook on perspective (1950), as well as a work on technical drawing by Hewitt
(1967). Meanwhile, other works on this subject have been published by Miller
(1941, 1955, 1958, 1960) and Hawksworth (1966).
IRELAND
Dublin
In Ireland, Dublin was the only centre, and it followed the English pattern.
Among the earliest publications were views of Irish cities by Smith (1750, 1756).
The eighteenth century saw three popularizing texts; a translation of Ozanam
(1756), an anonymous, Art of drawing in perspective, (1768, 1786, 1804) and
Ferguson (1778). The nineteenth century brought only a few works relating to
conic sections: Charles (1841), Salmon (1848, 1850) and Casey (1885, 1893).
5. NORTH AND SOUTH AMERICA
In North America, almost all publications were in the United States, with New
York as the pre-eminent centre. A half dozen centres produced between 10 and 56
91
books, namely, Philadelphia, Chicago, Boston, Scranton, Cleveland and New
Haven. In Canada, there were but a few publications in Toronto, Ottawa and
Montreal. In South America, Rio di Janeiro, in Brazil, has been the only centre
with scattered publications in a few other cities. Each of these will again be
considered in turn.
UNITED STATES New York
In New York, the earliest publication related to perspective was a work on conic
sections by Simson (1804), which had appeared previously in Edinburgh (1775,
1792). Translations of foreign works in the nineteenth century were limited to two
textbooks on drawing by Thénot (1834, 1838, 1844), and Armegaud (1854, 1855,
1856, 1857), which had appeared earlier in London. This tendency to adapt works,
which had already appeared in London, emerged as a pattern and included
Nicholson (1837), Whittock (1840), Chapman (1849, 1864), Miller (1887, 1892,
1895, 1914) and Burnet (1888). Perhaps the most interesting example was Ruskin,
whose, Elements of perspective, initially went through a single edition in London,
followed by at least 16 issues in New York.
Publications in the first half of the nineteenth century were dominated by a single
author, Davies, whose textbooks on perspective and related subjects amounted to
over 50 issues. His equivalent in the second half of the century was Warren, whose
texts amounted to over 60 issues. Both individuals combined mathematical and
technical interests with artistic ones, as if everything could be reduced to
pragmatic techniques. A similar approach was evident in the works of Honey,
Sullivan and Willson. Authors who focussed specifically on artistic perspective,
such as Cone (1889, 1899) and Ware (1895, 1900, 1905, 1914), were the
exception. With respect to mathematics and perspective, the nineteenth century
brought two standard textbooks on descriptive geometry: Church, with at least 11
issues, and Mahan, with at least 16 issues. In terms of architecture, there were
again two standard textbooks; Tuthill, which went through 10 issues and Wright,
which went through five. Those who dealt with shades and shadows in relation to
architectural perspective included Hill (1896), Willson (1898) and later Ware
(1912).
As in Paris and London, there was a particular vogue for books on technical and
mechanical drawing in relation to perspective. During the nineteenth century, three
authors dominated this field in New York: Appleton with 12 issues, Minifie with
17, and Krüsi with 6 issues. Other authors included Gedde, Maccord, Tomkins,
Tracy, and Willson. The twentieth century brought two important new authors:
French, with 10 editions, and Giesecke, with five editions, and four other
influential writers: Bartlett, Levens, Luzzader and Turner. In addition, the
twentieth century has brought at least 60 further authors concerned with some
aspect of drawing and perspective, including axonometric drawing, Roever (1941);
isometrical drawing, Jamison (1911), Locke (1911); engineering drawing, Adler
(1912, 1915), Leeds (1919), Mann (1930), Hobart (1941), Grant (1962) and a
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majority on mechanical drawing including Hawkins (1902), Oberg (1910), Cohen
(1913), Jones (1920, 1931, 1941), Paull (1936), Meyer (1944), and Barnes (1948).
In terms of mathematics and perspective, the twentieth century has seen a number
of texts on descriptive geometry including Ferris (1904), Moyer (1905), Smith
(1912), Kenison (1917), Kirby (1922), Hood (1926), Larkins (1939) and Douglass
(1948). The most popular works have been Bartlett, with nine issues and more
recently Grant (1948, 1952, 1956, 1965) and Slaby (1966, 1969, 1976). Striking
about these works is their emphasis on practical applications rather than theoretical
principles. The same characteristic applies to architectural perspective, with
authors including Brahdy, Buck, Forseth, Hicks, Morgan, Pile, Reznikoff, Rich,
Shelton, Tenle and Vrooman as well as the more influential Hornung (cf. 1910,
1949, 1950, 1955, 1956, 1971) and Fielding (1922, 1932, 1943).
In the nineteenth century, there were but two translations of foreign works in New
York. The twentieth century has seen a change. In terms of architectural
perspective there have been translations of Coulin (1966, 1982, 1983),
Schaarwächter (1967), Mori (1982, 1985), König (1984) and Prenzel (1985). With
respect to artistic perspective there have been a number of editions and translations
of Renaissance treatises including Barozzi (1923), Tory (1927), Pélerin (1938,
1973, 1975), Vredeman (1968), Serlio (1970) and Leonardo (1974, 1979) as well
as Baroque authors, Galli Bibiena (1971) and Pozzo (1971).
During the first half of the twentieth century, a textbook on freehand perspective
by Norton, with at least 15 issues, was the most popular work concerning artistic
perspective. Also influential were a half dozen other authors, including Richards
(1905, 1908, 1916, 1923), Lubschez (1913, 1915, 1921, 1926, 1927), Norling (cf.
1930, 1939, 1945, 1947, 1948, 1949, 1952), Freese (1930, 1938) and Postels
(1942, 1949, 1951, 1952). Less influential were Colvin, Hoyt, Kraus, Laning,
Lange, Reinhardt and Wilson. The decade 1943 to 1953 witnessed a slump with
only two new authors: Judge (1949) and Fuller (1952). This was followed by a
revival of interest through popular authors such as Amelio, Doblin, Gill, Hollis,
Shaw, Walters, Watson and White, as well as at least nineteen others, their
quantity alas not matched by their originality.
Philadelphia
The earliest work in Philadelphia was an edition of Bowles' (1794) text on artistic
perspective. The nineteenth century brought three further authors on this theme:
Ropes (1868), Brown (1883) and Jackson (1897). In terms of mathematical
perspective, there were textbooks by Simson (1807, 1809) on conic sections, and
Davies (1826, 1836, 1839, 1840, 1841, 1844) on descriptive geometry. Texts on
shades and shadows included Davies (1840), Hinckley (1851) and Pillet (1896).
As elsewhere, books on drawing and perspective dominated the field, notably
Armengaud (1863, 1865, 1866, 1867, 1869, 1870, 1871, 1875) on industrial
drawing, and Rose (1883, 1884, 1889, 1894, 1906) on mechanical drawing. There
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were also other texts on engineering drawing, Byrne (1853); isometric drawing,
Klein (1869), and mechanical drawing, Thorne (1889, 1890), Rooke (1895) and
Jackson (1896). The twentieth century has seen two further authors on this topic:
Starkey (1909) and Fry (e.g., 1912, 1916, 1919, 1927); one writer on instruments,
Wythes (1958), and two authors on artistic perspective, Burnet (1913) and Cole
(1920, 1921, 1922, 1925).
Chicago
Drawing in relation to perspective has also been the main theme of publications in
Chicago. The nineteenth century saw only a text on geometrical drawing, Eggers
(1882). In the twentieth century the most influential works were by Everett and
Lawrence, Kenison and the American school of correspondence. There were also
texts on architectural drawing, Radford (1912), Stegman (1966); engineering
drawing, Orth (1915), Giachino (1916); mechanical drawing, Webber (1904),
Westinghouse (1907), Adams (1914), Harrison (1914), Hutton (1915), Wood
(1927) as well as technical drawing, Beukema (1954, 1961), Giachino (1960).
Exceptions to this pattern have been Taylor (1910) on artistic perspective, and
Kellsey (1947), on photographic perspective.
Scranton
Of the 24 books published in Scranton during the twentieth century, four have
dealt with artistic perspective: Koller (1940), Jones (1961, 1966) and Jellico
(1966). All the rest have dealt with aspects of drawing in relation to perspective,
including architectural perspective, Lowndes (1930, 1935, 1938); engineering
drawing, Carter (1943), and mechanical drawing, Royce (1927, 1928), Hayes
(1941, 1948), and the International Correspondence Schools with eight textbooks
between 1902 and 1935.
Cleveland
In the nineteenth century, publications were limited to texts on artistic perspective,
Brainerd (1853, 1854), and drawing, Aborn (1893). The twentieth century added
two further texts on artistic perspective, Cooper (1900, 1925), Myslak (1967), a
textbook on mechanical drawing, Browning (1905) and a popular translation of
Barozzi il Vignola's, Renaissance treatise on the five columns of architecture
(1921, 1922, 1923, 1925, 1929, 1931).
New Haven
During the nineteenth century, there were three editions of Bridge on conic
sections; a work on linear perspective, Honey (1877), and textbooks on mechanical
drawing, Honey (1881), Lockwood (1873), Marshall (1897). The twentieth century
has seen further textbooks on this subject by Kirby, Kirschner and North. In terms
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of artistic perspective, there have been new editions of Renaissance treatises of
Alberti and Filarete.
CANADA
Since the late nineteenth century there have been at least nine publications in
Canada but these have been too scattered to speak properly of centres. In Toronto,
there were texts on perspective and geometrical drawing, McGuirl (1887), a work
on drafting, Jensen (1963) and treatises on map projection, Wray (1974), Lee
(1976). In Ottawa, the earliest work was a classic text on photographic surveying
by Deville (1895), which had an impact on European practice through Laussedat
and others. There was also a work on map projection by Senecal (1929). Montreal
has seen two works on artistic perspective, Carpentier (1975), Pansel (1975).
BRAZIL
In South America, Rio di Janeiro, in Brazil, with eight publications, in Portuguese,
is the only city that might be described as a centre. The earliest of these was a
treatise on applied geometry with a theory of shadows by Sampaio (1894). Since
then there has been a further text on shades and shadows by Pinheiro (1948), who
has also written on perspectival composition (1949). There have been four
textbooks on technical aspects, Carvalho, Medeiros, Negro and Rodrigues, and one
on artistic perspective, Azavedo Silva (1973). There was also a text by Doria
(1958) published in Curitiba, Brazil. Elsewhere in South America publications
have been scattered with no obvious pattern as, for instance, a text on geometrical
drawing in Sucre, Bolivia by Bardin (1852) or a technical treatise by Obrecht
(1893) in Santiago, Chile.
6. THE FAR EAST AND ELSEWHERE CHINA Beijing
In China, there have been two centres: Beijing and Shanghai. Publications in
Beijing began in 1729 (cf. 1735) with a translation of Pozzo arranged by the
Jesuits. Well over two hundred years then passed before there were further
translations from the West in the form of two Russian textbooks, namely,
Dobrjakov (1955), on descriptive geometry and Danilijuk (1956) on artistic
perspective. Since then, with the exception of a textbook by Xia (1956) on artistic
perspective, publications in Beijing have focussed on mathematical and technical
aspects including map projection, Fang (1957), shades and shadows, Jin (1959),
Wu-han-ce hui... (1959) and Tang-shan... (1965); geometrical perspective, Zhu
(1957); technical drawing, Tong-ji-da (1961) and architecture, Zhong-huacen...(1957).
Shanghai
Shanghai has been more obviously open to western influences with translations of
at least five authors in the twentieth century: Anthony, Cassagne, Lubschez,
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Ostrovskii, and Warren. While there has been work on technical drawing, e.g., Yu
(1931), Tong-ji-da... (1961), and architectural perspective, Huo (1954), Lin (1958),
there have also been a half dozen textbooks on artistic perspective, including
Huang (1931), Jiang (1933), Sun (1953, 1957), Wang (1954), Yan (1957) and Yen
(1957). Curiously enough, there is no record of publications after 1961.
TAIWAN
Taipei
Taipei only began publishing on these topics in the 1970's, with works on
architectural perspective, Huang (1972), Ke (1975), and works by Zhu (1975) on
technical drawing, and perspective drawing (1978).
JAPAN
Tokyo
Publications in Tokyo only began in 1967. Since then there have been 31 books, of
which over two thirds deal with architectural perspective. Indeed, this dimension
has become so important that, as Mitooka (1987) has pointed out in his
introduction:
In Japan perspectives known under the typical Japanese abbreviation pers
have come to mean architectural renderings used in the advertising
activities of the construction industry, rather than the painting technique
which developed remarkably in the Renaissance period.
These include translations of western works by Doblin (1971), Jacoby (1977,
1979) and Frank Lloyd Wright (1977), Japanese authors, Akezawa, Itihasi, Mori,
Onisi, Okamura, and the publishing house, Syokusya (1969, 1975, 1977). With
respect to artistic perspective there has been a translation of White (1969) and
editions by Kanazawa, Mijazaki, Nakamura, Ota, Takahasi and Tyuzenzi. No
works relating to the mathematical side of perspective have appeared in Tokyo.
Even more so than in the United States, the focus has been on practical
applications rather than theoretical principles.
AUSTRALIA
Not unlike Canada, publications in Australia have been too scattered to speak
seriously of centres. They began in Brisbane, with a practical textbook by
Kretschmer (1904), followed, more recently by two works by Millican (1962,
1970). With the exception of a textbook on artistic perspective, Shirlow (1932),
Melbourne has published only works on artistic perspective: Dean (1933), Bullen
(1941), Carter (1967), Center (1967). In Sydney, four of the five publications have
been by Sierp (1948, 1958, 1969, 1972), with one text intended for architects,
Thorne (1969).
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INDIA
Publications in India have been even more sporadic. In the mid-nineteenth century
there was a work on architectural perspective in Madras by Santz (1956), and on
the art of tracing in Bombay by Fritchley (1986). The twentieth century has seen a
work on a perspectograph in Calcutta, Bose (1944); a textbook on geometrical
drawing in Anand, Bhatt (1962), and two technical works by Ahmand and Sharma
in Delhi.
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3. TREATISES
1. Introduction. 2. Early Treatises. 3. Optics. 4. Geometry. 5. Architecture. 6.
Themes. 7. Categories. 8. Conclusions.
1. Introduction
The contents of the early treatises varied enormously because they remained in
manuscript form and because perspective was not an independent subject for
classification (see below 1.4). Accordingly, as a repertoire of themes emerged in
the latter sixteenth century, these dovetailed with at least four traditional
disciplines: optics, surveying (particularly in terms of instruments, see below 2.1),
geometry (two main methods, polyhedra, letters, human forms) and architecture
(e.g. scenography, columns, ruins, idealized buildings, interiors and quadrature).
A number of these themes evolved into independent topics, while others remained
minor themes in the perspective treatises for the next centuries.
Various branches of perspective also evolved. During the fifteenth century,
treatises dealt exclusively with one-point perspective. Pélerin (1505) introduced
two-point perspective to the literature. (Three-point perspective only became
current in the latter nineteenth century.) Meanwhile, Piero della Francesca had
introduced another branch: anamorphosis. The seventeenth, eighteenth and
nineteenth centuries brought further branches of perspective including cavalier,
axonometric, isometric, cylindrical, conic, spherical, aerial, colour, chiaroscuro as
well as shades and shadows. Each of these will be considered in turn.
2. Early Treatises (1434-1568)
The early treatises focussed on practical demonstrations. Alberti, in his On
painting (1434), the first extant treatise on perspective, began with basic
definitions, general remarks about optics, and a description how to make a
perspectivally foreshortened plane. In book two, he described the use of a
perspectival window (velo). If we believe the account of Vasari (1558) it was not
until the 1550s that Alberti invented such an instrument. Meanwhile, in Elements
of painting (1435-1440), Alberti gave examples of perspective involving
geometrical diminution, using combinations of squares (fig. 28.1), pentagons and
circles. Filarete (1464?), gave an even more elementary treatment in a brief section
on perspective in his Treatise on architecture (fol. 173v-178v): basic definitions, a
first diagram of the legitimate construction, and a few simplified examples of
perspectival diminution.
Piero della Francesca's On perpective of painting (c. 1470-1480), was the first
treatise devoted specifically to perspective. It opened with basic definitions and a
demonstration of the window principle. Book one contained examples in groundplan involving geometrical diminution, including a square, octagon, sixteen sided
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figure, oblique triangle, hexagon, pentagon and octagon. In book two, the same
principles were applied to three-dimensional objects: a cube, pentagon, octagon,
hexagon, columns, a hexagonal well on stairs, a four sided and an eight sided
building and a vault. Book three opened with a description of a second method,
involving a combined ground plan and elevation,1 which was then applied to a
mazzochio shape, a tilted cube, bases of columns, human heads and an apse. At the
end Piero provided three examples of anamorphosis including an egg which
became a sphere--an idea he used in his Brera Altar (pl.7.1).
By contrast, the section on perspective in Francesco di Giorgio Martini's treatise
on architecture, engineering and military arts, Codex Saluzziano 148 in Turin, was
only two pages (fol. 33r-33v) but, nonetheless, important because it demonstrated
principles of perspectival diminution in terms of surveying practice. His
contemporary, Leonardo da Vinci, gave a more systematic treatment in Manuscript
A (1492), beginning with basic definitions (point, line, surface), followed by
quantitative demonstrations, connections between surveying and perspective and
examples involving polygonal shapes.2 Luca Pacioli's discussion, in his Summa
(1494), was limited to four pages, with examples drawn from surveying
experience. While Pomponius Gauricus devoted ten pages to perspective in his On
sculpture (1504), he emphasized etymological and literary references, mentioned
classification (see below p. ) and merely included one paragraph of technical
description.
With the advent of Northern treatises in the sixteenth century, there was a greater
emphasis on illustration. For instance, Pélerin's On artificial perspective (1505),
introduced a first series of architectural exteriors (fig. 29.1-2) and interiors (fig.
66.1) of both sacred and secular buildings. These themes were developed in A
beautiful useful booklet (1531), edited by Hieronymus Rodler, and in Serlio's
works on architecture (1544 etc.). In the next decades, specialized treatises on
architectural perspective emerged with the works of Androuet Du Cerceau and
Vredeman de Vries (see below 2.4).
Parallel with these developments towards specialization, there was another trend in
the direction of compendia. Albrecht Dürer's Instruction in measurement (1525)
was an early example. It dealt with geometry, regular solids, letters, shadows,
methods of perspective and instruments. Daniele Barbaro, building on the work of
both Piero della Francesca and Dürer, took this approach further in his Practice of
perspective (1568) with sections on optics, geometry, the methods of perspective,
regular and semi-regular solids, irregular objects, columns, architecture,
scenography, anamorphosis, planispheres, shadows, human form and instruments.
Since later treatises usually contained most, and occasionally all of these subjects,
it will be useful to consider the history of each in turn.
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3. Optics
Optics and perspective shared a common etymological root in the Latin
perspectiva, and fifteenth century authors no doubt tended to see in optics a
theoretical basis for linear perspective. Hence, Ghiberti, active in protoperspectival demonstrations, also discussed optics at length in his Third
commentary.3 Alberti, in his On painting, referred briefly to concepts such as
visual angles and central ray, but carefully avoided details of optical debates.4 So
too did Piero della Francesca, Leonardo da Vinci, Pélerin and Dürer. Indeed, none
of these authors mentioned any specific sources on optics. One of the first to do so
was Serlio (1540), and then more as a disclaimer: "In this work I will not trouble
myself to dispute philosophically what perspective is, or from whence it hath the
original, for learned Euclides writeth darkly on the speculation thereof."5 Barbaro
(1568) referred to Apollonius' Conics and Euclid's Elements with respect to visual
angles, but did not mention Euclid's Optics explicitly, although he cited
introductory assumptions from that treatise. Egnazio Danti, who produced an
Italian translation of Euclid's Optics (1573), did cite the work specifically in his
edition of Vignola's The two rules (1583). No one at the time pointed out basic
discrepancies between theories of visual angles and principles of perspectival
planes noted above (see p. ). Hence, while most fifteenth and sixteenth century
treatises paid lip service to optics, there was no serious consideration of its
principles.
In the seventeenth century the situation became more complex. For instance,
Accolti (1625) cited not only Euclid's Optics, but also Heliodorus of Larissa,
Theon of Alexandria, Aristotle, Galen, Hippocrates and Witelo with respect to
theory. Nor did he cite blindly. For while acknowledging Witelo's great authority
as "the sole and principal head of the school of perspectivists,"6 Accolti noted his
mistaken claims with respect to the oblique passage of lights.7 On the other hand,
Accolti continued to claim that "perspective is nothing other in effect than a
representative section of the visual pyramid,"8 a view which remained popular
(see below 1.4), in spite of efforts by Desargues and Bosse to establish that the
laws of perspective had their basis not in Euclidean optics, but Euclidean
geometry.
4. Geometry
The links between geometry and perspective had been implicit from the outset in
Alberti's Elements of painting. For authors such as Piero della Francesca,
Leonardo, Barbaro and Danti, Euclid was considerably more than a source of
geometry: Euclid provided basic definitions (e.g. point, line, surface), principles of
proportional diminution and a model for the treatment of the regular solids.
Beginning with Piero della Francesca, there was increasing interplay between the
goals of mathematics and perspective, which helps explain why Piero's treatises on
the abacus, on the five regular solids and on linear perspective were all considered
100
works on perspective by Danti9 (1583). Leonardo da Vinci's quantatitive,
experimental demonstrations of perspective contributed to these links.
In Germany, this interplay between mathematics and perspective acquired new
connotations. Etymologically the Greek term for geometry, (γή µέτρών), meant
measurement of the earth. Hence, Dürer called his introductory book on geometry
Instruction in measurement and devoted a chapter thereof to perspective. The
author of A beautiful useful booklet (1531), in turn, equated perspective with
measurement. Hirschvogel (1543) went further by entitling his book: Geometry.
The book geometry is my name. All liberal arts at first from me came.
Architecture and perspective together I bring. Barbaro (1568), included a short
section on proportional principles of geometry. Danti (1583), added a larger
section and described the goals of perspective in terms of transformational
geometry
Since beyond the description of rectilinear figures it is very useful for the
Perspectivist to know how to transmute one figure into the other, I wish...to
show the normal way, not only to transmute a circle and any other
rectilinear figure that is wished into another but also move to expand and
diminish it in any proportion that is desired, in order that in this book the
Perspectivist will have all that which is required for such a noble
practice.10
In the decades that followed, mathematical aspects of perspective came
increasingly to the fore thanks to Commandino and his student Guidobaldo del
Monte (1600), who claimed that the nobility of architecture and painting were to
be attributed "to mathematical principles and especially to perspective."11 In the
Netherlands, Simon Stevin wrote a treatise because his patron, Prince Maurits,
wished "to design exactly the perspective of any mathematical figure with
knowledge of the causes and its mathematical proof."12 Through Leonardo,
Lencker (fig. 32.1), Commandino and Stevin formal mathematical problems such
as conic sections also found their way into treatises on perspective (see below pp.
). As a result, by the early seventeenth century perspective had become an area of
study for geometers and mathematicians generally, including Aleaume, Migon and
more powerful minds such as Desargues and Pascal. It was notuntil the nineteenth
century that further developments in mathematics threatened entirely to subsume
perspective (see below 1.4).
5. Architecture
The intimate links between architecture and perspective were due largely to the
Vitruvian tradition. Renaissance thinkers tended to translate Vitruvius' three
categories of ichnographia, orthographia and scenographia as ground-plan,
elevation and perspective with the result that perspective was seen as part of the
architect's profession. Indeed, the authors of fifteenth century treatises were
frequently architects, namely, Alberti, Filarete, Francesco di Giorgio Martini and
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Leonardo da Vinci, a trend which continued in the sixteenth century with Peruzzi,
Serlio, Cousin, Androuet Du Cerceau, Barozzi, Danti and Vredeman de Vries.
In Bellini's Sketchbooks (fig. 83.1-2), these connections between architecture and
perspective were evident from the outset. Elsewhere they emerged slowly.
Filarete's treatise contained only three schematic perspectival diagrams showing
the exteriors of an hexagonal, spherical and occtangular building. Piero della
Francesca's On perspective of painting, contained two perspectival views of a
square and an octangular building, plus a vaulted archway. Francesco di Giorgio
Martini's treatise contained various rough perspectival sketches of Roman
buildings, including both interiors and exteriors in section (fig. 84.2), using a
method associated with Brunelleschi (fig. 84.3) which, as already noted, was also
known in Northern practice (fig. 10.1-2) and was published by Pélerin who used it
in seven secular and three sacred buildings (fig. 10.3-4). Ringelbergius (1531)
provided five simplified versions of such interiors.
Rodler (1531) was the first to explore such architectural exteriors and interiors in
detail, pointing the way to a new category of books by Androuet Du Cerceau and
Vredeman de Vries in the next generation (see below 2.4). The treatises frequently
contained architectural sections and cutaways. Francesco di Giorgio Martini
employed these in a rough way. Leonardo da Vinci, applying his experience of
anatomical sections, improved upon them. Serlio published them often in
conjuction with a ground plan. Cousin (1560), employed a geometrical and
perspectival ground-plan combined with a perspectival view in section for various
idealized architectural buildings, which Androuet Du Cerceau (1576) developed
further. In Italy, Barbaro (1568) and Danti (1583) illustrated an alternative using a
combined ground-plan, elevation and profile, which became standard in treatises
on both perspective and architecture. Vasari, Jr. (1595) and Sirigatti (1596),
provided various architectural motifs in their treatises. Meanwhile, Serlio (1545),
had argued that the two subjects were not only interdependent, but that perspective
was a prerequisite for architecture:
And no perspective workman can make any work without architecture, nor
architecture without perspective.
To prove this, it appeareth by the architecture in our days, wherein good
achitecture hath begun to appear and show it self: for, was not Bramante,
an excellent architect, and was he not first a painter, and had great skill in
perspective art, before he applied himself to the art of architecture? And
Raphael of Urbino, was not he a most cunning painter, and an excellent
perspective artist, before he became an architect? And Baldassare Perruzzi
of Siena, was also a painter, and so well seen in perspective art, that he,
seeking to place certain pillars and antique works perspectivally, took such
a pleasure in the proportions, and measures thereof, that he also became an
architect; wherein he so much excelled, that his like was almost not to be
found. Was not the learned Jeronimo Genga also an excellent painter, and
most cunning in perspective art, as the fair works, which he made for the
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pleasure of his Lord, Francesco Maria, Duke of Urbino, can testify; under
whom he became a most excellent architect? Giulio Romano, a scholar of
Raphael of Urbino, who by perspective art and painting, became an
excellent architect, witnesseth the same.13
In the generation that followed, architects began to articulate clearly the need for
perspective. For instance, Pietro Cataneo, in his book on architecture, noted that
"what is of greater need to the architect and of so much importance is that he be a
good perspectivist,"14 adding by way of warning:
But if the architect is not a perspectivist he will never be able to honour
himself as well, nor show his concept by means of drawing, however
excellent a designer he may be. And he will know for himself how
important it is to be a good practitioner in perspective.15
Cataneo was so intent to impress upon his readers the need for perspective that he
included the phrase "its elevation by means of perspective"16 in no less than
eleven chapter headings, although some of the illustrations were simply elevations,
others sections, and then rough perspectival views. Meanwhile, the Vitruvian
commentaries of Cesariano (1521), Caporali (1536) and Ryff (1548) included
perspectival woodcuts as if these were literally a rebirth of Vitruvian methods, an
idea which Scamozzi took up explicitly in his Idea of architecture (1617):
As Vitruvius also says, perspective serves to represent all things by means
of artificial lines, [when one is] standing in a certain place. These
correspond to the rays of our natural sight in such a way that they carry to
our eyes the species and true images of buildings which are drawn in
forshortening in scenes and elsewhere.17
Scamozzi also emphasized the remarkable qualities of perspective:
And it is certainly a marvelous thing to behold such that the planes of
panels or pictures, with [the aid of] colours are so well placed and drawn
by art that to those who look at them they appear to be in relief, both higher
and deeper [than they actually are].18
Scamozzi added that he had written six books on perspective in his youth--alas
now lost--which he hoped to publish after finishing his work on architecture.19
By the eighteenth century, it was common for general treaties on perspective to
contain a section dealing specifically with architecture. For instance, Courtonne's
(1725) Treatise of practical perspective contained detailed ground-plans and
perspectival elevations. This tradition continued throughout the nineteenth century.
For example, Edwards (1803) Practical treatise on perspective on the principles of
Brook Taylor, gave ground-plans and perspectival views of isolated buildings,
buildings in context, and from different viewpoints. Guiot (1845), offered views of
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interiors and exteriors. Schreiber (1854), gave elevations, multiple views and
detailed drawings of historical buildings. Gennerich (1865), gave ground-plans and
elevations, not only for buildings, but also for canals.
Meanwhile, architecture increasingly found its way into the titles of perspectival
treatises: e. g. Hirschvogel (1543), Bassi (1572). Hence, the 1619 edition of Serlio
was headed All the works of architecture and perspective. Later examples included
Huret (1678), Oakley (1730), Galli da Bibiena (1740), Piranesi (1800), and Fabris
(1860). In the sixteenth century, titles frequently mentioned that the work was
dedicated to a number of professions of which architecture was but one of many.20
This continued into the seventeenth century, as in Dubreuil's Practical perspective
(1642-1649), which was addressed to "painters, engravers, sculptors, architects,
goldsmiths, embroiderers, tapestry makers and others using drawing."21 By the
end of the seventeenth century, this began to change. Pozzo's (1693-1700) treatise,
for example, was entitled Perspective of painters and architects.
The eighteenth century saw a continuation of this trend towards works on
perspective dedicated specifically, or mainly to architects, e.g. Bretez (1706),
Costa (1747), Kirby (1761) and Cobin (1794). In the meantime, the interplay
between architecture and perspective had become much more complex. On the
one hand there were now a number of architectural themes, which were regularly
included in treatises on perspective (see below pp. ). On the other hand there
were new categories of architectural literature, which incorporated perspectival
principles (see below pp. ).
6. Themes
In addition to these traditional disciplines which served as major topics, there
evolved a number of subordinate themes. Some were closely connected with
geometry, namely, the two main methods, polyhedra, irregular objects, letters and
the human form. We shall consider each of them briefly.
Two Chief Methods
Although we know from Danti (1583) and Guidobaldo del Monte (1600), that
there were many competing methods during the sixteenth century, including a
number of erroneous ones, there were two methods which gained ascendancy. The
chief of these which history has remembered as the legitimate construction,
deriving from Benedetti's (1585) phrase: this sole legitimate one (hunc solum
legittimam),22 was linked with the perspectival window, and began simply as a
verbal description in Alberti (1434). Filarete (1464?), added a scale diagram, such
that relative sizes and distances could be deduced. Piero della Francesca (c. 1480),
added actual measurements, as did Luca Pacioli (1494). But these involved only
isolated cases. Leonardo (1490-1500) described systematic measurements of the
diminutions involved. In Piero's treatise the legitimate construction became linked
with the ground plan/elevation method. Leonardo evolved new combinations
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thereof, variations of which were subsequently printed by Barbaro (1568), Danti
(1583) and Benedetti (1585).23
Alberti, in his Elements of painting (c 1435-1440), described an alternative
geometrical method involving proportional diminution. Piero della Francesca,
developed this in books one and two of On perspective of painting (c. 1480).
Francesco di Giorgio Martini made this a practical demonstration. With Pélerin
(1505), this method emerged as the distance point construction. Ringelbergius
(1531) gave quantitative examples of this method, demonstrating what happened
to squares positioned 10, 20 or 40 feet from the eye. Beginning with Serlio (1545),
it became customary to acknowledge that there were two methods. Danti (1583),
set out to demonstrate that they were actually equivalent. Meanwhile the earlier
geometrical version of this method in terms of proportional diminution continued.
Piero della Francesca's example using a cube was adapted by Barbaro (fig. 28.4).
His examples of foreshortened columns were adapted in a rough version by Serlio.
The architectural applications of the method, explored by Pélerin (fig. 29.1-2),
were developed dramatically by Androuet Du Cerceau (fig. 29.3) and later by
Bibiena (fig. 29.4). Discussion of both methods remained a standard topic of
perspective treatises until well into the eighteenth century.
Polyhedra
The regular and semi-regular solids became one of the most popular geometrical
themes in the perspective treatises. Plato had described the five regular solids in
the Timaeus24 and Euclid had outlined their geometrical construction at the end of
his Elements. Regiomontanus' lost work25 and Piero della Francesca's treatise on
the five regular solids, as well as his work on the abacus, continued this tradition.
Leonardo da Vinci's illustrations for Pacioli's Divine proportion (1496-1499),
made the regular and semi-regular solids a stock topic for treatises on perspective.
Dürer, in his Instruction in measurement (1525), published nets (i.e., ground
plans) of the regular solids, without giving their three dimensional equivalents.
Hirschvogel (1543), was the first to publish nets and perspectival views of the
solids together. This subsequently became a fairly standard practice, as witnessed
by Cousin (1560), Lautensack (1564), Barbaro (1568) and Danti (1583).
In Antiquity, Archimedes also considered thirteen semi-regular solids,
according to an account by Pappus. Leonardo illustrated these for Pacioli's Divine
proportion (1496-1499, e.g. figs. 36.1-2). A fascination for such forms and their
variants developed soon thereafter. Dürer (1525), provided nets or ground-plans
for nine of these. Stoer (1567), integrated regular and semi-regular solids into
imaginary scenes of architectural ruins in woodcuts intended as models for
marquetry. Lencker (1571), also produced a number of semi-regular solids. His
contemporary, the goldsmith, Wenzel Jamnitzer, created an extraordinary
collection of both regular and semi-regular bodies in his Perspective of regular
solids (1568) which, as he explained in his title, was based on Plato's Timaeus and
Euclid's Elements. Accordingly, he associated the tetrahedron with fire, octahedron
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with air, hexahedron with earth, icosahedron with water and dodecahedron with
heaven respectively. Using a "particular new adroit method never before in use"26
he provided six regular, six truncated, six stellated and six double stellated variants
for each of the regular solids to create a total of 120 versions which, as he pointed
out in his long title, was but an "introduction how, out of these five bodies, many
other bodies of various kinds and shapes may be made and found without end."27
Meanwhile, in Venice, Barbaro also explored these problems. His Practice of
perspective (1568), contained nets and perspectival versions of the five regular
solids and five truncated versions. In addition, he provided nets for 16 further
semi-regular solids and four stellated versions. His younger contemporary, Danti
(1583), was content simply to refer to the work of Piero della Francesca, Luca
Pacioli, Lencker, Jamnitzer and Barbaro with respect to polyhedra. Giorgio Vasari,
Jr., by contrast, in his manuscript treatise (1595), adapted a number of the forms
explored by Jamnitzer, and used them in new combinations (figs. 36.4, 37.4).
These, in turn, were adapted by Sirigatti (1596), in his published treatise (fig.
37.2). Hence, if Nürnberg artists such as Dürer, Jamnitzer and Lencker, at first
profited from their Italian colleagues, Italians such as Barbaro, Vasari, Jr., and
Sirigatti in turn learned from their Nürnberg colleagues.
The conscious cumulative dimension which had entered these developments by the
end of the sixteenth century was nowhere more evident than in a treatise published
by a Nürnberg practitioner, Pfintzing (1598), for his friends (cf. above pp.
).
While citing the contributions of predecessors, Pfintzing specifically discussed the
use of instruments in drawing the regular solids perspectivally (e.g. figs. 52.2, 4-5).
These themes remained popular throughout the seventeenth century. Marolois
(1614) continued the tradition of instruments. Halt (1625) in a book devoted
entirely to regular and semi-regular solids, provided over 170 illustrations of such
shapes often in unlikely combinations. Nicéron (1638, 1646, etc.), was at pains to
give abstract and concrete versions of the solids, an idea which Dubreuil (1647)
adopted in his popular work (figs. 35.1-2). Eighteenth century authors such as
Courtonne (fig. 35.3, 1725) and Highmore (fig. 35.4,1763) developed this
approach, relating several mathematical versions of a given object. The nineteenth
century added nothing fundamentally new. Indeed, authors such as Bennett (1837),
Catalan (1865), Pillet (1887) or Barbiani (1897), were more concerned with
standard examples, than with all the variants which had fascinated sixteenth and
seventeenth century artists. The main contribution of the twentieth century has
been in developing a systematic framework for explaining these forms, e.g. Cundy
and Rollett (1951 etc.)
Irregular Objects
Closely related to the regular and semi-regular solids, was a class of less regular
and irregular objects. Sometimes, this was a real object, such as a lute, another
form mastered in marquetry and painting practice (figs. 41.1-2) prior to appearing
in treatises on perspective. Dürer used a lute to illustrate the use of a variant type
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of perspectival window at the end of his Instruction in measurement (1525), an
image later adapted by Barbaro (1568). Other versions of lutes occurred in
Jamnitzer's manuscript (fig. 41.3), Vasari, Jr.'s (1595) manuscript and Sirigatti's
(1596) treatise (fig. 41.4).
Alternatively it involved a real object such as the mazzocchio, a Florentine hat,
which subsequently became transformed into an imaginary shape. Once again, this
form was found in painting practice prior to its appearing in treatises on
perspective. Paolo Uccello used it in his Battle of San Romano, particularly in the
Uffizi version, and in the Flood in the Chiostre Verde of Santa Maria Novella, in
Florence, as well as in drawings now in the Uffizi. Piero della Francesca illustrated
a simplified mazzocchio in his On perspective of painting. Leonardo (1400-1515)
drew several versions in his notebooks. Serlio (1545) adapted the form for
architectural purposes in his treatise on perspective. Lencker (1571) produced new
variants. Jamnitzer (1568) produced two, interlocking, partial mazzocchio forms,
while Barbaro (1568) devoted 16 variant figures to this shape making it a leitmotif
of his treatise. Several of these recurred in Vasari, Jr. (1595), and Sirigatti (1596),
and indeed the basic shape recurred in treatises over the next centuries, to become
one of the forms with which Escher played in his work.
To be sure, not every irregular shape was equally popular. In Nürnberg, Jamnitzer
produced stellar shapes (cf. fig. 37.3), including piles thereof, combinations of
pyramids, hexagonal towers, interlocking quadrangles, crosses, and even a sea
shell. Some of these recurred in Lautensack (1564), Vasari Jr. (e.g., fig. 37.4,
1595), Sirigatti (1596) and Pfintzing (1599), while others were not taken up by
later authors. One extraordinary polygonal shape, by the PP Master of Ferrara in
the 1470's (fig. 40.1), which looks like a prototype for one of Leonardo da Vinci's
tanks, was taken up by Barbaro in the manuscript version of his treatise, but not
published until the twentieth century.28
One of the most popular of these shapes was a four dimensional cross, which
Leonardo da Vinci sketched in his Codex Arundel (fol.223v, 1508). It recurred in
Dürer's Dresden Sketchbook, in a manuscript by Jamnitzer (fig. 38.1) and a
drawing by Stoer (fig. 39.4). In the seventeenth century, it was found in authors
such as Marolois (1614), Halt (fig. 38.2, 1625) and Dubreuil (1642-1649). It
remained a familiar theme in eighteenth century treatises, sometimes occurring in
unfamiliar contexts as in Kirby (fig. 38.3, 1755). Nineteenth century examples
included Gennerich (1853). In the twentieth century the form was adapted by Dali
(fig. 38.4) while becoming a symbol for both the international Red Cross and the
fourth dimension in art.29
The four dimensional cross was itself a variant of the ordinary cross, which was
equally popular (e.g. figs. 37.3-4, fig. 39.3) and, in turn, a variant of the more
universal theme of beams and columns, which had its own rich pictorial tradition,
as witnessed, for instance, by two examples from Dubreuil's popular text (figs.
40.1-3). Such examples are the more interesting because they illustrate the
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interplay between geometrical and architectural themes. Indeed there were a
number of irregular objects, which might conveniently be classed under either or
both headings. One was chairs. Giorgio Vasari, Jr., was perhaps to first to consider
the perspectival problems of chairs from different points of view in his manuscript
treatise (fig. 42.1, 1595). In the seventeenth century, Dubreuil popularized this
theme of chairs, (fig. 42.2, 1642-1649), while Nicéron (fig. 42.3, 1646) explored
its anamorphic possibilities. This prospect has continued to fascinate artists into
the twentieth century including Ames (fig. 42.4), and more recently, Berset (fig.
42.5, 1985).
Stairs constituted another such theme, and here a few examples will serve to
indicate another popular topic which persisted through the centuries. Circular
stairs, for instance, became a common theme in treatises on perspective and were
illustrated by Rodler (1531), Cousin (1560), Lautensack (1564), Jamnitzer (1568),
Androuet Du Cerceau (1576), in double form by Danti (fig. 43.1, 1583), Vredeman
de Vries (1604), Heinecke (fig. 43.2, 1727) and Frézier (1739) among others. The
same motif also occurred in painting practice as in Peale's Staircase Group (fig.
43.3, 1795). Regular stairs were no less popular. Here there was a fascination with
presenting them from unexpected angles, which often introduced ambiguities as to
what was up and what was down: a theme that intrigued Vredeman de Vries (fig.
43.4, 1604) and has continued to intrigue artists in our century such as Escher who
applied it not only to stairs but to waterways (fig. 43.5, 1961).
Human Form
The quest to impose geometrical regularity onto irregular forms extended to the
human form. It was found that, while simple geometrical shapes required
information from only two viewpoints, above and in front (i.e., ground plan and
elevation), complex organic objects required at least four viewpoints (above,
below, frontal and lateral), in order to arrive at a correct perspectival view. Piero
della Francesca illustrated this principle with respect to a human head in On
perspective of painting (c. 1480), showing the complications that arose when a
head tilted upwards was viewed from below.30 According to Lomazzo, these
problems must have been popular in Milan in the last decades of the fifteenth
century, for we are told that both Foppa and Bramante wrote on the quadrature of
the body--human and horse.31 We know that Leonardo devoted considerable
attention to the use of perspective in his anatomical studies.32 He was also
concerned with the geometry of movement in the human body as witnessed by the
Codex Huygens (fig. 68.5), and a later treatise by Thomas Coke (figs. 68.6-7). In
his manuscripts, Leonardo also outlined a simplified approach, which may have
been the source of Dürer's diagrams in his Four books on human proportion (fig.
68.1, 1528). The same Dürer, also offered a more pragmatic solution to the
problem: use of a perspectival window.
With Beham (1528) and Schön (fig. 18.3, 1538) human and animal proportions
and their geometrical forms became an independent theme, leading to treatises
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such as Bracelli (fig. 68.4, 1625). Nonetheless, the connection with treatises on
perspective continued in Germany with Lautensack (1564) and in Italy with
Barbaro (1568) who devoted the eighth chapter of his treatise to measures of the
human body beginning with the proportions of a young man taken from Vitruvius.
Barbaro also integrated the foreshortened figures of hands from Piero's and Dürer's
works for his own purposes (fig. 68.2).
Meanwhile, the perspectival foreshortening of the entire human body was a
problem again solved in painting practice long before it became a topic in the
treatises. Paolo Uccello dealt with it in the slain soldiers in all three versions of his
Battle of San Romano (London, National Gallery; Paris, Louvre; Florence, Uffizi,
1456), as did Mantegna with the putti in the oculus of the Camera degli Sposi, at
Mantua (fig. 70.2, 1473) and the Dead Christ (Milan, Brera, 1480, fig. 70.1). In
the treatises the problem was taken up in the Codex Huygens (fig. 70.4), which
served as the source of an extraordinary sheet33 by Carlo Urbino (fig. 70.5),
variants of which were popularized by Dubreuil (1649) and Houten (1705). Jean
Cousin, le jeune's Book of portraiture (1595), the first published treatise which
dealt systematically with perspective and human proportions (e.g. fig. 70.3),
enjoyed at least a dozen editions in the seventeenth, and five further issues in the
eighteenth century.
Perspective and anatomy, a combination which fascinated Leonardo, inspired little
interest in his successors. Indeed anatomy books tended to steer an independent
course. There were exceptions of course, as, for instance, Cheselden, who
regularly used perspectival windows in preparing his anatomical illustrations and
recently there have been at least two authors who have dealt specifically with
anatomy and perspective: Oliver (1972) and Smith (1984).
Letters
Letters of the alphabet were yet another irregular geometrical form, which became
a theme in treatises on perspective. Some early authors notably, Pacioli (1509),
Dürer (1525), Tory (1529), and Serlio (1545) dealt with both perspective and
calligraphy without discussing possible links between them. Lencker, by contrast,
devoted an entire book to the subject, Perspective of letters (1567, 1695) which, as
he explained in his title involved a clear instruction how one can render
perspectivally in a plane all the letters of the entire alphabet, in antique or Roman
letters in many a kind and position. In the seventeenth century Halt (1625)
continued this theme. De Bry (fig. 39.1) produced more ornamental variants
combining letters and human forms. Haesel (fig. 39.3) combined letters and
regular solids in a striking title page. But these were exceptions. By 1700, letters
were no longer a significant theme in treatises on perspective.
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Scenography
Among architectural themes in treatises on perspective, scenography was amongst
the most complex because its meaning was unclear. One interpretation, obviously
based on the passage in Vitruvius cited earlier (p. ), equated scenography with
perspectival stage design, whence the discussions of perspectival scenes for
theatres by Serlio (1544), Barbaro (1568), Danti (1583) and Guidobaldo del Monte
(1600). During the sixteenth century, scenography in this sense was discussed only
in Italian treatises and even here there were ambiguities. For, when Serlio
considered perspectival foreshortening in this context, he referred to
"sciographies," thus perpetuating a Renaissance confusion between sciographia
and scenographia.34 Serlio (1544), who was the first to include a chapter on
scenography in a treatise on perspective, provided a cross-section and view of a
typical stage and auditorium, several illustrations of stairs, plus examples of comic,
tragic (fig. 81.3) and satiric stage sets.
Barbaro (1568), reprinted Serlio's woodcuts of these three kinds of stage sets, and
reported briefly on the methods of Pompeo P(i)edemonte to make painted scenes
appear as if they were real buildings. Danti (1583), criticized Serlio's approach,
mentioned that the three kinds of sets had been dealt with sufficiently elsewhere,
offered his own technical advice, and alluded to examples of Florentine stage
practice such as the comedy presented at the ducal palace in 1569, on the occasion
of the visit of Archduke Charles of Austria. Guidobaldo del Monte (1600), devoted
the last book of his great treatise to a more detailed technical account of
perspectival stage design.
The seventeenth century saw the development of more specialized treatises on
stage scenery including Sabbatini (1637) and Chiaramonti (1675), some of which
remained in manuscript form, e.g. Gallacini (1641) and Aleotti (16__). Architects,
such as Furttenbach (1604), helped spread these ideas to the North. The Jesuits
also played a significant role in this process. Their efforts at politics through
education involved the use of theatre. Accordingly, Dubreuil's well known treatise
(1642-1649), contained a section on perspectival scenery. Even more famous in
this regard was the Jesuit, Pozzo's treatise (1693-1700) with editions in Latin,
Italian, English, German, French and even Chinese (1729, 1735) and Russian
(1737). From the outset, these perspectival scenes had been connected with court
life and as such were designed to reflect princely grandeur and magnificence. As
the courts of Europe evolved in the direction of absolutist states, the magnificence
and splendour of the performances blossomed accordingly and reached its heights
in the eighteenth century through the stage settings of individuals such as Juvarra
(1710) and families such as the Bibiena, particularly Ferdinando (1703, 1711,
1725) and Giuseppe (fig. 79.2, 1740).
The latter eighteenth and the nineteenth centuries brought a spread of these ideas
to more public theatres and treatises on perspective, such as Petitot (1758) or La
Gournerie (1884), frequently had a chapter devoted to these problems. There were
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also specialized treatises on perspectival stage design, including Landriani (1815,
1818, 1827), Taccani (1825), Cocchi (1851, 1855) and Burmester (1884), as well
as collections of stage scenery such as Sanquirico (1832, etc.). The twentieth
century has brought a few more specialist treatises on perspective in scenography
including Arola y Sala (1920, 1922), Sonrel (1943) and Morgan (1979).
Meanwhile, scenography sometimes had other meanings. Vitruvius, in another
passage mentioned earlier, referred to three types of architectural drawings,
ichnographia, orthographia and scenographia, which were commonly interpreted
to mean ground-plan, elevation and perspectival view respectively. Scenography,
thus became associated with architecture and had wider connotations to mean
perspective generally. Hence Pélerin's treatise, originally entitled, On artificial
perspective (1505), appeared subsequently as Treatise on artificial perspective or
scenographic architecture (1535, 1583) and On artificial perspective or
scenography (1599). Vredeman de Vries also assumed these connotations, when
he entitled his work Scenography, or perspective, as the ordinary painter calls
buildings which have been drawn optically. Occasionally, this wider context was
not acknowledged, but nonetheless assumed. For instance, Barbaro (1568), headed
part four of his book on the practice of perspective: "In which one deals with
scenography, that is the description of scenes,"35 but dealt therein, not only with
stage design but also with the five orders of columns and perspectival problems
relating to architecture in general.
Interiors
We have already shown that the mastery of perspective with respect to interiors
evolved in painting practice largely independent of the textbooks. Even so, it is
useful to recall that interiors constituted a minor theme in the treatises on
perspective. With respect to sacred interiors, Pélerin, (1505) was the first (fig.
10.3-4). In the generation that followed, Rodler (1531) offered another example
(fig. 16.4). It is noteworthy that during the sixteenth century no Italian treatises
included sacred interiors among their illustrations. Vredeman de Vries (1604),
provided one of the first detailed engravings of a church interior (fig. 17.1). In the
eighteenth century, an important treatise in this regard was Heinecke (1727),
which gave general views of church interiors (fig. 19.1) and detailed views of
confessionals, etc. (fig. 19.2). Isolated drawings of church interiors remained not
uncommon in treatises on perspective until the end of the nineteenth century as
witnessed, for example, by Guiot (fig. 19.3, 1845), or La Gournerie (fig. 19.4,
1884).
Secular interiors were a more popular theme in the treatises. Again, Pélerin (1505),
was the first to include a view of a room (fig. 66.1). The work edited by Rodler
(1531), contained a number of rooms, including artists' workrooms, a study (fig.
67.1), a bedroom and a small assembly hall. Lautensack (1564) included a larger
meeting place. Vredeman de Vries (1604) provided a rather luxurious vision of a
contemporary bed-sitter (fig. 66.3). Dubreuil (1642-1649) preferred to strip rooms
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down to their essential lines (fig. 66.2). By the eighteenth century, it was common
for perspective treatises to include an interior and these increasingly reflected the
taste of the time, for example, in Bischoff's (1741) living room (fig. 67.2). By the
early nineteenth century, such interiors had become veritable period pieces, as
shown by Wood (fig. 67.3, 1809). A recent example by Bärtschi (fig. 67.4, 1976)
confirms that rooms in perspective texts continue to reflect the taste of the day.
Quadratura
There were particular problems involved with paintings on ceilings seen from
below (di sotto in su). Again, artists, such as Mantegna (fig. 70.2), had mastered
the difficulties in painting practice, long before they were discussed in treatises on
perspective. Indeed, the first discussion occurred in Danti (1583), who
distinguished between flat and concave ceilings, and cited a number of examples,
such as Vignola at Caprarola (fig. 72.2, cf. 72.1), Giovanni Alberti dal Borgo in
the Palazzo de Mattei, and Tomaso Laureti in the Bolognese palace of Signore
Tasonne and Signor Pompeo Vizani.36 The same year as Danti, there appeared in
Vienna an extraordinary collection of 75 examples of such ceilings by Has (fig.
73.3, 1583). Vredeman de Vries (1604), offered examples both of scenes seen
from below and scenes seen from above (di su in sotto, fig. 72.1), again without
explanation. The Jesuit, Dubreuil (1642-1649), was among the first who set out to
clarify the principles involved. Another member of the order, Pozzo, used his
practical experience in painting the ceiling of Il Gesù, in Rome, as a starting point
for explanations, in his famous Perspective of artists and architects (figs. 73.1-2,
1693-1700). In the course of the eighteenth century, such explanations became a
common theme, particularly in perspective treatises associated with architecture
such as Decker (1711), Bretez (1751) and Kirby (1755). The continued fascination
of such problems in our century is witnessed by Escher (fig. 73.4 cf. 73.3).
Columns
The five orders of columns were probably the most popular architectural theme in
the perspective treatises. It evolved in the early fifteenth century as part of a
growing interest in the measurement of Roman antiquities. Manetti, for instance,
recorded how Brunelleschi and Donatello together:
made rough drawings of almost all the buildings in Rome and in many
places beyond the walls, with measurements of the widths and heights as
far as they were able to ascertain.... When possible they estimated the
heights [by measuring] from base to base for the height and similarly [they
estimated the heights of] the entablatures and roofs from the foundations.
They drew the elevations on strips of parchment graphs with numbers and
symbols which Filippo alone understood....
Filippo spent many years at this work. He found a number of differences
among the beautiful and rich elements of the buildings - in the masonry, as
well as in the types of columns, bases, capitals, architraves, friezes,
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cornices and pediments, and differences between the bases of temples and
the diameters of the columns; by means of close observation he clearly
recognized the characteristics of each type: Ionic, Donic, Tuscan,
Corinthian and Attic.37
According to Manetti, Brunelleschi and Donatello were the only individuals
interested in these problems at the time.38 But this soon changed. Starting with
Piero della Francesca (c. 1484), columns also became a topic in treatises on
perspective. Following the rules of Vitruvius and Alberti, Piero was concerned
specifically with a Roman Corinthian column, which he illustrated with four
diagrams of bases and three of capitals. Francesco di Giorgio Martini, in his
Codex Saluzziano, which also dealt with perspective, included a number of
drawings of columns and bases.
Meanwhile, Vitruvius offered a framework for a more systematic study of
columns, as witnessed by the editions of Fra Giocondo (1511), Cesariano (1521),
Caporali (1536) and Ryff (1547). By the 1530's, artists such as Peter Flötner,
Jacques Prevost, Sebastiano Serlio and Agostino Veneziano were producing
engravings of ancient bases, columns, capitals and architraves. These were
sometimes bound together in haphazard fashion, as in a Wolfenbüttel volume
entitled 93 engravings with studies of columns (1540): cf. a Washington volume
by Androuet Du Cerceau (1580?). Inspired by Vitruvius, Serlio organized his
material in a treatise specifically devoted to the five orders of columns entitled
General rules (1537). This was soon translated into Dutch by Pieter Coecke van
Aelst (1539), and was integrated as book four of Serlio's works of architecture.
In Switzerland, this idea of a specialized treatise devoted to the five orders of
columns was pursued by Blum (1550), whose work went through various editions
(e.g. 1596, 1627, 1635, 1674) and served as the basis for later treatises by
Kaessmann (1630) and Erasmus (1667). Blum's illustrations combined geometrical
ground-plans and perspectival elevations (e.g. 44.1). The most popular of all works
on columns was Giacomo Barozzi, il Vignola's Rules of the five orders of
architecture (1563), later versions of which stressed the use of perspective in the
form of shades and shadows, with editions in Italian (1808, 1814, 1818, 1831,
1832, 1850); French (1786, 1823, 1827, 1828, 1857, 1865, 1897), and English
(1902, 1905, 1910, 1912, 1923, 1931, 1940). This aspect was also stressed in a
treatise by Hondius, where the columns were rendered in perspective by Vredeman
de Fries (1617, 1620, 1628, 1638).
In addition to these specialized treatises, columns featured regularly as a theme in
perspective treatises. For instance, Jean Cousin (1560) provided full-page
illustrations with a geometrical and a perspectival ground plan as well as combined
perspectival views for each of the five orders. Barbaro (1568), who preferred to
illustrate elements such as bases, capitals and architraves individually, devoted 21
diagrams to the subject. A shorter treatment occurred in treatises by Danti (e.g. fig.
82.5, 1563), Vasari, Jr. (1595) and Sirigatti (1596). Fascination with the
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perspectival effects of columns continued throughout the seventeenth and
eighteenth centuries. Sometimes, as in the case of Nicéron (fig. 44.2, 1646), this
occurred as a chapter in a more general treatise on perspective. Alternatively, as in
the case of Viola-Zanini (1629), Bosse (1664, 1684) or Bosboom (1686), a
specialized treatise on the architectural orders was involved.
Illustrations varied considerably. Bosse (1664) produced geometrical ground-plans
and elevations, which he combined with their perspectival equivalents (fig. 44.3).
His opponent in the French academy, Grégoire Huret (1678), preferred a more
abstract approach with multiple views of a given object (fig. 45.4). Pozzo (16931700) was considerably more systematic. He related geometrical ground-plan and
elevation, perspectival ground-plan and elevation along with a perspectival view of
the appropriate part of a column or architrave (figs. 45.1-2). The clarity and
elegance of Pozzo's approach made his text one of the most influential works of
the eighteenth century (e.g. 1702, 1708, 1711, 1717, 1737, 1758, 1764, 1800,
1810). Also popular was Schubler (1719, 1732, 1735, 1749, 1758). Authors such
as Bretez (fig. 44.4, 1751) provided illustrations from unexpected points of view,
but added little in terms of method.
Eighteenth century treatises characteristically gave both abstract and realistic
versions of various parts of columns, as in Jeaurat (1750, 1760, 1770) or Kirby
(fig. 45.3, 1755-1761). By contrast, early nineteenth century authorsn, such as
Edwards (1803-1805) preferred to emphasize only abstract essentials. Specialized
treatises on columns continued until about the middle of the nineteenth century,
e.g. Lagardette (1797, 1823, 1833, 1835, 1851, 1853), Nicholson (1834, 1839) and
Rebout (1845), but it continued in reprints of Vignola, in general treatises, and
other genres of architectural treatise.
Ruins
As noted above, the study of columns was but one manifestation of a larger
concern with ancient monuments which began with Brunelleschi and Donatello
and, for which, Alberti's Description of the city of Rome (1430-1440) offered a
methodical approach. Even so, systematic treatises were not immediately
forthcoming. Francesco di Giorgio Martini's Codex Saluzziano included a number
of monuments in no particular order as was also the case with Bramante (c. 14951500), Maarten Heemskerck (1532-1536), Francesco de Hollanda (c.1538-1539),
and even Serlio (1545-1547), the first published treatise to include ruins, which
also dealt with perspective. In exceptional cases, an author such as Cousin (1560),
would include examples of ruins in a treatise on perspective. But unlike other
themes which became part of the ordinary repertoire of these treatises, ruins
effectively became an independent genre from the outset.
Androuet Du Cerceau (1545 etc.), was among the first to publish books which
specialized in perspectival ruins. These works in Orléans and Paris were soon
complemented by De Jode (1550), Cock (1551) and Vredeman de Vries (1560) in
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Antwerp; Pittoni (1551) and Palladio (1554) in Venice and Labacco (1550) in
Rome. In the next generations, with Lafréry (1575), Du Perac (1575), Cartaro
(1578), Stevens (1600) and Maggi (1601), Rome became and remained the centre
for this genre of views (vedute). The illustrations in these books went in two
different directions. One was archaeological in spirit, increasingly treated the ruins
as objects to be recorded for their own sake, and led via Heemskerck, Francesco de
Hollanda and Cock, to Du Perac (fig. 59.1, 1575), Stevens (fig. 85.1, 1600), and
eventually to Piranesi (fig. 59.2, 1750), whose work has rightly been compared
with actual photographs of the scenes (fig. 59.3). Another strand had little interest
in the ruins for their own sake, but used them as a springboard for the imagination
(fig. 89.1-4), which led not only to idealized ruins (see below 2.4), but also
dovetailed with a more general theme of idealized buildings.
Idealized Buildings
There was a natural link between perspective and idealized buildings for the
simple reason that such buildings conformed more readily to the systematic
geometrical grids imposed by perspective. As we have shown (see above p. )
such buildings were there from the outset. They dominated Bellini's Sketchbooks
(figs. 6.1-2, 9.3-4, 11.2, 82.1), and in painting practice, as characterized by the
Baltimore, Berlin and Urbino (fig. 96.3) panels. But these were exceptions in the
early period. Even in the sixteenth century interest in the theme varied
enormously. In Germany, for instance, where the emphasis was on individual
objects, particularly regular solids, such idealized buildings were rare, although
authors such as Lencker sometimes included an architectural example, as if it were
a variant of the semi-regular solids.
In the course of the sixteenth century, throughout Europe, and particularly in Italy
and the Low Countries, the Vitruvian tradition played a significant role in the
development of this theme, commentators providing their often phantastic
reconstructions of ancient and contemporary buildings, notably Cesariano (fig.
80.2, 82.1, 1521), who directly influenced Caporali (1536) and Ryff (1547). Even
more seminal was the work of four individuals: Serlio, Palladio, Androuet Du
Cerceau and Vredeman de Vries. Some of Serlio's examples were almost certainly
connected with his interest in scenography, and included idealized buildings with
colonnaded archways (fig. 82.3), as well as rows of buildings. Others served as
instances of his architectural drawing methods (fig. 84.1). However, the majority
of examples occurred in his other books in architecture, rather than in his second
book devoted specifically to perspective. These included idealized ancient and
contemporary buildings, both churches, such as Bramante's Tempietto (cf. fig.
96.4-5), and contemporary Venetian palaces and villas. Palladio took these themes
considerably further, particularly in terms of existing and planned country villas.
His systematic approach relating ground-plans, elevations and perspectival views
made his work a classic which became all the more influential because it was
subsequently adapted and transformed to suit English, French and other national
tastes.
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Androuet Du Cerceau's collections of engravings provided a new repertoire of both
idealized Roman ruins (fig. 9.1, 11.1, 86.2-5, 97.1) and contemporary buildings,
some real, such as Bramante's Tempietto (fig. 46.5), some purely imaginary (fig.
29.3). His work on the most excellent buildings of France (1576-1579), gave
versions of the great chateaux such as Annecy, Chenonceaux and Fontainebleau,
which were a curious mixture of fact and fancy. The collections of Vredeman de
Vries were also in this tradition, but with a greater emphasis on the imagination,
visions of possible architectural environments, rather than careful records of
existing ones (figs. 15.4-5, 87.1-2).
As in the case of ruins, this repertoire of images of idealized buildings went in two
quite different directions during the seventeenth and eighteenth centuries. On the
one hand, it led to ever more realistic chateaux and buildings, such as Pérelle
(1660), and eventually to photographs of famous monuments. On the other hand,
it led in a utopian direction with authors such Perret (1601 etc.) who produced
extra-ordinary edifices and towns in a roughly parallel perspective, or later
designers such as Decker (fig. 93.2, 1711), who gave artists' conceptions of
possible buildings appropriate for potentates and the like. Idealized buildings also
remained on theme in treatises on perspective such as Dubreuil (1642-1649), a
tradition which continued into the nineteenth century (fig. 62.1), although the
interplay between ideal and real elements became ever more subtle (figs. 62.2-3,
see below 2.4).
Towns
As mentioned earlier (p.
), views of towns became a regular feature in the
backgrounds of fifteenth century paintings. By the sixteenth century, these came
into the foreground, as with the views of Innsbruck attributed to Dürer (figs. 60.12). The treatise attributed to Rodler (1531), was one of the first to include such
townscapes in a work on perspective (fig. 60.3-4). Military interests also played a
role, spies being sent out to sketch a town about to be attacked (fig. 58.1, cf. 58.4),
as did documentary concerns: artist's sitting in church towers to make views of
battles serving as the sixteenth century version of reporter's cameras. These
concerns aside, in Italy, with the exception of views of Rome such as Ferrario
(166_), there was little interest in this theme. In France, Pérelle (1666-) published a
collection of views of Paris, chateaux of France and views of Rome.
In Britain, during the eighteenth century, this theme became more important.
Buck (1736) published proposals for six perspective views of Canterbury,
Rochester and Chicester and in the next decade (1745?) of York and the towns of
Leeds and Wakefield. Smith (1750) published perspective views of the chief
towns in County Cork. Anonymous views of Oxford (1753) and Shrewsbury
(1756) also appeared. In the nineteenth century, views of towns became a regular
feature of treatises on perspective. Sometimes, as in the case of Edwards (1805),
this involved more than one view of some city (fig. 64.1) or of buildings
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encroaching into a landscape (fig. 65.2). Sometimes, as with Wood (1809),
fashionable views of London were involved, including Portland Place and Hill
Street, (fig. 65.1, 3). Authors such as Tilscher (1865) provided a series of views of
a given park (fig. 65.4-5). In the twentieth century there has been at least one
book, Vlaardigen (1967) devoted specifically to the problem of drawing
townscapes.
Landscapes
In many treatises there was no clear separation between townscapes and
landscapes, as is vividly illustrated in the treatise by Edwards (1805). His
engraving of houses on a hill (fig. 65.2), with its division down the middle, could
be seen as a townscape on the left and a landscape on the right side. Indeed, most
of Edward's illustrations involved architectural features positioned with varying
degrees of prominence within a landscape (figs. 62.1-3, 63.1-3, 64.1), such that
clear boundaries between townscape and landscape disappeared. This ambiguity
had, in a sense, been present from the outset. Already in the sixteenth century,
when authors put their buildings into context (fig. 61.3), or when Du Cerceau did
so with his chateaux, the same ambiguity occurred. It arose also in connection
with themes such as reflection, as in Dubreuil (fig. 50.1-2), or Robert (fig. 51.3-4),
where town and country frequently appeared together.
In the latter eighteenth century, landscape gradually emerged as an independent
theme through individuals such as Werner, who extended the application of
perspective to various aspects of the organic world: flowers (1765), four footed
animals (1768) and humans (1768), as well as landscapes (1768) and views (1781).
In the nineteenth century, Basoli (1810, 1830) made a collection of landscape
views (paessaggio). In England, landscape often entered into the titles of treatises
such as Orme's (1801) Rudiments of landscape drawing, or Noble's (1805)
Practical perspective exemplified on landscapes. Subsequent examples included
Wood (1814), Varley (1815), Nicholson (1820, 1823), Fielding (1839, 1852),
Robert (fig. 51.3-4, 1895) and more recently, Vanderveken (1950).
Gardens
The theme of gardens was closely related to landscapes and in the sixteenth
century overlapped also with other themes, such as ruins and idealized buildings.
Androuet Du Cerceau, for instance, sometimes included reconstructions of ancient
gardens in his views of Roman ruins (fig. 92.1) and, in like manner, included
contemporary gardens in his views of modern chateaux and palaces. Vredeman de
Vries was the first to publish collections of perspectival views of gardens (fig.
92.2), some of which involved adaptations of the five orders of columns (fig.
92.3). These prepared the way for an approach to nature as pure artifice, which
authors such as Salomon de Caus completed, with the aid of automata, and other
feats of engineering (fig. 98.1). Books on gardening from the seventeenth century
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onward frequently contained brief instructions concerning perspectival effects (see
below 2.3).
It was not until the eighteenth century that books concerned with perspectival
views of specific gardens emerged in England, as for example, Serle's (1745) plan
of Mr. Pope's garden, Chatelain's (1753) views of the buildings and gardens at
Stowe or Chambers' (1763) views of Kew Gardens. The nineteenth century added
books specifically devoted to creating perspectival gardens such as Vergnaud
(1835) or Glindemann (1900).
Nature
Landscapes and gardens were in turn related to the theme of nature, which became
a regular feature of treatises during the nineteenth century. Sometimes, as in the
case of Nicholson (1820, 1923), the title referred explicitly to drawing and painting
landscapes from nature. Frequently the reference was to nature in general, as in
Th‚not (1826, 1829), Krane-Matena (1840), Locock (1852) or Nicholls (1858).
The influence of drawing academies and conflicting philosophies with respect to
drawing instruction in schools, gave new connotations to nature (see below 1.4).
For instance, some thinkers held that model drawing was a first step to drawing
from nature. Others acted, as if nature involved drawing from artificial models of
nature, more than actually drawing from life. Still others, such as Rosenbeck
(1895), saw drawing from nature as a simple alternative to memory drawing.
7.CATEGORIES
In addition to the above themes there were different categories or branches of
perspective, which served as topics in the treatises, many of which subsequently
evolved into independent genres of literature. These involved three sub-categories:
alternative picture planes, technical applications and special effects, each of which
will be considered in turn.
Alternative picture planes Anamorphosis
In linear perspective the picture plane is usually parallel with the plane in which
objects are situated. In cases when objects are at right angles to the picture plane
distortions occur. When done deliberately, as with the skull in Holbein's
Ambassadors, the effect is termed anamorphosis. Seventeenth century authors used
this term in a more general sense to include deliberate perspectival distortions
produced by alternative picture planes, particularly cylindrical, conic and spherical
ones.
In the early treatises, anamorphosis was a topic specific to Italian texts. Piero della
Francesca introduced it (c. 1480), with his famous example of an egg which
became a sphere when viewed from below, as in his Brera altar. Leonardo da
Vinci took up this theme in both the Manuscript A and Treatise of Painting. Even
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so, a clear knowledge of the principles cannot have spread quickly, for Barbaro
(1680) continued to discuss it in a veiled manner in a chapter entitled: "a beautiful
and secret part of perspective."39 Danti (1583), by contrast, gave clear
descriptions of two basic anamorphic tricks.40 One, which may have been
invented by Leonardo, involved the parts of a portrait being spread out on one
surface of a series of triangular slats tilted such that the portrait could only be
recognized when viewed in a correctly positioned mirror.41 The second case
considered by Danti (1583), involved the face of a man which was greatly
extended horizontally along the side wall of a peep show, and required that one
viewed it from the side in order that it again appear normal. Anamorphic effects
produced by a reclining human body have already been mentioend earlier under
the theme of the human form, and were explored by the author of the Codex
Huygens (fig. 70.4, 1560-1580), Cousin, le jeune (fig. 70.3, 1595, etc.), Carlo
Urbino (fig. 70.5), Dubreuil (1642-1679) and Houten (1701).
In the seventeenth century, Marolois (1614-1617) explored the effects of
alternative picture planes, notably cylinders, V shapes and inverted V shapes.
Vaulezard (1630) began a more systematic study of anamorphic effects produced
in cylinders and cones. The Jesuits were fascinated by these problems as a
manifestation of God's subtle laws of nature and for didactic reasons.
Accordingly, Nic‚ron (1638), wrote a first treatise devoted specifically to
anamorphosis. His contemporary, Father Dubreuil, (1642-1649), popularized
these findings in his textbook, as did the later Jesuit, Father Pozzo (1693-1700).
Aside from new gadgets to produce some of these effects mechanically by Leupold
(1713) and summaries in encyclopaedias, such as Martius (1797), the eighteenth
century added nothing to the topic. Indeed the principles involved were
increasingly discussed in separate publications devoted to conic, cylindrical and
spherical perspective.
Conic Perspective
Ptolemy used conic projections in his Geography (fig. ), a theme which Schubert
(1784) pursued and which has continued to interest twentieth century thinkers such
as Arden-Close (1925). Vaulezard (1630), the first author to devote a treatise to the
subject, began a tradition of discussing conic and cylindrical projection in tandem,
which continued with Le Poivre (1704), Morton (1830), in the context of
descriptive geometry with Leroy (1834, 1837, 1846, etc.) and more recently with
Ridderhof (1925) and Giovanardi (1934). The topic was implicit in more
specialized treatises on conic sections by Pascal (1640), La Hire (1673) and others.
Since the late nineteenth century, there have been several French authors who have
written specifically on conic perspective, namely, Lebon (1887), Aubert (1895),
Raull (1921), Faling (1955) and Fradin (1966, 1980). But the topic has held most
fascination in Spain with works by Robira y Rabassa (1910), Adroer (1953), Perez
Asensio (1964), Carreras Soto (1960, 1975), Sandoval Guerra (1967), Bonet
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Minguet (1968, 1979), Martinez La Madrid (1968), Corbella Barrios (1968),
Fuentes Alonso (1973), Grajales Carbonnel (1977), Lopez Gonzalez (1962) and
Martin Morejon (1983). Meanwhile, Adams (1976) has explored a method of
tetraconic perspective to approximate visual perception.
Cylindrical Perspective
In cartography, Mercator initiated a serious interest in cylindrical projection (fig.
). However, for many authors on perspective, optics provided the first incentive to
studying this alternative, namely, concern with producing a picture plane
equidistant from the plane of vision. Leonardo explored this problem in
Manuscript A and elsewhere in his notebooks, which subsequently inspired the
author of the Codex Huygens (1560-1580) and Cardi (1612). In seventeenth
century France, Vaulezard (1630, etc.), explored the anamorphic potentials of
cylindrical perspective, a theme which Dubreuil (1642-1649), pursued. Bosse
(1643, 1653, 1660, etc.), on the other hand, was more concerned with
distinguishing between cylindrical projections, which he associated with vision,
and the plane projections of linear perspective.
In the eighteenth century, Pozzo's influential treatise focussed interest back to
anamorphic aspects of the problem. The nineteenth century saw examination of
geometrical aspects, in the context of descriptive geometry, by authors such as
Leroy (1834, etc.) and Bailby (1976), as well as a renewed interest in optical
connections through authors such as Herdman (1853) and Ware (1882, 1883, 1894,
1895, 1900, etc.). The twentieth century has seen continued interest in cylindrical
perspective by Garnier (1934) and Hammerschmidt (1940), with short sections in
treatises on perspective of Abbott (1950) and Vero (1978).
Spherical Perspective
Sixteenth and seventeenth century treatises on perspective almost always avoided
questions of spherical perspective, except in connection with astrolabes (see below
p. ), but by the eighteenth century this theme emerged with respect to projection
problems in astronomy and geography with contributions by Karsten (1768, 1773),
Wright (1772), Kautsch (1784) and Schubert (1784, 1788, 1789, 1790) and later by
Germain (1866). In the nineteenth century, spherical projections were subsumed
as a branch of descriptive geometry by Davies (1826, 1832, etc.), Lacroix (1840),
Leroy (1850) and Church (1868, etc.).
In connection with optics, there has been some confusion between spherical and
cylindrical perspective, the sphere of vision frequently being represented simply as
a circle equidistant from the eye. This confusion led Dürer (1525), for instance, to
adopt his method of negative perspective, whereby objects further from the eye
were represented as larger in order that their apparent size remain constant. Serlio
(1545) took up this principle, as did Barbaro (1568) and thereafter it became a
commonplace in both treatises on perspective and architecture (cf. fig. 2.1). In the
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nineteenth century, Hauck (1879), believed that the subjective curvatures of Greek
architecture corresponded to spherical theories of vision. These possible links
between architecture and optics were also touched upon by Maertens (1884) and
taken up seriously by Borissavlievich (1921, etc.), who gradually evolved a
personal theory of spherical perspective with respect to architecture.
Connections between spherical projections and optics also arose from unexpected
quarters such as landscape gardening. Seventeenth century authors, such as
Tacquet (1668, etc.) had suggested that trees should be planted in rows of half
hyperbolas in order to appear parallel. This problem was taken up by an
anonymous author (1719) and Varignon (1720), only to be challenged by Bouguer
(1755). Debates concerning curvature of parallel rows continued in the twentieth
century with experiments by Hillebrand (1902), Blumenfeld (1913) and Luneberg
(1947). In the nineteenth century, Helmholtz (1866, 1896), developed a new
demonstration involving a curved checkerboard to illustrate subjective curvatures.
Two other important demonstrations evolved: one using the vault of the heavens,
e.g. Reimann (1890-1891) and Zoth (1899), the other using the apparent bending
of light from lighthouses on the horizon, e.g. Bernstein (1904).
The twentieth century has seen an increasing interest in relating spherical
projections of optical theories with painting practice. Deininger, in a lecture to the
central organization of Austrian architects on 15 August 1914, outlined what he
believed was a new theory of artistic painters' perspective, and its practical results,
in which he claimed that: “only (on such) a spherical surface is it possible to
represent graphically all those lengths, i.e., all the perspectival dimensions in their
correct relations and proper sizes.”42 In New Hampshire, an artist and a physicist,
Ames and Proctor (1921) did experiments together:
for the purpose of determining the exact nature of the image received by
the human eye in the belief that a knowledge of its nature would be of aid
in suggesting how the various parts of a picture should be painted to give a
technically pleasing and artistic effect.43
Birker (1923), took out two patents for a mechanical means of producing spherical
perspective. Stark (1928) and Hegenwald (1932), wished to use the spherical
surface of the retina as the basis for their theories of spherical perspective, but
were hesitant in their application thereof. An important book, in Canada, by Jobin
(1932), argued that with the development of skyscrapers one needed to apply
perspective to the vertical as well as the horizontal axis. In part two Jobin set out:
to show that the curved line, determined by the principles of the optical
sphere, today constitutes a theory of vision superior to that of the straight
line established by the principles of the optical cone.44
He illustrated his theories with an impressive series of illustrations using a four
point, spherical perspective. Similar ideas were explored two years later by
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Garnier (1934) and Serrano (1934, 1952). These works were virtually ignored,
however, and it was over a decade before a next wave of interest was initiated, this
time largely by architects, i.e. La Grassa (1947), Giorgi (1947), Mohrle (1949) and
Zanetti (1951) and an opthalomologist, Graf (1949). These again had no sustained
impact. Another decade passed before the matter was taken up afresh by Barre
and Flocon (1962, 1964, 1968). This work excited more attention and was
eventually translated into German (1983), Spanish (1985) and English (1988).
During the 1970's problems of spherical perspective inspired the imagination of
American artists. Hansen (1973), who has since translated Barre and Flocon into
English, developed a five point spherical perspective, which he termed hyperbolic
linear perspective. Independently, Termes developed 4, 5 and 6 point spherical
perspective methods (fig.**). Turner (1976) and Casas (1983) developed
alternative methods to accommodate the complexities of visual perception. An
exhibition by Marcia Clark (1988) attested that a number of artists, notably
Jacqueline Lima, have been developing their own empirical methods. At the same
time there have been developments elsewhere. In Buenos Aires, Reggini
(e.g.1973) has written a number of articles on the problem. In London, Shaw
(1977) has devoted an important thesis to spherical perspective. In Paris, Blotti
(1986, 1987) has created a series of demonstrations including spherical and other
alternative projection methods for the Musée des sciences et de l'industrie de la
Villette. There have also been books by Elias (1973), Fuentes Alonso (1975), and
Bonbon (1983). Indeed, these interests are leading to new links between objective
and subjective elements (see below pp. ** ).
TECHNICAL APPLICATIONS
Various methods of parallel perspective were developed for military purposes and
different types of technical drawing (e.g. geometrical, linear, machine, etc., cf. 1.4
below). These methods included cavalier and military perspective, orthogonal or
parallel perspective, cabinet perspective, axonometric perspective with its three
branches, isometric, dimetric and trimetric, and multiview perspective. Because a
number of these distinctions only emerged in the twentieth century, historical
discussion thereof must be approximate.
Cavalier and Military Perspective
Today, cavalier perspective is defined as a dimetric projection and distinguished
from military perspective, which can be either dimetric or trimetric (cf. above, p.
and fig.
). In the sixteenth century, these distinctions were not made. Military
perspective was an ambiguous term. On the one hand, it could refer loosely to
presentation drawings designed to impress patrons by artist engineers such as
Francesco di Giorgio Martini and Leonardo da Vinci. This led to commemorative
paintings of battles such as those of Giorgio Vasari in the Palazzo Vecchio, books
with elaborate military drawings, such as Perret (1601, 1602) and a tradition of
military examples in regular treatises on perspective such as Androuet Du Cerceau
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(1576), Marolois (1614) and Dubreuil (1642-1649). On the other hand, it also
referred to simplified methods adapted for military purposes, as outlined by
Cataneo (1567), or Specklin (fig. 58.4, 1589). At the turn of the seventeenth
century, Romano (1595), Hulsius (fig. 58.1, 1605), and Faulhaber (1610) adapted
the perspectival window for these purposes. But in the heat of a battle there was
frequently not time for even these methods. As a result, practitioners developed
rough and ready methods of parallel perspective, technically inaccurate, yet
sufficient to convey essential information concerning a site.45
It was particularly in France that these new methods evolved, heralded by practical
theorists such as Hérigone (1634, 1642). Bourdin (1635), was the first to devote a
published treatise to this new kind of military perspective and the Jesuit, Dubreuil
soon incorporated it as an appendix to the second edition of his influential
Practical perspective (1663). The following year analogous methods were outlined
by Luders (1664). In the mid eighteenth century, Dupain de Montesson, wrote a
basic treatise which related military perspective directly to professional surveying
and drawing techniques (1750, 1760, 1712, 1790, 1799, etc.), followed by The art
of drawing up plans (1763, 1792, 1804, 1811) and a text for officers (1774). Other
treatises were by Dupuis (1773), Keller (1856) and Philibert (1898).
The nineteenth century brought a number of works which related cavalier
perspective to axonometric and isometric perspective, including Adhémar (1852,
1866, 1875), an anonymous author (1867), which have continued in our century
with Corsanego Wauters-Horcasitas (1926), Labalette (1927), Bonet Minguet
(1944), Gomes de los Reyes and Cano de la Torre (1966) and Alonso Misol
(19__). Breithof (1881, 1905), in his treatise on cavalier perspective, compared the
advantages of linear perspective to those of orthogonal projection methods.
Authors who wrote specifically on cavalier perspective included Ciani (1900,
1903), Darcheville (1914), Carreras Soto (1943), Breton (1970) and Garcia
Gutierrez (1970).
Orthographic Perspective
The evidence of the early treatises suggests that orthographic or parallel
perspective began less as an alternative, and more as a complementary method to
linear perspective, particularly in the case of complex organic objects for which a
simple ground plan and elevation did not suffice. Piero della Francesca (c. 1480)
and Leonardo da Vinci (e.g.W 12605r, c.1490-1492) used it in their
representations of human heads. Gauricus (1504) used a variant. These principles
were adapted by Dürer (fig. 68.1, 1525) and further standardized by Barbaro, (fig.
68.2, 1568). These principles were then extended to the entire human body by
Cousin, le jeune (fig. 70.3, 1595, etc.) and Carlo Urbino (fig. 70.5,c.1580).
However, it was not until the mid-eighteenth century that thinkers in London
began to describe orthographic perspective as an independent method. Emerson
(1749, 1769), for instance, consciously compared orthographic, stereographic and
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gnomonic projections. Walker (1777) wrote one of the earliest treatises devoted
specifically to this method. In the mid-nineteenth century, Binns (1857, 1961,
1863, etc.), produced a standard textbook on orthogonal perspective which went
through thirteen editions by 1899. Other authors included Bradley (1861, 1862),
Davidson (1868, 1873), Plunkett (1885) and Carroll (1888). In Germany, there
were some works on orthographic perspective, e.g. Gerke (1881), Kröger (1911),
cf. Fliesen (1877, 1880), Reutter (1948); as was later the case in Italy, with authors
such as Monti (1900), Magri Tilli (1967), Mondino (1968) and Bartoli (1975).
In France these problems were usually classified under descriptive geometry (cf.
fig.
) and drawing (dessin). In the United States, works entitled orthographic
perspective were also the exception, e.g. Church (1911) or Ashley (1975), the topic
usually being dealt with in various types of drawing books: geometrical, industrial,
linear, machine, mechanical, etc.
Parallel Perspective
Raverta (1627), was probably the first to refer to parallel lines in connection with
perspective in the title of a treatise. Even so, it was not until the mid-nineteenth
century that German publications in Czechoslovakia referred specifically to
parallel-perspective, e.g. Schnedar (1856, 1864) and Skuhersky (1958). The term
soon spread to Austria with Klamminger (1865) and Barzala (1882) and Germany,
where it was used by a number of authors including Müller (1865), Koutny (1867),
Delabar (1870, 1888, 1893, 1907), Hauck (1888), Freyberger (1897, 1899, 1903),
Hertzer (1902), Papperitz (1906), Vonderlinn (1920), Brunschwiler (1939), MayerSidd (1940) and Schumacher (1951). In the United States, there were some
publications under this title by Noble (1886), Cooper (1900), Adler (1912) and
Koller (1940). Elsewhere there were works by Werner (1904, 1908, 1915, 1923,
1930, 1935) and Lagerquist (1963) in Sweden; Ridderhof (1913, 1918, 1925) and
Keulen (1957) in the Netherlands, and Kirchmayr (1935) in Italy.
Axonometric Perspective
Awareness that parallel perspective might be further divided began in the
eighteenth century with preliminary distinctions between parallel, and military or
cavalier perspective. The nineteenth century gradually brought formal distinctions.
For instance, the term axonometric perspective made one of its earliest
appearances in a bilingual title of a work by Engel (1854) in Berlin. Other German
authors soon took up the term including Meyer (1855-1863), Weisbach (1857),
Largiader (1858), Schmidt (1859), Hertel (1862), Weishaupt (1863), Sellar (1865),
Butz (1870), Pelz (1870) and Beyel (1887). This trend has continued in our
century with Vonderlinn (1905, 1920) who distinguished between right-angled (i.e.
isometric) and oblique (dimetric, trimetric) axonometry; Schüssler (1905),
Papperitz (1906, 1916), Haase (1907), Meyer (1922), Pechwitz (1950), Berns
(1962, 1968) and Thomae (1976).
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Use of the term was by no means restricted to Germany. It soon spread to Italy
with Sella (1861), where there have been works since by Capelli (1905),
Tomasinni (1943), Roversi (1945, 1948, 1949, 1952, 1954), Calloni (1948), and
Aterini (1980). It reached England through an article in the Athenaeum (1865). In
the next decades it spread to Sweden with Bergh (1872), the Netherlands with
Versluys (188*) and later Thiel (1913) and Reynders (1951), as well as Denmark
with Seidelin (1890) and Gjerding (1967), and Spain with an anonymous author
(1867), Valenzuela (1896), Corsanego Wauters-Horcasitas (1926), Bonet Minguet
(1944) and Garcia Gutierrez (1979). In the twentieth century, there have been
further authors in Poland, Plamitzer (1925), Piotrowski (1956), Lange (1962) and
Lewandowski (1973); the United States, e.g. Roever (1941) and Bartholemew
(1944); Finland, Nystrom (1943) and Kivela (1979) and Portugal, e.g. Aires de
Silva (1945).
In addition to these texts where axonometric perspective was specifically
mentioned in the title, there were numerous other works on drawing, architecture
and mathematics which dealt with these problems. Axonometric perspective was,
in turn, subdivided into three branches: isometric, dimetric and trimetric
perspective (cf. above p.
and fig. ). In Britain, during the Second World War
special templates were used to produce these variants. While all three branches
were discussed in books, only the first of these, namely, isometrical perspective
inspired an independent literature.
Isometrical Perspective
The term isometrical perspective emerged some three decades before axonometric
perspective, which was subsequently to become the more universal term.
Isometrical perspective was developed as a formal method by Farish (1821, 1923)
as a means of best conveying information about models of the more important
machines used by British manufacturers at the time.46 In the decade that followed
his ideas were spread by Bradley (1831), Jopling (1833, 1834, 1835, 1839, 1842)
and Sopwith (1834, 1836, 1838), and were subsequently taken up by other English
authors, including Heather (1851), who related isometrical perspective to Monge's
descriptive geometry, Burn (1853, 1855), Atkinson (1860), Binns (1864),
Davidson (1868, 1873), Spriggs (1871), Spanton (1895), Middleton (1919), who
applied it to architecture and Parkinson (1953). Through the Oxford press, there
was also a work by Dean (1933) in Australia. In Europe, isometrical perspective
made no dramatic impact as an independent topic. Nonetheless, there were authors
such as Möllinger (1840) in Switzerland; Adhémar (1852, 1866, 1875), Car‚nou
(1880) and Labalette (1927) in France; an anonymous author (1867) in Spain;
Versluys (188_) in the Netherlands, as well as Schmidt (1888), Grimshaw (1902)
and Vogel (1902) in Germany.
In the United States, by contrast, isometrical perspective inspired more interest
than anywhere else. At the outset this was sparked by authors concerned with
drawing, notably, Minifie (1849, 1851, 1855, 1857, 1868, 1873, 1875, 1877, 1882,
125
1890), Appleton (1857, 1862, 1864, 1866, 1869), Beard (1858) and subsequently
Klein (1869), Palmer (1894), Jamison (1911), Jameson (1932) and Locke (1981).
But as early as 1860 Warren sought to put this discussion in a wider mathematical
context as suggested by his title: General problems from the orthographic
projections of geometry with their applications to oblique - including isometrical projections, graphical constructions in spherical trigonometry, topographical
projection and graphic transformation. The relationship between descriptive
geometry and isometrical perspective was next considered in an influential work
by Church (1864, 1865, 1867, 1868, 1870, 1875, 1877,1892, 1911), and later by
Randall (1905) and Bartlett (1911). Others, such as Comfort (1874), were content
to discuss its connections with projections generally, while Richards (1903), was
concerned merely with showing that this branch was the only practical perspective.
Multiview Projection
Axonometric perspective, and its branches (isometric, dimetric and trimetric),
assumed that the objects considered were in some way oblique or tilted in relation
to the picture plane. In multiview projection it was assumed that the face(s) of the
objects were parallel to the picture plane. In Britain, these methods were typically
discussed in works on practical geometry or machine drawing, such as Abbott
(1930). In the United States, by contrast, these problems were usually considered
in works on machine drawing, solid geometry or more general works on drawing
or architectural drafting such as Weidhaas (1981). The solutions reached also
differed widely. In Britain a preference evolved for first angle projection (fig. ),
which could be seen as almost a direct development of the picture plane tradition
(figs. 30-31), or Pozzo's methods in architecture (fig. 45.1-2), i.e., a looking out at
projections on planes beyond the object. This method of first angle projection was
accepted as a standard by the British Standards Institution in 1927 (Report No.
308). Meanwhile, American texts favoured third-angle-projection, i.e., a method of
looking in at the projections of an object as if encased in a transparent plane (fig.**
). Although this so called glass box method was in common use by the First World
War, it was not accepted as a standard until 1935.
Special Effects
Already in the fifteenth century, thinkers recognized that linear perspective alone
could not achieve all the spatial effects of three-dimensional objects. Hence,
Leonardo da Vinci, explored the role of colour perspective, aerial perspective and
what he termed disappearance of form perspective. He also noted the importance
of shading in creating contours and saw these effects of chiaroscuro or relief
(relievo) as an extension of perspective. This later emerged as an independent
topic of shades and shadows. In addition, Leonardo recognized that motion
perspective was also important. Since most of these categories have developed an
independent literature, each will be considered in turn.
126
Colour Perspective
In his Optics, Ptolemy (c. 150) referred briefly to an empirical use of colour by
Roman artists in representing effects of distance.47 During the Renaissance,
Fontana was the first to explore these principles in his now lost treatise, of which
we have only a description by Pompilius Azalus:
From this natural experience, pictorial art took its optical rules as was described
clearly in a book dedicated to Jacopo Bellini, the famous Venetian painter, and by
which means he knew how to oppose dark and bright colours such that, by means
of ratios, not only the raised parts of an image were seen depicted on a plane, but
actually seemed to be seen extending beyond the hand or foot. And those things
which were in the same plane of men, animals or mountains, by these means
appeared to be distant by miles and so on. Indeed, the art of painting teaches that
nearby objects should be tinged with bright colours, remote ones with dark
colours, and medium range distances with mixed colours.48
In the period 1480-1518, Leonardo da Vinci explored the principles of colour
perspective in his notebooks. Curiously enough, this theme was not taken up in
published treatises during the sixteenth century. Zaccolini (c. 1600), who may have
drawn on now lost works of Leonardo, devoted two manuscripts to problems of
colour perspective.49 Accolti (1625), was one of the first to mention colour
perspective in a published treatise. Even so, it was not until the turn of the
nineteenth century that colour emerged as an independent category as indicated,
for instance, in the title John Wood's (1799, 1801) treatise Elements of perspective,
containing the nature and light of colours, or simply found in a chapter of Cloquet
(1823).
Awareness of colour perspective went hand in hand with a growing attention to
shades and shadows (cf. below p. ), as witnessed by Schrank (1812), Hummel
(1830, 1842) and Delabar (1875), as well as colour itself by authors, such as Le
Blon (172_, 1756, 1916), Schreiber (1868) and Bracquemond (1885), which led to
a gradual distinction between coloured lights of optics and coloured pigments of
painting. Since then Scharf (1949) has written on tensions between colour
stereoscopy in vision and effects of drawing in linear perspective.
Authors who have written specifically on colour perspective include Roux de
Valdonne (1898), Adam Leonard (1905) and Cloquet (1913). The last decades
have also seen at least one important work in Russia, namely, Aksenov (1976), and
increasing interest in the Far East as witnessed by Ota (1968), Yamasiro (1975)
and Takahasi (1977) in Tokyo, as well as Wang (1977) in Hong Kong.
Aerial Perspective
Leonardo da Vinci (fl. 1480-1519), was one of the first to discuss aerial
perspective at length. Even so, it was not until the latter eighteenth century, that
127
this topic emerged as an independent category through the publications of Lambert
(1776), Saint Morien (1779, 1788) and Casanova (1794). In the first half of the
nineteenth century authors frequently referred to linear and aerial perspective in
tandem in their titles, as with Valenciennes (1803), Clinchamp (1820, 1840),
Vallée (1821, 1838), Isabeau (1827, 1832), Kercado-Molac (1932), Fielding
(1836-1843), Laurent (1840) or Howard (1840, 1876) who reversed their order.
Bayliss (1855) wrote more specifically on The elements of aerial perspective or
light, shade and colour. Sutter (1858, 1870) wrote on the Philosophy of the fine
arts applied to painting containing the aesthetics of aerial perspective. An author
known only by the initials R.B. (1916) wrote on aerial perspective in relation to
photography. Cole (1920) devoted a section of his textbook to the subject, while
Baier (1955) wrote an entire book on it. Meanwhile the precise meaning of the
term varied considerably as becomes clear when one compares various definitions
given by authors of treatises. Brunel de Varennes (1830), for instance, claimed
tersely: “We divide perspective into two principal sections. The first is linear
perspective, the second is aerial perspective, in which are included, the theory of
shadows, that of reflections, and the reflection of objects in water and on polished
surfaces.”50
Vergnaud (1835), in his Manual of perspective, provided a more detailed and
poetic distinction between linear and aerial perspective:
Perspective has as its goal to represent on one and the same surface the
whole and details of objects which nature spreads at unequal distances on
surfaces infinitely varied. To attain this end, there are two distinct parts in
perspective. One needs to determine the apparent contours of objects and
their respective positions on the surfaces where they are located. The other
needs to take the actual colour of these objects, with all the modifications
brought upon it by both the accidents of light and the more or less thick
layers of atmospheric air which separate them from one another. The first
is a positivistic science, where one is rigorously guided by the simplest
principles of geometry. This is linear perspective, without which one
cannot be an adept at drawing. The second, which would at first sight
appear to be obtained by a no less rigourous means, with the aid of
geometry and physics, is aerial perspective, without which one cannot be a
painter. But one should not hope to attain the magic of colours or the
sublime, unless one is endowed by that warmth of imagination, sparks of
the sacred fire without which the true artist cannot exist. In a word, one
can, with the help of linear perspective, produce fine statues, the forms of
which are pure and pleasant, but for which aerial perspective will never
cease to be the creative breath of Prometheus.51
Brisson (1838) in his Theory of shadows and perspective which served as an
appendix to Monge's Descriptive geometry saw this distinction in more clear cut
ways:
128
As in the theory of shadows, one has to admit two distinct parts. The one is
purely geometrical and its object is to determine in a precise manner on the
canvas the position of each point that is represented. The other has as its
object a study of the tint of the shadow and light which one needs to give to
each part of the canvas, and it is by means of physical considerations that
one can deal with it in general. This latter part, which one designates under
the name of aerial perspective, enters wholly into the circle of studies,
which we shall attempt to expose later to complete the theory of shadows.
Hence we shall occupy ourselves here only with the first part, called, linear
perspective.52
Jules de la Gournerie (1859), by contrast, associated aerial perspective with colour,
and as something dispensable “Perspective is the art of representing objects on a
canvas while maintaining their appearance. It is either linear or aerial depending
on whether it deals with forms or coloration. In this work there will no question of
aerial perspective.”53 Just over a decade later, the Larousse encyclopaedia, in an
article on drawing, cited the views of Delacroix on the subject (see below p. ),
which attributed to aerial perspective a more fundamental importance. Brücke
(1878) was of a similar view, but for different reasons, when he devoted a chapter
of his Scientific principles of the fine arts to "Aerial perspective and the apparent
size of objects,"54 his main concern being to relate it to problems of steroscopic
vision. The Dictionary of pedagogy (1883) was, nonetheless, able to provide a
simple distinction: “Linear perspective studies the reproduction of contours of
objects. Aerial perspective is concerned more specifically with the modifications
that the layers of air interposed between objects and the eye of the spectator brings
to shadows and tints.”55
Delaistre (1897), writing at the end of the century, was closer to La Gournerie's
view that the distinction was between line and colour, although he decided that
both should be dealt with:
Perspective, considered as a whole is the science, art of representing
objects onto a surface in accordance with their optical effects, that is, in
accordance with the laws of vision and of light, which means that one
divides it into two classes. The one is what one calls linear, the other is
what one calls aerial. Linear perspective is made by lines alone. Aerial
perspective is made by the degradation of colours resulting from the greater
distance of the light, as well as from the greater distance of the objects, as
well as the greater or lesser intensity of the vapours which interpose
themselves between the eye of the spectator and these same objects.56
Chiaroscuro
Alberti mentioned colour perspective in his treatise, On painting, but concluded
that the highest goal of art lies in knowing how to use black and white, because
light and shade make things appear in relief.57 Piero della Francesca's definition
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of colour also referred to effects of chiaroscuro: "By colour we mean giving
colours as they are shown in things, bright (chiari) and dark (oscuri) as the lights
make them vary."58 Leonardo da Vinci pursued problems of chiaroscuro and
relief, which he saw as an extension of perspective.59
Again, it was not until the end of the eighteenth century that this emerged as an
independent category with Breysig's (1798) attempt to explain relief perspective.
In the nineteenth century, the term, relief perspective, was more popular than
chiaroscuro, and works were often addressed to a specific discipline: Amati (1840)
and Berti (1841) to architecture, Burnet (1827, 1828, 1830) to painting; Noelli
(1917) to sculpture, Poudra (1862) to theatre. More frequently, they were
addressed to mathematics as with Anger (1834, 1836, 1840), Morstadt (1867),
Tessari (1880, 1883), Vecchi (1891), Becchetti (1894, 1900) and Loria (1924).
There were also a number of more general works, frequently with a mathematical
slant, by Poudra (1860, 1866), Staudigl (1868), Burmester (1883), Cloquet (1913,
1934), Stuhlmann (1914), Berger (1944) and Steen de Jehay (1964, 1965, 1966).
Shades and Shadows
Although shades and shadows is listed as one of the offical subjects in the Library
of Congress classification, its precise meaning is elusive indeed. One reason was
etymological. Renaissance thinkers sometimes thought sciographia was
synonymous with scaenographia with the result that shadows and perspective
were sometimes treated as if they were interchangeable as in Piranesi's (178_)
Sciographia of four old temples, or Puckett's (1808) Sciography or radial
projection of shadows. Notwithstanding this tradition, systematic treatment of
shadow in treatises on perspective evolved only gradually. Alberti (1434)
mentioned shadows,60 but did not explore them. Leonardo da Vinci explored them
in his Manuscript C (c. 1490), in a lost treatise on light and shade, and elsewhere.
Dürer (1525) was the first to publish rough principles of shadow projection (fig.
46.1), which were taken up by Barbaro (1568) and Danti (1583) and thereafter
became a stock theme in treatises on perspective.61 By the mid-seventeenth
century the study of perspectival shadow included attention to objects in a room, as
for example, in Dubreuil (fig. 46.3 1642-1649). These examples became
increasingly subtle as seen in Huret (fig. 46.4, 1670), and by the early nineteenth
century included veritable tour de force cases, as in Cloquet (fig. 47.3-4), which
uncannily prefigures pointilist techniques by half a century. Meanwhile,
corresponding attention was being given to complex arrangements of individual
objects as seen in Highmore (fig. 46.2, 1764), or Cloquet (fig. 47.1, 1983), who
was at pains to correlate the geometry of individual objects with views showing
context. In the next generation, Gennerich (fig. 47.2, 1865), included penumbral
effects.
While almost every treatise on perspective from the latter sixteenth century
onwards included a brief chapter or section on shadows, more detailed studies
emerged on at least three fronts. First, there were a number of treatises which made
130
direct reference to the importance of shadows in their titles. Second, there were
some books dedicated specifically to this theme. Third, there were a series of other
books on shades and shadows which arose in the contexts of architecture, drawing
and geometry. Each of these will be considered briefly.
Salomon de Caus' (1612), Perspective with an explanation of shadows and
mirrors, was among the first treatises to mention shadows and mirrors in its title.
In the eighteenth century, Hamilton (1738) pursued these themes in his Compleat
body of perspective together with their projections on shadows and the reflections
by polished surfaces, and it was developed in Clinchamp's (1826) New theory of
perspective of shadows and theory of reflections for the use of artists. Thereafter,
the twin themes of perspectival shadows and reflections were taken up by a series
of authors, including Berg (1854), Smith (1857), Heyn (1885), Charles (188 ),
Kleiber (1892), Crosskey (1901), Petty (1901), Fuchs (1902), Beuhne (1907),
Swinstead (1907), Tagliavini (1910), Masriera (1912), Arjona Lechuga (1918) and
Bonbon (1986).
More frequently, authors referred only to linear perspective and shadows in their
titles, as in Ozanam's (1686) Theoretical and practical perspective and how to
represent the shadows caused by the sun or a small light or Curel (1768). The
nineteenth century saw a dramatic rise in such works including Richard (1828),
Davies (1832) Treatise on shades, shadows and linear perspective, Francke (1836),
Barnes (1842), Hummel (1842), Kempees (1846), Menzel (1849), Leve (1858),
Warren (1863), Fliesen (1877) and Neel (1879). The 1880's brought at least seven
new authors on this topic including Nielsen (1884), Böklen (1886), Chizzoni
(1886), Lebon (1887), Hauck (1888), Gut (1888) and Kajetan (1888). The 1890's
brought four new authors, Hill (1894), Freyberger (1897), Sparton (1898) and
Willson (1898). In the first decade of the twentieth century, interest in this topic
reached a peak with no less than eight further authors including Hertzer (1902),
Johnson (1902), Lafarga (1902), Fernandez Casanova (1907), Haase (1907),
Heubach (1908), Hauck (1910) and Spink et al. (1910). Thereafter interest faded
temporarily.
Since the 1930's there have been a series of further works by Giombini (1934),
Erremes (1934), Brunschwiler (1939), Kirchmayr (1945), Pasman (1947), Pinheiro
(1948), Holmes (1950), Nordlindh (1950), Parrens (1961), Boccaleone (1963),
Geiger (1965), Fradin (1966, etc.), Carreras Soto (1967), Folina (1975) and
Mondino (1976). While most authors have emphasized the relation of perspective
to shades and shadows, some have discussed the problem in terms of lighting as,
for instance, Schwedler (1852) in Practical introduction to making a perspective
drawing and lighting of same; Rohn and Papperitz (1906) in Axonometry,
perspective, lighting or Vries de Hecklingen (1907) in Teaching of projection and
lighting.
The earliest manuscripts specifically on light and shade in connection with
perspective were probably Leonardo da Vinci's (1490) Manuscript C and his now
131
lost treatise. Theriaci's (1551) Discourse and explanation of shadows, may well
have been the first published work on the subject. The seventeenth century brought
several more works including a manuscript by Zaccolini (c.1600) On the
description of shadows produced by rectilinear opaque bodies; an optical text by
Maurolico (1612), often classed as perspective; Albrecht (1622) etc. who devoted
the second of his two treatises on perspective specifically to shadows; Kircher's
(1646, etc.), Great art of light and shade, an encyclopaedic tome which dealt with
gnomonics, surveying and optics as well as perspective and shadows. The
eighteenth century added at least one interesting title: Philip Jacobszoon's (1785)
Scientific, mathematical and perspectival introduction to the placing of the sun
and moon in a picture in order to determine their cast shadows.
The nineteenth century saw more than a dozen works devoted specifically to
perspective and shadows including Marconi (1812) On the theory of shading,
Schrank (1812), Muhlert (1821), who set out to determine shadows following
optical principles; Similien (1842), Hinckley (1851), Fournet (1859) with
Researches into coloured shadows which manifest themselves at different seasons
and on the application of the phenomenon, Rätz (1864), Schreiber (1868), Delabar
(1871), Seeberger (1876), Landriani (1879), Steindorff (1884) and Cabuzel (1887).
Such works have continued in the twentieth century with Weishaupt (1901),
Vonderlinn (1904), Jaulin (1909), Luckiesh (1916), Arola y Sala (1921), Opitz
(1926), Gromort (1932) and Grondona (1932) with a Treatise on the theory of
shadows and more recently Bärtschi (1978). This interest has also spread to the
Far East with Jin's (1959) Research on shadows in perspective and a work by the
association, Tong-ji-da-xue-gong-cheng-h (1961), on Shadows and perspective.
Shades and shadows have played an important role in architecture from the outset
as, for instance, in the method of representing cross-sections of buildings attributed
to Brunelleschi (fig. 84.3), and particularly in connection with the five orders of
columns (figs. 44-45) as evidenced by an early compilation of engravings by
Veneziano, Serlio, Prevost and Flötner (c. 1540), or the classic treatises by Blum
(1550 etc.), Barozzi, il Vignola (1583, etc.) and Hondius (1617, 1620, etc.) On the
five orders of architecture with some fine architectural designs rendered in
perspective invented by Jan Vredeman de Vries and his son Paul.
The latter seventeenth century saw new examples of shades and shadows in
Bosse's (1664), On the orders of columns in architecture, and Huret's (1678) New
treatise on architecture, as well as adaptations of earlier works, such as Erasmus'
(1682) version of Blum and Bosboom's (1686) edition of Scamozzi. The latter
eighteenth century brought treatises on shades and shadows intended as a direct
complement to Vignola, including Spampani and Antonini (1770), Lagardette
(1797, etc.), Heidelhoff (1834, c. 1851, 1859, 1888, 1812), Bourgeois (1838) and
Rebout (1845). It also brought direct additions to Vignola's work such as
Elementary lessons of shadows in architecture demonstrated by principles taken
from nature. (e.g. 1786, cf. 1792, 1823, 1902, 1905, 1910, 1912, 1923, 1940).
132
Meanwhile, Nicholson, who also wrote a new work on the five orders of columns
(1795, 1804, 184_), published a more general work (1795, etc.) on Principle of
architecture containing...the true method of drawing the ichnography and
orthography of objects; geometrical rules for shadows. In the nineteenth century
such books, which applied perspective and shadows to architecture generally
emerged as an independent genre, with authors such as Rossi Melocchi (1805),
Heidelhoff (1888), Watelet (1896) and Planat (1899). Some books were addressed
specifically to students at schools of architecture, e.g. L'Eveille (1812), Ribbans
(1843), Pillet (1888) and Lawrence (1893).
The nineteenth and twentieth centuries saw a development in two opposite
directions. On the one hand, there were ever more specialized works (cf. fig. ),
such as Beuhne's (1907) Textbook of linear perspective with construction of
shadows and reflections and application to drawing of furniture and interiors or
Gründling, who wrote on descriptive geometry, projection and the perspective of
shadows specifically for masons (1912), and a similar work specifically for
carpenters (1912). On the other hand there was a trend towards more universal
books such as Burg (1830) or Robinet (1855), which combined architectural and
machine drawing. Tessari (1880) took this approach further, when he made his
theory of shadows and chiaroscuro volume one of his applications of descriptive
geometry "for the use of engineers, architects and designers."62 In the twentieth
century works on shades and shadows officially addressed to architects, have
frequently assumed applications to engineering and other disciplines, as in
McGoodwin (1904), Ware (1912), Holmes (1929), Buck (1930), Shelton (1931)
Vriend and Arendzen (1934), Morgan (1950), Turner (1952), Doria (1958),
Mandino (1962), Parrens (1962), Fradin (1966), Carter (1967), Klimukhin (1967),
Hasegawa (1977), and Vroman (1978, 1983).
One of the earliest drawing books which dealt with perspective and shadows, was
produced for the military: Bouchotte's (1721, 1743, 1754, 1755) Rules of drawing
and wash drawing. This connection with water-colours, or wash drawing,
continued in the nineteenth century with Tripon (1848), Armengaud (1849),
Delaistre (1855), and Pillet (1875), who produced a Theory of shadows and wash
drawings. From the mid-eighteenth century onwards, there was increasing
emphasis on the scientific dimensions of drawing. Seminal in this respect were
Dupain de Montesson's (1750, etc.) Science of shadows with respect to drawing
and Vallée's (1821) Treatise of the science of drawing, containing a general theory
of shadows, linear and aerial perspective.
As in the case of architectural books, drawing books on shades and
shadows also went in two directions. On the one hand, there was greater
specialization as shades and shadows became associated with different kinds of
drawing, such as construction drawing, e.g. Arbesser (1824), Muller (1865); linear
drawing, Laurent (1827), Burg (1845), Edelmann (1871), Anonymous (1875),
Segerborg (1896, etc.); machine drawing, Astolfi (1824) and technical drawing,
133
Dietzel (1864), Bretagne (1967). On the other hand, there was a growing
conviction that the laws of drawing were universally applicable as with Ryan
(1860), Pereda y Lopez (1866), Davidson (1868, etc..), Ryan (1869), Krüsi (1876,
etc.), Spanton (1896), or Curtis (1909), who entitled his work, Elements of
graphics, orthogonal projections, shades, shadows and perspective.
The conviction that the principles governing perspectival shades and shadows were
indeed universal owed much to connections with mathematics. It is noteworthy
that Desargues, among the first to establish the mathematical laws of perspective,
was also the author of a now lost Lessons on shadows (163_). In the eighteenth
century Murdoch (1746) explored the origins of curves by means of shadows.
Dupuis (1793) wrote a Memoir on the geometrical determination of tints in
drawings. In the early nineteenth century Bordoni (1815) wrote On the
geometrical determination of shadows and (1816) On the contours of ordinary
shadows. His contemporary, Magistrini (1816) described An easy and universal
delineation of geometry of shadows which round objects undergo. As the
nineteenth century progressed, a branch of geometrical drawing evolved with Burg
(1845), Minifie (1849), Schmidt (1863), Rheims (1865) and Spriggs (1871). This
has continued in our century as witnessed in a work by Xu (1979).
Meanwhile, even closer connections developed between descriptive geometry,
perspective and shadows. One of the first studies by the father of descriptive
geometry, Monge, was concerned also with shadows (1780): Memoir on properties
of several kinds of curved surfaces, particularly those of surfaces which can be
developed with a theory of shadows and penumbra. He also wrote (1785) On
shadows. By the 1820's, thinkers such as Harchette (1822), Ohm (1826) and
Schreiber (1828) saw shades and shadows as applications of descriptive geometry.
Important in this connection was Brisson's (1827) Theory of shadows and
perspective, which was added as an appendix to the fifth edition of Monge's
Descriptive geometry. A series of such works followed including Sevastianov
(1830), Wolff (1835-1840), Leroy (1844, etc.), Pasi (1844), Bielsa (1846), as well
as Olivier and Terte (1847). Fialkowski (1851) added a new feature: Pocket
models to aid the study of descriptive geometry with the help of shadow
construction and perspective. Bardin (1855) also advocated the use of models.
In the latter half of the nineteenth century, the application of descriptive geometry
to perspective and shades and shadows became a regular feature in textbooks by at
least fifteen authors including Nigris (1853), Bardin (1855), Schnedar (1856),
Heissig (1859), Hieser (1861), Church (1864, etc.), Alix (1867), Cardona y
Escarrabil (1869), Butz (1870), Riess (1871), Tessari (1880), Gerke (1881),
Warren (1884) and Schmehl (1894). These connections have continued in the
twentieth century with further works by Bernhard (1901, etc..), Randall (1902),
Alonso Misol (1911), Ranelletti (1921), Loria (1924), Roversi (1945), Mondino
(1962), Soto Hidalgo (1967), Gaman (1976).
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Motion Perspective
In his notebooks, Leonardo da Vinci also explored the effects of motion on
perspective. Some of these ideas were published in his Treatise on painting (1651,
etc.). Even so these problems were largely ignored until the development of
cinema in the latter nineteenth century which led to works such as Mannheim's
(1880) Course of descriptive geometry of the Ecole polytechnique including the
elements of cinematic geometry. One of the first works devoted specifically to
these problems was Nico's (1920), Theory of perspective in relation to movement
in space. Pizzigoni (1951) produced an illustrated perspective book "for painters,
architects, scenographers and cinematographers." In terms of technical drawing
there has been Krames (1952) Descriptive and kinematic geometry for machinists.
At a theoretical level Gibson (1979)63 has emphasized the significance of motion
perspective, but as yet there has been no satisfactory text in this domain.
8.Conclusions
Our survey of the contents of treatises on perspective points to some important
trends. Already in Antiquity, authors such as Ptolemy, noted that distance affected
the optical vision of lines, colour, the air and even the clarity of form of objects.
Early fifteenth century thinkers working in the optical tradition were fully aware
that distance also affected the perspectival representation of these same
characteristics. Indeed Fontana, in his now lost treatise set out to explore aerial and
colour perspective. But he was an exception. The Florentine ideal of creating
effects of depth through chiaroscuro reduced colour problems to black and white
questions of linear forms and, as a result, fifteenth century treatises were limited to
geometrical themes such as the two chief methods, and regular solids, as well as
aspects of human form, notably the head, which could readily be reduced to
geometrical regularity. It is no accident, therefore, that we associate the
Renaissance with linear perspective.
Other branches, such as colour perspective, aerial perspective and diminution of
form perspective were systematically excluded. Thinkers such as Leonardo (fl.
1490-1515) and Accolti (1625) made serious efforts to re-introduce them, but to no
avail. To this day, standard works such as Cole (1920) or Abbott (1950) effectively
limit themselves to perspective of lines.
Implicit in this approach was a new emphasis on instruments in the process of
representation (see below 2.1). Alberti was convinced that perspective required
the use of a window to be carried out properly. Piero's methods assumed at least a
ruler and compass. Francesco di Giorgio Martini used strings to demonstrate the
distance point. Leonardo considered all these possibilities. In short the fifteenth
century authors lay the foundations of what is now termed construction drawing
(see fig.
cf. pp.
). The Nürnberg practitioners of the sixteenth century made
explicit and codified this instrumental approach such that, by the end of the
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century, Pfintzing (fig. 54.2, 4-5) served almost as a catalogue of available
devices.
In terms of contents, German treatises of the sixteenth century added a
considerable number of semi-regular solids and related shapes to the repertoire of
available forms, including the entire human form. But the scope was limited
almost entirely to geometrical themes. This continued to be the case. For as we
showed in our chapter on the various centres, many German cities, notably Berlin,
Leipzig, Stuttgart, Darmstadt and Braunschweig published almost exclusively
technical and mathematical works on perspective. Indeed, it is significant that in
one of the basic catalogues of drawing books (1888) perspective was classified
simply as a branch of construction drawing (fig. cf. pp. ), as if it had nothing to
do with freehand drawing, colour, air and many other effects.
Meanwhile, architectural themes in perspective emerged largely in Italy, the
Netherlands and France, in the context of Vitruvian commentaries and Serlio's
works on architecture. Almost from the outset, some of these themes, including
perspectival ruins, columns, and idealized buildings tended to become independent
genres of literature. Cousin (1560) in France, and Barbaro (1568, etc.) in Italy,
integrated geometrical and architectural themes to produce a new type of
perspective treatise which has served as a model ever since. The seventeenth
century added many new examples of geometrical and architectural forms. The
eighteenth century, particularly in England, added new architectural themes such
as towns, gardens, landscapes and nature as part of regular treatises. The
nineteenth century saw these themes spread through Europe and the addition of
both historical reconstructions of buildings, as well as modern buildings. The
twentieth century added to this repertoire mainly modern buildings and views,
many in the form of photographs.
Authors were slow in considering alternative picture planes. In the fifteenth
century, it was assumed that the picture plane would be rectilinear, with objects
positioned regularly to produce one point perspective. Cases of anamorphic
distortion, although studied by Leonardo, and mentioned by Barbaro (1568) and
Danti (1583), became fashionable for a brief period in the 1630's and 1640's in
Paris with Vaulezard and the Jesuits, Nicéron and Dubreuil. Some thinkers classed
these methods independently (fig. ), but they never assumed an important role in
basic texts. Similarly, conic and cylindrical projections were considered in
isolated sixteenth century treatises, and some seventeenth century texts, but
subsequently tended to emerge as independent works, rather than becoming a
typical feature of treatises on perspective. This happened also in the case of
spherical perspective, which was considered by isolated figures in the nineteenth
century, a number of individuals in the first half of the twentieth, although only
recently inspiring more popular interest as an independent genre.
In the case of alternative projection methods there were analogous trends. During
the sixteenth and seventeenth centuries, the treatises contained rough examples of
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parallel perspective which, in retrospect, could be seen as prototypes of cavalier,
military and axonometric projection. But as thinkers defined them more precisely,
these methods tended to become independent genres of their own. For instance,
isometric perspective, once Farish had described it, was usually not added as an
additional chapter to regular treatises on perspective. Instead it became part of a
new genre of alternative literature on technical drawing, frequently appearing in
books devoted specifically to isometry. With effects such as colour, aerial
perspective, chiaroscuro and shades and shadows, the same principle obtained.
While some works did attempt to deal with linear and aerial perspective together
(see above p. ) these were the exception. Innovations were usually not integrated
within a corpus of linear perspective as a whole, and were relegated instead into
other genres of literature, such as architecture, drawing and mathematics,
particularly descriptive geometry.
This was no coincidence. It reflected a deeper problem, namely, that perspective as
a concept never obtained any serious independence of its own. In the early period,
perspective was classed as a branch of optics and linked with architecture (see
above pp. ), and traces of this heritage have remained to the present. In addition,
perspective also became classed under two other headings, drawing and
mathematics. Hence the process outlined in this chapter, how optics, architecture,
drawing and mathematics, were themes within treatises on perspective is only half
the story. For it is also necessary to examine how perspective functioned as a
theme within these larger classes: to outline the effects of perspective on the
history of optics, architecture, drawing and mathematics and to sketch some
aspects of the history of classification. This will be the challenge of the next
chapter.
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4. CLASSIFICATION
1. Introduction 2. Optics 3. Architecture 4. Drawing
6. Mathematics 7. Conclusions.
5.Drawing Education.
1. Introduction
From the outset, the classification of perspective posed problems. Etymologically
it was linked with optics, which could not be classed simply. Historically it was
linked with architecture, which equally eluded simple classification. By the
nineteenth century the nature of the problem began to come into focus. Systems of
classification had forged clear distinctions between (subjective) art and (objective)
science, as well as between (theoretical) science and (practical) technology.
Perspective had the embarrassing characteristic of belonging clearly to all of these.
It belonged to art, because it created spatial effects in paintings and it was
accordingly classed under drawing. At the same time its theoretical principles
were so clearly connected with the mathematical projections underlying scientific
demonstrations, that it came to be listed under descriptive geometry. Finally, it
also involved instruments, such that it was also classed under technology. These
three headings, plus the historical one connecting it with architecture, have been
maintained in the Library of Congress classification to this day.
On the surface, this was merely a matter of semantics, a search for convenient
cubbyholes in the case of a borderline subject. There were, however, dramatic
consequences. It meant, for example, that numerous innovations pertaining to
perspective accrued to the larger categories to the extent that, when the artistic
aspects of perspective came under fire, it could reasonably appear to some that
perspective had died although the number of treatises on perspective in these other
fields continued to grow. The continued association with optics perpetuated a
confusion between subjective optical questions of how an object is seen, and
objective geometrical questions of an object's projections. The connection with
drawing meant that perspective became entangled in conflicting philosophies of
artistic education and was affected by changing fashions therein.
Ironically, the connection with mathematics, which seemed the most obvious of
all, proved to be the most perplexing. By the mid-sixteenth century
mathematicians such as Commandino had established the mathematical
foundations of perspective. These were further clarified by Guidobaldo del Monte
and Stevin, and consolidated by Desargues. In the nineteenth century, with the
development of descriptive geometry, it seemed obvious to class perspective as a
branch thereof. In the twentieth century, with the development of algebraic
geometry, this more general concept embraced both descriptive geometry and
perspective. The problem was that algebraic geometry was non-visual, which
posed a curious paradox: perspective, the chief means for visualizing space and
objects, was classed as a subset of a non-visual method. Meanwhile, where
perspective stands in relation to other branches of projection such as isometry,
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affinity and topology has become an open question. In order to gain further insight
into these problems of classification it will be useful to consider each of them in
turn.
2.Optics
Etymologically, both the term for linear perspective and for optics stemmed from
the Latin, perspectiva.1 Already in Antiquity, optics had eluded attempts at simple
classification. The ancients had partially sidestepped this problem by dealing with
its geometrical, philosophical and physical aspects separately. Aristotle had
included optics among the mixed sciences,2 which subsequently led to its being
classed among the mechanical arts by some mediaeval thinkers.3 Considered less
important than astronomy and music, optics was excluded from the quadrivium
section of the mediaeval seven liberal4 arts and yet, ironically, by the late
thirteenth century, it emerged as chief of the mathematical sciences. In the words
of Peckham, archbishop of Canterbury:
Among the investigations of physics, light is most pleasing to students of
the subject. Among the glories of mathematics it is certitude of
demonstration that most highly exalts the investigators. Therefore, optics
(perspectiva), in which demonstrations are devised through the use of
radiant lines, and in which glory is found physically, as well as
mathematically, so that optics (perspectiva) is adorned by the flowers of
both, is properly preferred to [all] the teachings of mankind.5
The Renaissance continued to class optics as a branch of mathematics. This
continued into the seventeenth century when two trends emerged: one listing
optics as merely another item in a growing list of mathematical sciences, the other
distinguishing between optical, mechanical, geographical and other sciences.
Some examples from both traditions will be needed to reveal the constantly
shifting interplay between optics and perspective. The idea of listing disciplines
grew out of the mediaeval tradition of the seven liberal arts, by means of which
optics was subsumed under geometry as one of the basic disciplines. In Gregor
Reisch's Philosophical pearl (1517), for instance, this list included: grammar,
dialectic, rhetoric, arithmetic, music, geometry, astronomy, natural philosophy,
alchemy, vegetative and sensitive soul, rational soul and moral philosophy.6 In
the works of Joachim Fortius (1531), this list was reduced to grammar, dialectic,
rhetoric, mathematics and divination, but the branches of mathematics were
correspondingly expanded to include the sphere, astronomy, cosmography, book of
time, table of time, perspective (optice) and mathematical chaos (which included
practical geometry, surveying, cosmography, astrology, meteorology and
dreams).7 John Dee's (1570) list, in his mathematical preface, included optics,
amidst a number of more exotic branches: "perspective [i.e. optics], astronomie,
musike, cosmographie, astrologie, statike, anthropographie, trochilike,
helicosophie, pneumatithmie, menadrie, hypogeiodie, hydragogie, horometrie,
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zographie [i.e.
archemastrie."8
perspective],
architecture,
navigation,
thaumatargike,
In the seventeenth century, these lists continued to change, with optics emerging
increasingly as an independent category. Valentin Andreae (1614), for instance,
included geometry, arithmetic, statics, astronomy, gnomonics, automata, optics,
architecture, fortification, surveying, and polyhedra.9 Robert Fludd's (1617) list
included arithmetic, music, geometry, optics, pictorial art, military art, science of
motion, science of time, cosmography, astrology and geomancy.10 Blancanus
(1620) listed only six branches of speculative mathematics: geometry, arithmetic,
optics, mechanics, music and astronomy,11 to which he added six others which
were their practical equivalents.12 Ciermans (1641) also chose a dozen disciplines
in order to have them correspond with the twelve months: geometry, arithmetic,
optics, statics, hydrostatics, nautical science, architecture, war, military machines,
geography, astronomy and chronology.13
Schwenter (1651) increased the list to sixteen: arithmetic, geometry, stereometry,
music, optics and perspective, catoptrics, astronomy and astrology, gnomonics and
clocks, statics, motion, pyrotechnics, pneumatics, hydraulics, writing, architecture
and chemistry.14 Four decades later, with the Jesuit, Milliet de Chales (1690),
optics had moved to twentieth place in a list of thirty-one treatises on: the fourteen
books of Euclid, the Sphaerics of Theodosius, conic sections, arithmetic,
trigonometry, algebra, practical geometry, mechanics, statics, geography,
magnetism, civil architecture, art of dyeing, stone cutting, military architecture,
hydrostatics, fountains and rivers, hydraulic machines, navigation, optics,
perspective, catoptrics, dioptrics, music, pyrotechnics, astrolabes, gnomonics,
astronomy, astrology, meteors and calendars.15
When the librarians at Göttingen developed their systematic subject catalogue
(1730's ff.) their list for mathematics was effectively a new combination of these
disciplines: 1) speculative and practical geometry, arithmetic, algebra; 2) optics,
catoptrics, dioptrics; 3) cosmography, on the sphere, globes etc.; 4) astronomy, 5)
gnomonics; 6) judiciary astrology; 7) physiognomy, chiromancy and other
divinatorial arts; 8) civil architecture; 9) military architecture; 10) military art; 11)
art of navigation, 12) hydraulic art and hydrostatics, machines; 13) art of painting
and sculpture; 14) art of writing; 15) music, 16) mechanical and illiberal arts.16
While many more lists could be cited the above examples amply confirm that there
was no fixed order for listing the mathematical sciences, that optics was sometimes
listed as a general category including perspective, and sometimes listed separately
from perspective. Similar conditions obtained in another tradition, which arranged
the mathematical sciences in groups. For example, Hérigone (1644), in his new
course on mathematics, divided his work into five tomes (adding a sixth as a
supplement). The first tome dealt with theoretical geometry; a second with
arithmetic, computus, algebra and analysis. A third tome contained trigonometry,
practical geometry, art of military and mechanical warfare; a fourth contained the
140
doctrine of the sphere and geography while a fifth dealt with optics, catoptrics,
dioptrics, perspective, spherical trigonometry, planetary theories, gnomonics and
music.17 Ozanam's (1697) five tomes were somewhat differently arranged: 1)
introduction to mathematics and Elements of Euclid; 2) arithmetic, trigonometry
and sine tables; 3) [practical] geometry; 4) mechanics and optics (perspectiva); 5)
geography and gnomonics.18
Wolff (1730-1738) reduced this scheme to four tomes: 1) mathematical method,
arithmetic, geometry, trigonometry; 2) mechanics, with statics, hydrostatics,
aerometry and hydraulics; 3) optics, perspective, catroptrics, dioptrics, the sphere
and spherical trigonometry and astronomy, both spherical and theoretical; 4)
geography with hydrography, chronology, gnomonics, pyrotechnics,, military and
civil architecture.19 Frobes (1743-1746) preferred to further subdivide Wolff's
third to fourth categories thus producing six parts: 1) arithmetic, geometry and
trigonometry; 2) mechanics, hydrostatics, aerometry and hydraulics; 3)
pyrotechnics as well as military and civil architecture; 4) optics, catoptrics,
dioptrics and perspective; 5) astronomy; 6) geography, chronology and
gnomonics.20
Clemm (1764) chose to distinguish between five kinds of sciences: arithmetical
sciences (computation of numbers, letter computation, practical computation);
geometrical sciences (elementary geometry, trigonometry, plane and spherical;
practical geometry, higher geometry); static sciences (statics or mechanics,
hydrostatics, aerometry, hydraulics), optical sciences (optics, catoptrics, dioptrics,
perspective) and astronomical sciences (astronomy, spherical and theoretical
geography, chronology, gnomonics, civil and military architecture).21 By the time
of Wiegleb's edition of Martius' Instruction in natural magic (1796-1798) this list
of different sciences had been transformed into eight realms of artifice
(Kunststücke): electricity, magnetism, optics, chemistry, mechanics, computation,
economics and cards (sic!).22
Meanwhile, Kästner (1792) reduced the sciences to two basic divisions: 1)
mechanical and optical sciences; 2) astronomy, geography, chronology and
gnomonics.23 Lorenz (1798) devoted a first book to arithmetic and geometry; a
second book to mechanical, optical and astronomical sciences and a third book to
general computation of sizes.24 Such examples confirm that even in this second,
more organized tradition, there was still no fixed order for listing the mathematical
sciences, that optics25 was sometimes listed as a general category including
perspective, and sometimes listed separately from perspective.
If there was debate about the relationship of optics and perspective within a
general framework of the mathematical sciences, there was an even greater
difference of opinion concerning the respective branches thereof. In John Dee's
(1570) table, for instance, "perspective" [i.e. optics] was that "which demonstrateth
all maners and properties of all radiations direct broken and reflected," while
"zographie" [i.e. perspective] was that "which demonstrateth and teacheth, how,
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the intersection of all visuall pyramids, made by any plaine assigned (the center,
distance and lightes being determined), may be, by lines and proper colours
represented".26 Another author divided optics into theoretical and practical;
dividing the latter into technical, perspectival, planisphaeric and anamorphic;
subdividing perspectival in turn into vertical (with its categories united or pictorial
and separated or scenical) and horizontal; while subdividing anamorphic into
ithyoptic, catoptric and dioptric.27
Guldin (1635) divided optics into optics proper, catoptrics, dioptrics and
diocatoptrics; subdividing optics proper into perspectiva [i.e. optics] and
perspectiva [i.e. perspective], the latter of which he further divided into
orthography, stereography and scenography28 (an adaptation of the Vitruvian
scheme, cf above p. ). He also subdivided catoptrics into plane, convex, concave
and burning mirrors. Haesel's (1672) scheme bore some resemblance to this. He
began by dividing optics into general and specific, the latter of which he
subdivided into parts which dealt with 1) straight or direct ray (including
ichnography, orthography, scenography and sciography); 2) reflected ray or
catoptrics (as in plane, concave and convex mirrors) and 3) a refracted or infracted
ray (as in mesoptics through glass, water or air).29
Rather different again was the view of Adelung (1781) who also looked upon
perspective as a branch of optics:
Perspective in turn divides itself into [1] linear perspective which, with the
help of geometry, teaches the proper foreshortening of straight lines as, for
example, the parts of a building; [2] aerial perspective, which falls entirely
within the domain of the painter and teaches how to establish light and
shade in accordance with changes which colour of the air brings to bodies
and their colours at a certain distance and [3] mirror perspective, which
teaches one how to draw irregular and distorted figures, which spherical,
conic and other mirrors again restore to their regular shape.30
Meanwhile, Ciermanns (1641), subdivided optics into eight categories:
perspective, orthography, scenography, practice, compendious [perspective],
scenography, curious [perspective] and problematic [perspective].31 Wiegleb
(1786-1798) focussed on eight quite different subdivisions: 1) the eye and its
imitation; 2) curious perspective [i.e. anamorphosis]; 3) plane mirrors; 4) concave
and convex mirrors; 5) prisms and prismatic colours; 6) convex and concave
lenses; 7) perspective; 8) instruments and machines for drawing.32
Von Schlosser (1935) assumed that the discovery of perspective led to a clear
distinction between optics (perspectiva communis) and perspective (perspectiva
artificialis).33 Panofsky (1927) spread this idea.34 However, as the above
examples confirm, there was no ready consensus about either the relation of optics
and perspective or their further subdivisions. Granted there were cases when linear
perspective was distinguished by an extra adjective as in prospectiva pingendi, or
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prospectiva pratica, but in general, the terms for optics and perspective tended to
remain interchangeable. Indeed Leonardo, adopted the title of Peckham's treatise
on optics, when he headed a section on perspective in his Treatise on painting:
prospettiva comune.35 And Leonardo's contemporary, Cesariano added a basic
diagram relating to perspective in a manuscript version of Peckham's text.36 This
continued interplay of meanings helps explain the enduring impact of optics on
perspective in terms of both titles and content, although it varied from country to
country. In Italy, for instance, because the term prospettiva continued to mean
both "optics" and "perspective," these connections remained largely implicit. In
Germany, works which specifically mentioned optics in their titles, were rare, as,
for example, Mühlert's (1821) Art of shadows following optical laws, Öttingen's
important article (1906), Judgment of perspective images with references to the
viewpoint of the observer and Riegel's (1952) The visual image, Handbook of
Perspective.
In France, this connection between optics and perspective, became explicit in the
sixteenth century. Hence the Antwerp encyclopaedist Ringelbergius (1531), whose
works were published in Paris, had a section on perspective headed optics
(Optice), while Androuet Du Cerceau (1551) entitled one of his works Twenty
figures for they contain most ancient optical views which they call perspective. In
the seventeenth century, Nicéron (1638) wrote Curious perspective or the artificial
magic of wonderful effects of optics, catoptrics and dioptrics, and Huret (1670)
entitled his treatise on perspective simply, Optics of portraiture.
The eighteenth century saw only isolated examples such as La Caille's (1750, etc.)
Elementary lessons of optics, which dealt with perspective. In the nineteenth
century Vallée's (1844), Theory of the eye played an important role in asserting
that the laws of descriptive geometry, perspective and vision coincided. He began
his work with a survey of famous contributions to optics by Leonardo da Vinci,
Kepler, Soemmering, Brewster and Young, noting that his own interests had begun
more than two decades earlier:
...in 1821 we published the Treatise of the science of drawing. In this
work we consider painting, drawing in its different genres and in general
the art of imitating objects in order to produce a greater or lesser illusion,
as an application of the rules by means of which one can deceive the eye.
Hence the theory of vision serves as the basis of our treatise, where it is
explained in some detail and often envisaged under new aspects. In this
work, of which perspective and shadows are important parts, geometry
guides us constantly and has led us to an explanation of the achromatic
nature of the eye based on the non-homogeneity of the vitreous body.37
The second half of the nineteenth century saw a number of new works, which
assumed close links between optics and perspective, such as Babinet's (1855),
Studies and readings on the sciences of observation, Charles' (1884), Elementary
treatise on linear perspective and perspective of view, Payen's (1884), Extract of a
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treatise on ocular perspective, and numerous works on perspective of observation
including Pierre (1885), Daniel (1891), Tensi (1895), Watelet (1893), Chevrier
(1900), Legrand (1903, 1908), Lienaux (19135-1949) and more recently Raynaud
(1962).
In the Netherlands emphasis on the optical aspects of perspective began with
Vredeman de Vries (1560), who entitled one of his earliest collections of
engravings, Twenty most select buildings of scenography or perspective, as
buildings summoned forth to the eye are called to the ordinary painter, and later
wrote (1604-1605 etc.) Perspective, that is, the most famous art of looking in or
through the axis of the eyes, a title which recurred in subsequent editions by his
student Marolois (1628, 1638) etc. Another of Vredeman de Vries' students,
Hondius (1623, etc.), wrote an Instruction of optics or perspective, as if the two
terms were fully interchangeable. Similarly, a later edition of Marolois (1653) was
entitled simply, Optics or perspective.
In England, the work of Hondius and Marolois was a starting point for a treatise by
Moxon (1670): Practical perspective or perspective made easie teaching by
opticks. In 1701, Lamy published his Traité de perspective, ou sont contenus les
fondemans de la peinture, which was translated into English the following year
(1702) as: Treatise of perspective or the art of representing all manner of objects
as they appear to the eye in all situations, which almost certainly influenced Brook
Taylor (1715, etc.) when he entitled his seminal work: Linear perspective or a new
method of representing justly all manner of objects as they appear to the eye in all
situations. Meanwhile, Shuttleworth (1707), had written A treatise of optics
direct...to which is added an appendix on perspective. Later in the century, Harris
(1775), also dealt with perspective in A treatise on optics containing elements of
the science. The nineteenth century saw further works linking optics and
perspective, such as Keating's (1812) Eidometria or optic mensuration and
(corollary) perspective or Burnet's (1837, etc.), An essay on the education of the
eye with reference to painting. This tradition continued in the twentieth century
with works such as Roberts (1904), Perspective of sight, and Myslak's (1967),
Point of view perspective.
These analogies between optics and perspective affected both fields. In the
sixteenth century, Leonardo had explored tensions between a spherical--or
cylindrical--plane of vision, and the rectilinear plane of perspectival
representation. In the seventeenth century, Bosse deliberately contrasted a
cylindrical plane of vision, with a rectilinear plane of perspective, to demonstrate
why one must not draw what one sees. By the nineteenth century, the development
of descriptive geometry encouraged the assumption that there were universal laws
of reality, which applied equally to geometry, vision and representation. The
window principle now served to demonstrate that the laws of optics and
perspective were identical, and became a standard example in introductions to
textbooks on perspective, as in Ruskin (1859):
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When you begin to read this book, sit down very near the window, and shut
the window. I hope the view out of it is pretty; but, whatever the view may
be, we shall find enough in it for an illustration of the first principles of
perspective (or, literally, of "looking through").
Every pane of your window may be considered, if you choose, as a glass
picture; and what you see through it, as painted on its surface...
...Every picture drawn in true perspective may be considered as an upright
piece of glass, on which the objects seen through it have been thus drawn.
Perspective can, therefore, only be quite right, being calculated for one
fixed position of the eye of the observer; nor will it ever appear deceptively
right unless seen precisely from the point it is calculated for.38
Ruskin quietly relegated to an appendix the problem of visual angles39 (cf. p. )
which implicitly challenged this equation between vision and representation.
Cassagne (1879), referred to equally sized objects positioned at different heights
strictly in terms of their projections, without references to their different visual
angles. For him the visual angle was only of interest as applied to the ensemble,
particularly with respect to establishing the proper distance for viewing and
drawing objects.40
In the meantime, the initial wave of enthusiasm for descriptive geometry had
passed, and thinkers had become aware that there were problems with these easy
equations between geometry, perspective and optics. Jules de la Gournerie (1859),
for instance, noted that:
Perspective is a graphic art of a special kind. It poses practical difficulties
peculiar to it alone and which, in the course of several centuries have
occupied a great number of learned men and artists. Authors who have
treated it as a simple application of descriptive geometry have not been
able to give it the necessary developments. There are moreover grounds to
believe that several of them deigned not to study the older treatises. In fact
practically all the students of Monge believed that all the graphic arts
presented only uncertainty and confusion prior to [the coming] their
master. One finds in the writings of several of the most famous of these,
assertions which are completely erroneous in this regard.41
At about the same time, the researches of Hering and Helmholtz42 were
suggesting that the perceptual space of optics might be non-Euclidean, and hence
fundamentally different from the Euclidean space of perspective. This led
gradually to a whole body of literature on alternative projection methods designed
to approximate more closely the realities of visual perceptions (cf. pp. and ).
When Panofsky wrote his landmark essay on perspective as a symbolic form
(1927),43 he assumed that the discovery of linear perspective brought about a
change in Euclidean theories of visual angles. This did not occur in the sixteenth
century, as he imagined, but rather in the nineteenth, and then only briefly under
145
the impetus of descriptive geometry. And even then, perspective remained under
the spectre of being classed as a branch of optics such that whenever there were
innovations in optical theory, there were usually corresponding innovations in
perspectival methods. This has continued to the present day such that works
relevant to perspective are still sometimes classed as optics.
3. Architecture
In the case of architecture, this question of classification posed an even greater
problem. For in a sense it could be argued that every illustrated architectural book
related somehow to perspective. We have already noted some of the chief
architectural themes contained in actual treatises on perspective (pp. ). And while
it is clearly beyond the scope of this essay to provide a comprehensive survey of
all architectural works which might have a bearing on perspective, it will be useful
to outline some of the more obvious points of contact. At the most obvious level,
there were architectural books with sections on perspective, and some books
specifically devoted to architectural perspective. In order to understand the larger
context of these problems, a brief excursus into the history of classification of
architecture itself will be required. This will lead to a consideration of links with
descriptive geometry and specialized categories, such as architectural drawing and
drafting. Each of these will be considered in turn.
Just as there were general treatises on perspective with sections on architecture (cf.
p.
), so too were there general treatises on architecture with sections on
perspective. For instance, Furttenbach's Recreational architecture (1640),
contained numerous perspectival views and a special section on stage design.
Caramuel de Lobkowitz (1678) offered various perspectival methods of interest to
architects. Guarino (1737), included an important discussion of perspective in his
Civil architecture, while Amico (1750), in his Practical architect added a
"Compendium of perspective." Vittone (1760, 1766) also discussed perspective at
some length. This tradition continued into the nineteenth century with general
works such as Gwilt's Encyclopaedia of architecture (e.g. 1842, 1851, 1861).
Stonecutting was a branch of architecture, which involved perspective in a special
way. During the middle ages knowledge of this trade was kept a secret by the
guilds. Roriczer (1486) published on the topic in a secretive way. Philibert de
l'Orme (1567), began to explore the relations of stonecutting and perspective in
veiled terms. Yet it was not until the 1640s that the writings of three French
architects explored these connections in greater detail, namely, Jousse (1642),
Desargues (1643) and Derand (1643). In the 1730s, these connections were taken
up anew by Gaurino (1737) and exhaustively by Frézier (1737-1739) in his
monumental three volume, Theory and practice of stonecutting. As the eighteenth
century progressed, this subject emerged as the new field of stereotomy, which
was subsequently subsumed as a category of descriptive geometry.
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A class of books devoted specifically to architectural perspective emerged slowly.
In the sixteenth century, there was a tradition of dedicating perspectival treatises to
a number of professions (cf. p. ). This tradition continued in then nineteenth and
twentieth centuries. A number of authors addressed their texts to painters and
architects as, for example, Palaiseau (1818), Hummel (1825), Klette (1867),
Longfellow (1901, 1908) and Denev (1948). There were numerous variants on this
theme. Girardon (1850, 1900) addressed his work to schools of fine art, artists and
architects; Holmes (1937, 1938, 1946, 1948, 1954, 1957, 1962, 1967) to artists,
painters and art students; Clark (1936) to artists, architects and students, while
Pyne (1870), specifically addressed young students and amateurs in architecture,
painting. Mols (1816), extended the scope to painting, architecture, mechanics.
Berger (1867) mentioned architects, construction workers, painters and amateurs.
Adamo (1899) limited himself to architects and construction workers. Others
included architects and designers, e.g. Sierp (1958, 1969,1972), White (1968,
1969,1974, 1976), Coulin (1966, 1962). Capelle (1969), addressed architects and
engineers. Pizzigoni (1951), addressed painters, architects, scenographers and
cinematographers, while Gratry (1855) included artists, painters, architects,
engravers, decorators and all persons concerned with drawing.44
In the latter half of the nineteenth century, there evolved architectural treatises
addressed specifically to architects, such as Schaap (1856), Schoen (1863), Krause
(1876), Wright (1885, 1890, 1892, 1898) and Ferguson (1891, 1895). In rare
cases, they were even more specialized as in Bailby's (1876) Complements of
perspective. Application of linear perspective to the architectural decoration of
ceilings. The first decade of the twentieth century saw no less than four new
authors with works on perspective dedicated specifically to architects: Lawrence
(1902, 1908, 1922, 1927, 1931, 1947), Ferguson (1903, 1915), Middleton (1903,
1907, 1915, 1919) and Hicks (1909). The next decades saw more examples with
Rudd (1916), Dean (1933), Mashkov (1935), Bullen (1942), Retera (1946),
Schutte (1949) and Woord (1953). The 1960's saw another upsurge, with Parrens
(1962, 1967, 1973, 1971, 1982), Georghiu (1963), Schaarw„chter (1964, 1967),
Gomolozewski (1966), Danielowski (1968, 1969, 1976, 1982) and Rosati (1969).
More recent texts on architectural perspective, dedicated to architects, include
Docci (1972), Suzin (1974) and Bonbon (1977).
In addition to this obvious level of books specifically devoted to architectural
perspective, there were other connections between architecture and perspective,
which will become more apparent through a brief excursus on classification of
architecture. In the mediaeval period written architectural knowledge was imparted
mainly via the Vitruvian tradition and model books45 such as those of Villard de
Honnecourt,46 which contained a variety of other topics including surveying,
geometry, machines and drawing (fig.
). The fifteenth century saw a further
distinction between books of mechanical inventions (e.g. Taccola)47 and those
which focussed on architectural inventions (e.g. Francesco di Giorgio Martini),
though vestiges of other topics remained in both. By the end of the fifteenth
century, a distinction emerged between pleasurable drawings (e.g. Leonardo da
147
Vinci, Windsor, Royal Collection) and useful drawings (e.g. Leonardo, Codice
atlantico). In the sixteenth century there were further distinctions between useful
mechanical drawings (e.g. Besson, cf. below p.
) and useful architectural
drawings (e.g. Serlio), between modern (Serlio), and ancient buildings (Du
Cerceau); between civil (Palladio) and military architecture (Cataneo).
In terms of perspective, there were works which dealt specifically with military
architecture such as Specklin (1589, 1608) and Perret (1601, 1613). Perspectival
fortifications gradually found their way into standard works on perspective such as
Dubreuil (1642, etc.), Pozzo (1693, etc.), Bretez (1751); manuscripts such as
Sovero (16__), Leturc (17__), as well as a considerable literature on military
architecture proper by authors such as Marolois and Hondius, who also wrote
treaties on perspective, Le Duc, Pagan, etc.
Meanwhile, (fig.** ), there were also categories of literature to distinguish between
sacred and secular architecture, or dealing with specific parts of buildings such as
columns (Porta) or chimneys (Vredeman de Vries), or special problems such as
gardening (Mollet, cf. below 2.3) or stonecutting, mentioned earlier. Gradually
more subtle distinctions emerged (fig.** ). Drawings could deal with the past
(buildings that had existed), the present (existing buildings), the future (planned
buildings) or be a-temporal (imaginary buildings). Drawings of past buildings
could be based on archaeological evidence (cf. fig. 84.1, 2, 4) or be artists'
reconstructions (e.g. fig. 97.3) of what a building or monument might have looked
like. Drawings of existing buildings could be idealized (e.g. fig. 86.1-4), realistic
(e.g. fig. 85.2) or actually measured. A temporal drawings could involve possible
buildings, such as Steven's anachronistic view of Emmaus (fig. 85.2), or purely
fanciful constructions, as in some of Piranesi's more exotic prisons.
Perspective played a complex role in these developments. On the one hand, it
undermined such distinctions by creating images which subjected archeological
record (fig. 96.1), architectural plan (fig. 96.2), architectural phantasy (fig. 96.3),
architectural reality (fig. 96.4) and artist's reconstruction (fig. 96.5) to the same
spatial rules. On the other hand, precisely because of its window principle, which
introduced a possibility of testing and measuring potential matches between
representations and object, perspective was crucial in making these distinctions
possible (cf. below 2.4).
The details of these distinctions cannot concern us here.48 It will suffice merely to
note that their evolution went hand in hand with the rise of treatises on perspective
and indeed a whole corpus of technical literature on drawing (fig. cf. below p. ).
Already in the sixteenth century professions such as surveying developed their
own literature49 and by the nineteenth century this had led to a special branch of
plan drawing. Cartographers developed a literature on map drawing (cf. fig. );
engineers on engineering drawing and architects on architectural drawing. The
distinction between existing and projected buildings led to a special branch of
planned drawings called architectural drafting. A branch devoted specifically to
148
shadows (considered earlier on p. ) also evolved which became linked in turn
with geometry. At least some of these developments must be considered in more
detail.
Hirschvogel (1544), had consciously cited perspective as bringing together
architecture and geometry (cf. p. ). By the nineteenth century, these links between
architecture and geometry had developed considerably. In some cases they
involved traditional Euclidean geometry as in Toussaint's (1812) Simplified
treatise of theoretical and practical geometry and architecture, Bennett's (1837)
Original geometrical illustrations or the book of lines, circles, triangles, polygons
indispensable to architects and Burns (1853) Illustrated London practical
geometry and its application to architecture drawing.
Tabacchi (1844), was one of the first to link descriptive geometry, perspective and
architecture. This Italian work was followed by a French treatise by Peyrat (1865):
Descriptive geometry applied to graphical instructions in general, to architecture,
drawing of perspective and the determination of shadows. The next decades
brought Tessari (1860, 1883), Applications of descriptive geometry, The theory of
shadows and of chiaroscuro...for the use of engineers, architects and designers,
and Schreiber (1884 cf. 1822, etc.). Twentieth century examples included Smutz
(1938), Fischer (1942) and Lippold (1949). In rare cases, such as Mondino's
(1962), Perspective and the theory of shadows. Applications of descriptive
geometry and central projection for the use of students of the faculty of
architecture, perspective, descriptive geometry, shades and shadows and
architecture were all discussed together. Meanwhile, each of these had also
emerged as independent themes (cf. p. ).
In a general sense, architectural drawing had emerged with the study of Roman
ruins in the fifteenth century (p. ). Even so, one of the first works specifically
devoted to the subject was Nicholson's (1795), Principles of architecture
containing the true method of drawing ichnography and orthography of objects,
geometrical rules for shadows, which went through numerous editions (1809,
1827, 1831, 1841, 1848). Shortly afterward in France, Lagardette (1803), also a
pioneer with respect to shades and shadows, published, New rules for the practice
of drawing and wash drawing in architecture. As the nineteenth century
progressed, there were efforts to relate architectural drawing within a larger
context of technical drawing. For example, authors such as Weale (1841) and Burn
(1854, 1856, 1860, 1882, 1893), wrote on architectural, mechanical and
engineering drawing. Willson (1898) wrote on science, engineering and
architectural drawing. Burg (1830) and Robinet (1842, 1855, 1859) wrote on
architectural and mechanical drawing, a theme which Armengaud (1848) pursued
in his Course of industrial drawing applied principally to mechanics and
architecture. Henry des Vosges (1843, 1845, 1846), and Reid (1848, 1858, 1859),
wrote on architecture and surveying. Pyne (1864, 1894) addressed operation
builders and architects. Davidson (1869, 1871, 1882, 1896) addressed building
constructors and architects. Linear drawing, as a branch which applied to all the
149
building trades, was also emerging through authors such as Heissig (1855, 1863),
Julien (1861) and Anonymous (1875).
Meanwhile, by the 1850's, a trend towards specialization was also evident, with
books specifically on architectural drawing by Etex (1850), Graeb (1855), Gantz
(1856), Spiers (1887, 1888, 1892, 1902, 1905), Edminster (1899, 1902). This
trend continued in the twentieth century with Roberts (1906, 1907, 1916), Field
(1922, 1932, 1943), Loundes (1930, 1935, 1938), Hake (1929, 1948) and Farey
(1931, 1949). The nineteen sixties saw an upsurge in publications with Halse
(1960), Bonfigli (1962), Coulin (1966), Müller (1967), Lockard (1968) and Jacoby
(1969). More recently there were publications by Bruzda (1971), McGinty (1980)
and K”nig (1979, 1984). Many of these were more primitive than their nineteenth
century predecessors, mainly because traditional tasks in this field were
increasingly coming within the realm of computers (see below p. ).
The nineteenth century also brought a gradual distinction between drawings of
existing buildings (architectural drawing), and plans for further buildings
(architectural drafting), though this varied from country to country. In France, for
instance, both drawing and drafting, remained part of a more general concept of
dessin. In England, there was again no standard term for drafting. Burn (1857)
dealt with it under Ornamental drawing and architectural design, while Tuthill
(1881, 1891, 1892, 1894, 1897, 1902, 1905, 1914, 1915) did so in, Practical
lessons in architectural drawing or how to make working drawings and write the
specifications of buildings.
In Germany,,there evolved a branch of drawing concerned specifically with plans
(Entwürfsdarstellungen) as in Seeger (1969). Drafting emerged as an independent
field particularly in the United States, where Armengaud's (1848) Cours de dessin
industriel, was translated as The practical draughtsman's book of industrial design
forming a complete course of mechanical, engineering and architectural drawing
(1853, etc., cf. André, 1874). In the twentieth century Hornung's (1910),
Architectural drafting became a standard work with at least five subsequent
editions (1949, 1954, 1955, 1966, 1971). Other significant works have included
Stegman (1914, 1966), Fischer (1942), Barnes (1960) and Bellis (1961). But here,
even more so than in the case of architectural drawing, the development of
computer aided design (CAD) has been changing the field so rapidly that there is
at present no standard textbook (see below p. ).
While there have been many innovations, there has also been a striking continuity
of images and problems within architectural treatises. For instance, the vault has
been a regular theme ever since Piero della Francesca used it in On perspective for
painting. Serlio (1544, etc.) used it as did Lautensack (1564). In the seventeenth
century, Dubreuil (1642-1649) used it a number of times and it remains a stock
image as witnessed by Schaarwächter's (1967) Perspectives for architecture. A
similar continuity is evident in terms of problems. In the nineteenth century,
authors such as Edwards (fig. 64.1-2, 1803) and Schreiber (1854) offered multiple
150
perspectival views of a given building. Morgan (1950) provided a more systematic
treatment of this problem in Architectural drawing, perspective, light and shadow,
rendering, and the latest developments in computer aided design (p. ) can be seen
as a direct elaboration of these principles. Or one might cite the example of
Cloquet (1823), who offered both abstract geometrical and photograph-like
perspectival drawingsw of various scenes in his Treatise of picturesque
perspective, a method which was taken up by La Gournerie (1859, 1884, 1898)
and which has become widespread in the last decades through a juxtaposition of
photographs and line drawings (p.
). Authors such as Hiss (1985), who
distinguish between three levels of perspective drawing--base perspective, design
study and final perspective--have simply taken this approach one step further.
4. Drawing
To understand the larger context of these developments it is necessary to return to
the distinctions between pleasurable and useful drawings, mentioned earlier (p. ).
In the sixteenth century useful drawings were divided into architectural and
mechanical drawings. The latter category led to collections of different machines
such as Besson and Ramelli and specific mechanical devices such as fountains and
wells (e.g. Vredeman de Vries,1568). Such books had straightforward examples
with little or no explanation. By the nineteenth century, books on specific
mechanical devices such as mills (e.g. Böckler 16xx) with some explanation
appeared. By the eighteenth century engineers such as Leupold (1727) moved in
the direction of general principles of machines, an idea which F. Reuleaux
developed in his Kinematics of machinery.50
To convey this knowledge also required developments in drawing techniques.
Literature on drawing of machines, as noted earlier was frequently linked with
architectural and engineering drawing, but gradually emerged as an independent
branch of machine drawing or mechanical drawing.51 As in the case of
architecture, further distinctions arose between existing and planned states, which
led to specific books on machine drawing and machine drafting or design.
Meanwhile, because all technical drawings involved constructions with the aid of
instruments a distinction arose in Germany between construction drawing, and
freehand drawing which applied to artistic and aesthetic domains. Construction
drawing included applications to professions such as architecture and engineering
and various trades such as bricklayers, carpenters, decorators, locksmiths, masons,
etc. These distinctions varied from country to country. In France, dessin remained
the general term for both technical and aesthetic domains. Industrial drawing
became a term for technical applications involving professions, while linear
drawing applied to trades in general. The Larousse Encyclopédie asserted that
linear drawing included "tracing of working drawings, of elementary, descriptive
and analytical geometry, ordinary and isometrical perspective, drawings of
architecture, machines and topography."52 In England, construction drawing was
frequently referred to as geometry applied to art (cf. fig.
), while freehand
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drawing was simply called drawing. In the United States these distinctions
between useful and pleasurable drawing emerged as technical drawing versus fine
arts.
If the precise relations between drawing and descriptive geometry or mathematics
as a whole varied from country to country, the net result of these relations was the
same everywhere. They introduced a vision of a single set of laws underlying the
near infinite diversity of applications. As a result, in the nineteenth century,
literature began to go in two opposing directions. One involved ever more
branches of drawing: architectural, engineering, industrial, machine, map, plan,
technical, etc. (fig.
). The other involved a quest for a universal graphic
language which would encompass all these variants, which has been inherited by
the realm of computer aided design and which helps explain why distinctions
between technical and aesthetic drawing have never become as clear cut as some
might have wished.
Even so there had been a number of developments specifically related to
pleasurable or aesthetic drawings. At the beginning of the sixteenth century an
implicit distinction had arisen between drawings of artifice (luxuries of the man
made world) and nature (luxuries of the natural world. With respect to the former,
Leonardo devoted a section of his Treatise on Painting to drapery,53 and drew
various examples thereof in his notebooks. He also made several hundred drawings
of grotesques, as well as numerous costumes, hats and ornaments. Some of these
themes became subjects of separate books later in the century, as in the case of
costumes (Amman
)54 and ornament (Cock, Liefrinck, Dietterlin),55 while
others such as hats, were treated in sections of drawing books (e.g. Vogtherr).56
By the nineteenth century most of these had become independent topics and in the
case of ornament or costume there were even independent bibliographies.
As for nature, the situation was more complex. With respect to topics such as the
human figure, a considerable literature evolved in the sixteenth century,
proceeding in no less than four directions: anatomy (e.g. Leonardo, c. 1480-1815);
proportion (Dürer, 1528); geometry (Stoer,1567) and subsequently, perspective
(Lautensack, 1564; Cousin, le jeune, 1595, etc.). In the case of animals such as
horses there were apparently treatises on their geometry, i.e. quadrature, and
perspective by Foppa (148_) and Bramante (14__). In Soden Smith's catalogue of
drawing books, the earliest examples date from the 1640's, namely, A. Cuyp's
(1641), Various qaudruped animals drawn from life, and G. Fyt's (1642), Etchings
of dogs.57
As far as aesthetic treatment was concerned, the botanical realms of nature evolved
later. To be sure Leonardo, Dürer and their contemporaries drew a number of
isolated examples of flowers, fruits and trees. Nonetheless, most sixteenth century
treatises focussed on the useful and necessary aspects thereof, particularly with
respect to their medicinal purposes. Indeed, in Soden Smith's list, the earliest
152
aesthetic book on flowers was Syme's (1810), Practical directions for learning
flowers, and in the case of trees, Laporte's Sketches of trees (1798-1801).58
Landscape, on the other hand, had begun in sixteenth century treatises on
perspective such as the one edited by Rodler (1531), although the earliest
examples recorded by Soden Smith were Stoer (1617), Preissler's (1734),
Introduction which one can use in imitating beautiful landscapes in perspective,
and Smith's (1797), Remarks on rural scenery with twenty etchings of cottages
from nature.59 As for marine scenes, by the 1550's, Cock had produced a number
of engravings of ships. In the seventeenth century, Robert Dudley produced
remarkable manuscripts60 on the subject. Even so the earliest work in Soden
Smith's list was an anonymous (1827) Book of shipping of various classes from
the cutter to the first rate from drawings by Lieutenant Luna and others.61
Hence by the nineteenth century, what had begun as a simple category of
pleasurable drawings, had spawned literature involving various aspects of the man
made world (notably costumes, drapes, hats, grotesques, ornament) and nature.
Soden Smith's standard catalogue, for instance, included 123 works on the human
figure, 43 on animals, 7 on flowers, 29 on trees, 88 on landscapes and 13 on
marine subjects.
5. Drawing Education
These practical changes in drawing were accompanied by institutional ones, which
reflected both theoretical and philosophical developments, which had begun in the
sixteenth century with efforts by Leonardo to create a systematic framework for
representation. Lomazzo (1585), reduced these precepts to a list of five basic
concepts: proportion, force (and motion), colour, light and perspective.62 De
Piles63 and others produced their own variants on this list of ingredients.
Bracquemond (1885) expanded it to include: drawing, colour, warmth, reflections
(and chiaroscuro), value, outline (and modelling), line (mass and silhouette),
perspective, effect, execution, ornament and decoration.64
As for the goals of art, each country seemed to go in a different direction. In
Germany, the tradition of Dürer, Fürst, Testelin, Bloemart, Preissler and Herz
emphasized geometrical drawing.65 In Italy, ever since Alberti, there had been an
emphasis on composition and aspects of the story (istoria). In addition there were
also major regional differences ranging from the Venetian preoccupation with
colour, to the Florentine concern with chiaroscuro, to create effects of relief
through line drawing. In the Netherlands, thinkers such as Van Mander and
Hoogstraeten developed their own version of the story telling goal. Hoogstraeten,
for instance, described nine types of story telling to correspond to each of the
muses.66 In France, debates shifted to questions of technique, namely, to relative
values of line versus colour, which sparked a major controversy between
Poussinists and Rubenists.67
153
By the mid-seventeenth century it appeared that perspective was losing the
significance it had once had. Indeed the decision of the French Academy to oust
Bosse as professor of perspective (see above p. ) appeared only to confirm this
trend. Then there is the as yet untold story of the role that perspective played in the
eighteenth and nineteenth centuries as the academies of (fine) arts, particularly in
Rome, Florence, Milan, Paris, London, Vienna, and Copenhagen became public
institutions and, alas all too often, prisons for the imagination as members of the
avante garde would one day complain.
At the same time there were other currents, which led in the opposite direction and
were destined to make perspective a fundamental aspect of drawing. Part of this
impetus came from philosophers such as Locke (1693)68 and Rousseau (1762),69
who decided that perspective should become a basic ingredient in the education of
children.70 How to teach drawing properly, and what should be the goals of
drawing became a matter of increasing debate. Leonardo da Vinci had considered
at least three distinct goals of representation: at one extreme, nature; in between,
models, and at the other extreme, imagination. By the latter seventeenth century,
the ideas of Lairesse, which favoured the copying and imitation of models had
gained ascendancy. By the later eighteenth century two intermediate positions
found powerful new exponents. The Swiss philosopher of education, Pestalozzi
(1746-1847) argued that models might be used to develop the imagination,71
while Thibaut (1757-1826), professor of perspective at the school of architecture in
Paris argued that models and perspective might be used in nature drawing.
Pestalozzi's position was developed by Joseph Schmid (1809), who argued that
this approach to imagination via models could be aided by the use of geometry and
perspective which led, in turn to no less than five further responses in the early
nineteenth century: 1) Reissmann (1801, etc.), who claimed that one could
stimulate imagination via geometrical forms and perspective; 2) Boniface (1823),
who emphasized perspective as a stimulus to the imagination; 3) Ramsauer (1821),
who proposed the use of models, geometry, perspective and even some nature in
stimulating imagination; 4) Francke (1833, 1836), who emphasized copying
examples using perspective and; 5) Harnisch and Platz (1815), who favoured
stigmographic drawing with some perspective. Later in the century there were two
further responses; 6) Glinzer (1868), who insisted on dictation drawing to help the
imagination, which method Pillet (1882) subsequently linked with perspective; 7)
Soldan (1830) and Bes (1891, 1896), who believed that projection drawing and
perspective offered a key to the imagination.
Meanwhile, Thibault's opposing school, which emphasized the use of models for
nature drawing, led to two important responses. The chief of these was by his
student, Thénot (1803-1857), who emphasized (1826) the use of perspective and
some models. His work proved influential and was soon translated into Dutch
(1829), German (1833, etc.), American (1834, etc.), English (1836, etc.) and
subsequently Italian (1870). A second response to Thibaut came from Peter
Schmid (1828) who emphasized models, but adcknowledged the use of
154
perspective, shades and shadows in the process. This in turn inspired a clearer
formulation by the brothers Ferdinand and Alexandre Dupuis (pl. 1820-1840), who
argued for the use of both geometrical and perspectival models in the process of
nature drawing.72 This approach won such acclaim that it was introduced into
Germany in the next decades by Wolfgang (1825-1874), Fürstenberg (1854) and
Domschke (1876), and into the Netherlands by Parv‚ (1852), Bergmann (1857)
and Braet von Ueberfeldt (1863). The next generation saw a series of German
books on nature drawing which emphasized the use of perspective, namely,
Seeberger (1871), Huther (1872), Audel (1880), Kuchinka (1880), Lang (1880),
Steigl (1880), Kajetan (1881) and Gennerich (1882).
The result of these developments was that perspective became integrated into the
whole spectrum of drawing, ranging from natural objects, and man made models
through purely imaginary objects as becomes evident from a brief examination of
some of the key programmes. In the Encyclopédie (1754) drawing was defined as
the art of imitating and the chief objects of study were listed as the human figure,
animals, landscapes, draperies, flowers and fruits.73 Joseph Schmid's programme
for imagination via models had five basic steps; 1) exercises for the education of
the hand for drawing; 2) drawing exercises in making and inventing beautiful
forms; 3) exercises which lead to development and strengthening of the
imagination; 4) exercises in real or mathematical copying of natural objects and; 5)
exercises in perspectival development.74 Peter Schmid's programme for nature
drawing via models had four steps: 1) bodies of plane figures; 2) bodies of curved
figures; 3) practical perspective; and 4) shades and shadows.75
His successors, the brothers Dupuis, took for granted the use of perspective in their
programmes and concentrated on defining more precisely the models to be used.
Ferdinand Dupuis outlined five levels of inorganic models: 1) simplest geometrical
figures; 2) straight lined geometrical figures; 3) composite figures including
characteristics of one and two; 4) stereometric figures; and 5) furniture, ceilings,
pillars, columns and ornaments.76 Alexandre Dupuis had a four stage programme
for more organic forms: 1) heads, plastercast, and live; 2) human form; 3)
ornament; 4) flowers.77 Bergmann's programme (1857) read like a synthesis of
the two: geometry, light, flowers, ornament, landscape, figures, animals,
perspective, light and shade.78
The Universal dictionary of the nineteenth century ( 1870), in its article on
drawing, cited a passage by Delacroix, which gave some indication of how
important perspective had, in the meantime become:
Drawing, he said, is not to reproduce an object as it is, that being the task
of the sculptor, but as it appears and this is the task of the person who
draws and the painter. The latter achieves by means of gradations of tints
that which the other began by means of proper disposition of lines. In a
word it is perspective which one needs to place, not in the spirit, but in the
eye of a student. I will say to the instructor: with your proportions and
155
perspective by A plus B, you will not teach me other than truths and in art
all is lies....Whatever be the object that a person who draws proposes to
reproduce, they are still obliged above all to know and to respect the laws
of perspective. There is linear perspective and aerial perspective. The
former, for which descriptive geometry furnishes the rules, suffices for
drawing, which only makes use of projections [and] contours. The second,
which has as its object the apparent modifications, which plays of light and
shade cause forms to undergo, finds its application in coloured images,
either monochrome, as are drawings in sepin or china ink, or
multicoloured. One might say that on a canvas, drawing gives the linear
perspective and colour the aerial perspective.79
The latter part of this passage is particularly interesting because it suggests that the
earleir debate of line versus colour, of the Rubenistes versus Poussinistes, had now
been resolved through a synthesis of linear and colour perspective.
Even more instructive was the section on drawing in the Dictionary of Pedagogy
(1881). The author emphasized the importance of perspective and noted that:
the developed theory of perspective gave cognisance of the procedures
imagined by geometers in order to obtain optical appearances in all cases in
which it is necessary for a professional painter and especially an architect
to know how to execute the same.80
It was conceded that: "the goal of study is drawing after nature but it is here that
deeper study begins. In an elementary study one will not go beyond drawing based
on a model."81 This elementary course was, however, considerably more complex
there one might imagine as becomes clear from the teaching in elementary schools
as reported in the Dictionary (1881):
Elementary Course
Tracing of straight lines and their division into equal parts. The evaluation
of the relation of lines to one another; reproduction and evaluation of lines.
First principles of drawing of ornament. Circumferences regular polygons,
stellated roses.
Copies of plasters representing ornaments in plan of low relief.
First notions of geometrical drawing and elements of perspective.
Geometrical representation in projection and perspectival representation in
projection, then with shadows of geometrical solids and simple ordinary
objects.
Geometrical drawing. Use (at the board) of instruments serving the tracing
of straight lines and circumferences: rule, compass, square and protractor.
To limit oneself in this part of the course, to have pupils understand the use
of these instruments of which they will acquire skilled use in the upper
level course.
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Upper Level Course
Drawing with a raised hand
Drawing after an engraving and after a relief of purely geometrical
ornaments, mouldings, ovals, heart-shaped spokes, indentures, etc.
Drawing after engraving and relief ornaments taking their form from the
realm of vegetation, leaves, flowers, fruits, little palmettes, foliated scrolls,
etc.
Elementary notions on the architectural orders given on the blackgoard by
the teacher (3 lessons).
Drawing of the human body: its parts and proportions.
Geometrical drawing. Execution on paper, with the help of instruments,
geometrical traces which have been made on the board in the middle level
course.
Principles of wash drawing with flat tints.
Drawing reproducing motifs of decoration of plane surfaces or of a low
relief: tiling, parquetry, windows, panels, ceilings. Wash drawing in china
ink and in the colour of some of these drawings.
To bring into relief with dimension figures, with sides, and geometrical
representation in projection of geometrical solids and simple objects such
as assemblages of timber, woodwork, exterior dispositions of apparatus of
stone, big pieces of ironwork, furniture of the most ordinary type, etc. Use
of wash drawing to express the nature of materials. Wash drawings of plans
and maps.82
Most interesting of all was the philosophy that lay behind this process. It was not
just a matter of teaching the gifted to draw well. There was a conviction that the
study of:
drawing should not only guide a group of these who would devote
themselves to acquire the talent of representing visible things either by pure
imitation or in imagining and in inventing in this way to the point of art,
but also for those who would not succeed in acquiring this talent or who
would only acquire it in a feeble measure, this study, if one founded it on
the imitation of excellent models would teach them what is, in fact, exact
or inexact, correct or incorrect, beautiful or ugly, graceful or ungraceful,
suitable and unsuitable, such that it would thus teach to see better and to
judge better and that it would form, finally, [a good] eye and taste, the
usefulness of which is almost universal.83
This passage helps to understand why drawing had become universal, why
methods which had in the sixteenth century been aimed only at a select body of
professions (painters, architects, goldsmiths, etc.), had spread in the seventeenth
and eighteenth centuries to artistic schools and academies, and in the nineteenth, to
trades, secondary schools, primary schools and ultimately all interested laymen.
Drawing, and the perspective it entailed had become part of learning how to see, a
basic ingredient to a level of taste which was seen as equivalent with civilization
157
itself. Ironically once perspective had become so integral a part of drawing, it
became typical to think of it as a part of drawing and hence overlook the many
titles relating to perspective as they appeared.
6. Mathematics
The changing relations between mathematics and perspective are no less complex.
Any attempt at a thorough treatment would lead far more deeply into the history of
mathematics than is here possible. For our purposes it must suffice if we outline a
few major shifts in the classification of mathematics and mention their
consequences for books on perspective.
The latter fifteenth century brought a particular fascination with the concept of
proportion which led the Dominican friar, Luca Pacioli (1494), to compose his
monumental Compendium of geometry, proportion and proportionality. For
Pacioli, perspective was a branch of proportion and for this reason his
compendium became the first printed book to deal with perspective In a
subsequent sermon in August 1508 (see p. ) he praised the universal applicability
of proportion, mentioning perspective in connection with painting in a long list of
disciplines which it affected, namely, theology, philosophy, medicine, astronomy,
chorography and cosmography, architecture, inventors of machines, painters,
sculptors, musicians, poets, rhetoricians, grammarians, lawyers, mathematicians
and the pious.
In the latter part of the century Belli (1573), wrote a book on measurement of
distance, heights and depths to which he added three books on proportion and
proportionality. This fascination with proportion as an organizing category was an
inspiration for the proportional compass or sector in the early seventeenth century
and the resulting books by Faulhaber, Bramer, etc. maintained the idea of
perspective as a branch of proportion (see below 2.1).
Meanwhile, Euclid had included surveying propositions in his Optics, and during
the mediaeval Arabic tradition, surveying emerged as an important part of optics.
With the development of perspective there were also connections between
perspective and surveying, whereby perspective became associated with
measurement in the tradition of Dürer, and actually identified with measurement
by the author of the book edited by Rodler (1531). But since Boethius it had
become customary to treat the etymology of geometry literally, to mean
measurement of the earth, (yn µέτρωv). As a result geometry and perspective were
in some senses synonymous.
However, the systematic programme of reviving classical mathematics which
began at Urbino with Commandino and Guidobaldo del Monte, meant that
perspective was increasingly listed under optics as a subalternate branch of
geometry. This process continued after Paris had replaced Urbino as the European
centre for mathematical studies (cf. p. ). Indeed, by the sixteen thirties, thinkers
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such as Descartes, Pascal and Desargues had raised the level of abstraction to a
point which implicitly required distinctions between different levels. In addition to
their high level, there emerged a level of high divulgation (e.g. Bosse),
popularization (e.g. Dubreuil), and several levels of simplification (e.g. Frobes),
which echoed in readers digest form the ideas of others.
The level of high mathematics was continued in the eighteenth century by thinkers
such as Brooke Taylor, Lambert and Euler. In the final decades of the century this
tradition led individuals such as Tinseau d'Amondas (1777, 1780) and Monge
(1785, 1795, 1798, 1799) to integrate developments in practical disciplines such as
architecture, dialling, stonecutting, (Frézier), perspective, and surveying in the
form of descriptive geometry.
In the first decades of the nineteenth century this new field evolved mainly in
Paris, through Monge (1811, etc.), Hachette (1815, 1817, 1820, 1827, 1838),
Potier (1816, 1817) and Vallée (1819, 1822, 1828), Duchesne (1828, 1829),
Olivier (1831, 1839, 1840, 1842, 1844, 1844, 1847), Leroy (1834, 1837, 1838,
1842, 1845, 1846), Bardin (1837), Mathieu (1843), Cirodde (1844), Narrien
(1846), Biston (1848), Poudra (1849). It soon spread to other centres including
Milan (Tabacchi, 1813), Karlsruhe (Schreiber, 1822, 1828, 1833, 1839), Rome
(Sereni 1826), New York (Davies 1826, 1844), Cambridge (Hayward 1829),
Berlin (Wolff 1835, 1847), Munich (Haindl 1835), Nürnberg (Gugler 1842),
Wintherthur (Ziegler 1843), Vienna (Stampfl 1847), Pavia (Pasi 1844) and Padua
(Tabacchi 1844).
Descriptive geometry now became a general heading under which perspective was
classed. Tabacchi (1813) was one of the first to relate precepts of descriptive
geometry to drawing. Cloquet (1823) consciously became one of the first to
include descriptive geometry in his New elementary treatise of perspective. As he
explained in his preface:
It happened to me on several occasions that I asked artists who told of their
desire to know perspective, whether they had any hint of the first elements
of geometry. They replied negatively saying that they had no need thereof,
that they wished to know only one perspective or rather painter's
perspective. And yet there is only one sole perspective and in my opinion
expressing such a desire would be like asking to write without wanting to
learn to read. My way of reasoning soon convinced them, but never quite
persuaded them altogether. I did, however, observe that among those who
turned to me, those who resigned themselves to study the preliminary
principles, learned perspective easily and truly, a science of which the
painter should not be ignorant.
This has led me to reduce the elements of perspective to its essential
elements and place them at the disposition of readers without any notion of
mathematics, which is fortunately quite rare. I have therefore divided this
work into five parts. The first part deals with elementary geometry which I
159
have stripped of all matters foreign to our subject, such as those concerning
the measurement of surfaces, solids, etc. The second contains purely
elementary principles of descriptive geometry, which is nothing more than
a consequence or application of the the principles of part one. The third
deals with that part of optics which concerns our subject directly, namely
optics considered with respect to painting rather than to physics. The fourth
deals with the rules of projections of shadows very necessary not only for
painters, but also for architects, designers, etc. Finally the fifth deals with
perspective which is the last and principal subject with which I propose to
deal.84
Haindl (1835), included descriptive geometry as part one of his, Course on the
science of drawing and, as mentioned earlier, Brisson (1827) developed a Theory
of shadows and perspective, which was subsequently appended to editions of
Monge: (e.g. 1838, 1847, etc.). In the second half of the nineteenth century Paris
remained a major centre for descriptive geometry with a number of further editions
of Leroy (1850, 1859, 1861, 1865, 1867) and Olivier (1851, 1863, 1866), a popular
new work by Catalan (1850, 1857, 1861, 1864, 1867, 1868) and others by Babinet
(1850), Amiot (1852, 1869), Bisson (1856), La Gournerie (1860), Hughes (1864),
Du Peyrat (1865), Dufailly (1869, 1894), Pillet (1879, 1899), Lagrange (1877) and
Martin (1897).
Cunningham (1867) in his, Notes on the historical method and technical
importance of descriptive geometry,85 assessed these developments in terms of
three trends: a move towards descriptive geometry as a science in France; in
relation to the art of drawing in Germany and an independent movement in
England, which emphasized practical geometry (fig. ). With the advantage of
hindsight it is possible to recognize further trends which offer a corrective to this
picture. For instance, in the 1850's, London also became an important publishing
centre for texts on descriptive geometry by Wooley (1850), Heather (1851), who
was translating the ideas of Monge; Binns (1865, 1867), and Millar (1878). In
New York, interest which had been sparked by Davies (1826, 1844, etc.) was
developed by Warren (1860, etc.) and Mahan (1867). In Italy, interest in
descriptive geometry was focussed in Northern cities such as Padua (Bellavitis,
1851), Turin (Tessari 1880, 1883), and Milan (Aschieri, 1883; Suini, 1886).
Meanwhile, there were four German speaking centres which emerged: Leipzig
(e.g. Bünau, 1852; Schreiber, 1865 and Wiener 1885), Berlin (Stoevesandt, 1856;
Pohlke, 1860, 1873; Wolff, 1861; Flohr, 1866); Vienna (Heissig, 1859;
Schlesinger 1871; Fialkowski 1882) and Stuttgart, (Gugler, 1856, 1875, 1880;
Böklen, 1866; Riess, 1871; Vonderlinn, 1888, 1893). Links between publishing
houses meant that works appeared in both Leipzig and Berlin (e.g. Schmidt, 1869;
Müller 1872; Papperitz, 1893) or in both Leipzig and Vienna (Peschka, 1883). A
network of mathematical centres thus emerged, which were simultaneously at the
forefront of other developments also.
160
Higher or Projective Geometry
Ancient mathematicians had distinguished clearly between arithmetic and
geometry in terms of number versus extension. The mediaeval and Renaissance
emphasis on practical geometry which equated geometry and measurement
undermined the clarity of this distinction. In the 1630's Desargues' work suggested
a more abstract approach to geometry as a study of projections. Even so almost
two centuries passed before Victor Poncelet, left behind by Napoleon, imprisoned
on the plains of Saratov (1813-1914), wrote his fundamental book on projective
geometry, which appeared in 1822. Durell (1838) wrote an early English work on
the subject. K. G. Ch. von Staudt (1847), in his Geometry of position established a
basic distinction between descriptive and metrical geometry. The next decades saw
further work by Hertzer (1865), Poncelet (1865), and Cremona (1871, 1878, 1885,
1893). Projective geometry, which also became known as higher geometry, now
emerged as a heading under which both descriptive geometry and perspective were
classed.
Meanwhile, the frontiers of projective geometry were being expanded by new
discoveries. Traditionally it had been assumed that Euclid provided the foundation
for the whole of geometry. Bolyai (1832), Lobachevsky (1840) and Riemann
(1854) demonstrated that non-Euclidean geometries were possible. French
translations of Lobachevsky (1866), Bolyai (1868) and Riemann (1870) by Houel
made these ideas accessible and forced thinkers to reconsider the nature of
projective space at the very time that the optical researches of Hering and
Helmholtz were challenging thinkers to reconsider the nature of visual space.
By the 1880's thinkers were writing on projective and descriptive geometry
together: e.g. Aschieri (1883, cf. 1895), Peschka (1883, 1889), Vries de
Hecklingen (1902), Gallucci (1935), Mondino (1961) and Nannoni (1978).
Doehlemann (1898, 1901, 1905, 1918, 1924) wrote books on both projective
geometry and perspective (1916, 1919, 1928). Schaufler (1906) wrote an
Introduction to perspective and projective geometry and more recently Morehead
(1955) wrote. Perspective and projective geometries: a comparison. Perspective is
still frequently classed as a branch of projective geometry. Other developments
have, however, shifted this classification anew.
Analytic and Algebraic Geometry
Serious interest in conic sections began in the sixteenth century with Werner
(1522) and with Commandino's (1566) edition of Apollonius and Serenus. In the
1630's, Descartes' explorations of analytical geometry (cf. above p. ), drew
attention to different kinds of lines such as ellipses, parabolas and hyperbolas
which, it was recognized were all sections of cones. Some of these properties were
explored by Descartes' colleagues, Mydorge (1631, 1639) and Pascal (1640). The
following decades saw important works on conic sections by Schooten (1646,
1656), Saint Vincent (1847), Courcier (1662) and La Hire (1673). These interests
161
continued in the eighteenth century with thinkers such as Le Poivre (1704),
L'Hospital (1707, etc.) and Simson (1735, etc.) and it was gradually recognized
that conic sections were connected with more universal principles. Murdoch
(1746), for instance, wrote Genesis of Newton's curves by shadows or elements of
universal perspective illustrated with examples of conic sections and lines of third
order, and Vince (1800), Elements of conic sections as preparatory to reading of
Sir Isaac Newton's Principia.
The 1820's, which saw the emergence of projective geometry, also saw new
attention given to conic sections. Plücker (1826-1827), for instance, explored new
methods of visualizing these problems and Ohm (1826) wrote a basic work on
Analytical and higher geometry in its elements with particular attention to the
theory of conic sections. The 1850's and 1860's saw much new activity in this
field, including Salomon (1851, 1870), Puckle's (1854), Elementary treatise on
conic sections and algebraic geometry, Gerling (1865, 1875) and Staudigl (1875).
Leipzig became a centre for these interests. Möbius (1855), for example,
introduced homogeneous coordinates in projective space. The work of Salmon
was translated from the English and appeared in a number of editions (1860, 1870,
1873, 1878, 1887, 1888, 1898). Erler (1862, 1893) wrote on analytic geometry
and conic sections. There were numerous works on conic sections: Geiser (1866,
1867), Eckhardt (1866), Drach (1867), Steiner (1867), Schröter (1867), and Grelle
(1869). These interests continued into the twentieth century with Leipzig
remaining as a centre until the first world war: e.g. Dette (1909) and Staude
(1910).
By this time thinkers were exploring connections with other branches of geometry.
For example, Rudolphi (1914, cf. 1912) published Analytical geometry of space in
relation to descriptive geometry. In Italy, there was a particular interest in
comparing analytic and projective geometry with authors such as Martinetti
(1926), Fano (1930, 1957), Campedelli (1945, 1970) and Chisini (1960). The work
of Van der Waerden (1931-1939) established algebraic geometry as a more
universal class, which subsumed projective geometry, descriptive geometry and
perspective. Van der Waerden limited himself to exploring algebraic varieties of
projective space. Weil (1962) in another fundamental contribution considered
algebraic varieties of affine space. As a result of these developments, perspective,
our chief means of visualizing the world tends to be classed under algebraic
geometry which is non-visual.
Two other basic developments in mathematics deserve brief mention. Felix Klein's
(1872) Erlangen program proposed that geometries should be classed according to
groups of transformations that can be applied without changing basic concepts,
axioms and theorems.86 This led Wolf and Wolff (1956)87 to search the secrets of
geometry in nature in terms of thirteen transformations (fig. ) while thinkers such
as Coxeter and Greitzer (1967)88 reduced these to seven basic types in their
genealogy of transformations (fig. ). Efforts to class geometry have also varied
162
considerably. Coxeter (1969)89 distinguished simply between absolute and affine
geometry. Psychologists such as Hagen (1986)90 distinguished four kinds of
geometry: metric, similarity, affine and projective. Architects such as Steadman
and March (1972),91 drawing on analogies between geometry and geography,
whereby methods of geometry become different kinds of mapping, identified six
basic types: identity, isometry, similarity, affinity, perspectivity and topology (fig.
** ). In the process perspective has effectively lost any privileged status as a
means of spatial organization.
7. Conclusions
Perspective is often described as something particularly linked with the
Renaissance which continued until the nineteenth century and then died out. In the
opening chapters we showed that this was not the case, that perspective has in fact
continued unabated to the present. In this chapter we explored an underlying cause
for its apparent demise. Perspective never became an independent concept and
was therefore subject the the vagaries of classification of four branches of learning:
optics, architecture, drawing and geometry. This had two important consequences.
First, changes in classification, particularly in geometry, have shifted the definition
of what actually constitutes perspective. In the nineteenth century, perspective
included not only one-, two-, and three-point perspective but also various branches
of parallel perspective. In the twentieth century, the scope of the term has
frequently been restricted to one, two and three point perspective, whereas all
parallel versions are classed as projections (e.g. fig.** ).92 Indeed, some would
see perspective merely as an example of dilatation, as one of a number of
mathematical transformations with no special role in spatial organization. A
second consequence has been no less dramatic. A good deal of literature
pertaining to perspective has simply been classed as part of the larger fields.
Hence, although work on perspective has continued, it has been classed as work in
optics, architecture, drawing or geometry.
Our bibliography has ignored the artificial barriers imposed by these fields,
collecting hitherto disparate materials relating to perspective. Part one has created
a framework for a larger picture of the phenomenon of perspective. Part two will
explore the consequences of this phenomenon.
163
5. INSTRUMENTATION AND SCIENCE
1. Introduction 2. Astronomy 3. Optics 4. Perspective 5. Mathematics
6. Mechanics and Physics 7. Centres 8. Modern Developments.
1. Introduction
The development of perspective had fundamental consequences for science, art,
the environment and the imagination. Each of these domains will be considered in
turn in the chapters that follow.
In terms of science, perspective stimulated the use of instruments particularly in
astronomy, optics and surveying and introduced a number of mechanical aids
including the mirror, window, pantograph, camera obscura and camera lucida.
The practical consequences of such instruments for the development of technical
drawing have already been noted (see above p. ). Their theoretical consequences
lay in focussing attention on the problem of scale and fostering quantification in
science. This occurred partly through links between perspective and proportion
and partly through the nature of perspectival representation which permitted
various scales and views of an object to be related systematically (cf. above p. ).
In the case of machines, individual parts could be segmented, and at the same time
related back to the whole. Functions could be isolated and catalogued. Thinkers
such as Leonardo da Vinci saw in these functions of machines a possibility of
cataloguing the powers of nature. Perspective thus became involved with the
development of the mechanistic world-view, with its new emphasis on
observation, experiment and measurement. We shall show that centres such as
Nürnberg, Antwerp, Paris, and London were important in this context and shall
also consider more recent developments. By way of introduction, however, it will
be useful to return to the traditions of astronomy, optics and surveying.
2. Astronomy
Ever since the Babylonians, there had been observation of the heavens and, already
in Antiquity, there were instruments to observe the apparent motions of the planets
and stars. Yet the focus of attention was on finding a pattern for phenomena such
as eclipses of the sun and moon. Since the heavens were assumed to be
unchanging, astronomy became primarily a conceptual problem of accounting for
a set of recurring events. Indeed, once a basic catalogue of stars visible to the
naked eye had been made, there was little incentive to look more closely. Hence,
paradoxically, although ancient astronomy produced various instruments for
observation of the heavens, it remained in many ways unvisual: a question of
deceptive appearances1 rather than of visual truth.
164
The development of the planisphere and astrolabe2 imposed a deductive grid on
the heavens, not unlike that of Ptolemy's projection in his Geography. Implicitly
Ptolemy's planisphere introduced a new assumption: that the same projection
principles apply on earth as in the heavens. Yet this had little impact on cosmology
until the Renaissance. The astrolabe shared these assumptions and had the added
feature that its scale for angular measurements could be applied equally to
terrestrial surveying and celestial observation. The optical commentaries of Biagio
Pelacani (c. 1390), and the perspectival studies of Commandino (1558), made
explicit the universal mathematical principles involved in these instruments, a
theme pursued by Commandino's student, Guidobaldo del Monte (1581, 1600) and
popularized by Barbaro, who took Commandino's text as the starting point for part
six of his Practice of perspective (1568). Contemporaries such as Egnatio Danti,
who wrote a perspective (1583), also designed more practical astrolabes.
The same Egnatio Danti was involved in the design of sundials for the facade of
Santa Maria Novella in Florence and elsewhere. He was working in a long
tradition. Gnomonic devices had been associated with astronomy at least since
Babylonian times. Yet, Renaissance perspectival theorists had a basic impact on
this tradition. They developed sundials into highly complex polygonal devices,
which used shadows to demonstrate anamorphic effects (figs. 48.1-49.4).
Meanwhile, thinkers such as Desargues (1643) and Maignan (1648), showed that
these instruments too were based on universal mathematical principles. In so
doing, the perspectival authors of the sixteenth and seventeenth centuries prepared
the way for Monge's famous insight of the eighteenth century that various practical
applications in sundials, stonecutting and surveying all had a common theoretical
basis in (descriptive) geometry. Perspective focussed attention on the theoretical,
mathematical aspects of instruments and thus helped make them an integral part of
the scientific revolution.
3. Optics
The optical tradition also played its role in these developments. Euclid's Optics,
although concerned primarily with psychological aspects of vision, dealt with
surveying problems in four propositions. This introduced important links between
what one sees and measures. Among the Arabs (e.g. Al-Farabi),3 and later in the
Latin West (e.g. Gundissalinus),4 these evolved into links between what one sees
and what one measures with instruments. By the latter thirteenth century Witelo, in
his optical thesaurus, could describe how it is "possible for a plane mirror to be
positioned in a room such that in it are seen those things which recur in another
house or places or streets" and explain that this could be done "using an astrolabe,
or quadrant or some other instrument for the certification of sight."5
Criteria for the certification of sight to guard against the potential deceptivenes of
vision, had been a concern among the Stoics.6 Witelo's claim that one could use
instruments in this process of certification marked an important advance. It meant
that optical theorists were developing criteria for testing the veracity of visual
165
images at about the same time that artists began painting images which could be
tested in terms of optical veracity. Hence Witelo's concerns went hand in hand
with a new interest in naturalism introduced by the Franciscans, and which Duccio
and Giotto developed a generation later, creating what we would term visual
metaphor (see below p. ). Indeed, Witelo's use of a mirror to record what was
happening outside an enclosed space, presaged in an uncanny way essential
elements of Brunelleschi's demonstration of perspective nearly a century and a half
later.
The optical tradition linked what one sees and what one measures with
instruments. The advent of perspective linked what one sees, measures with
instruments, and what one represents. In the latter fifteenth century, with
Francesco di Giorgio Martini, this amounted to little more than physically
recording one's measurements on an interposed rod or plane. In the sixteenth
century, these links between optics, surveying and perspective increased
dramatically. For instance, Gemma Frisius (154 ) explicitly described how an
architect or painter could use his surveying instrument in drawing architectural
views, townscapes and topographical maps.7 In the latter sixteenth century the use
of surveying instruments for drawing views and maps had become common
practice. Indeed, Bassentin (1555) could claim that instruments were essential for
proper measurement:
Since it is not at all possible that the sense [of sight] and reason can know
well the true quantity of acute and variable angles, it would be very
difficult to comprehend the true quantity of a thing by the science of optics
(perspective) alone. For this reason the ancient geometers and measurers
invented certain artificial instruments and by means of these made it
possible to know the quantities of things easily with the certitude of these.8
Bassentin mentioned the use of various instruments for these purposes, including
the quadrant, geometrical triangle, Jacob's staff, geometrical rod and the astrolabe.
With authors such as Bartoli (1564), the quest emerged to measure everything,
lines, areas and volumes and to represent these systematically. The quest emerged
also for a single instrument which could achieve this. Besson's (1567) cosmolabe
was an early attempt. It was designed to record all dimensions of planes and
heights geometrically, as well as descriptions made by perspective and surveying,
to describe the stars of the heavens on a globe and to transform regular paintings
into anamorphic ones.9 By the end of the sixteenth century, the military
advantages of these surveying instruments with perspectival applications had been
clearly recognized by Specklin (pl.58.4,1589) and Romano (1595), an approach
which Hulsius (1605, pl. 58.1) and Faulhaber (1610) pursued.
4. Perspectival Instruments
Mirror
166
Meanwhile a number of perspectival instruments had emerged, which played an
important role in making vision and representation into quantitative activities. The
simplest of these perspectival aids was the mirror which had interested Witelo, and
which Brunelleschi used in his original perspectival construction as suggested by
Manetti10 and according to accounts by Filarete:
look at a pavement of square blocks of wood that is stretched out in front of
you.... All the sides are equidistant from one another and [yet] looking at
them it will seem that they are greater and less, such that those which are
closer to you will appear more equal and to the extent that they are more
distant, the more they appear attached together in such a way that they all
appear to be one. And if you wish to consider the matter better, take a
mirror and look into it. You will see clearly that it is thus. And if they were
directly in front of the eyes they would all appear equal. And thus I believe
that Pippi di ser Brunellescho, the Florentine, found the way to make this
plane, which was truly a subtle and beautiful thing, which finds by
demonstration that which shows itself to you in a mirror.11
Whether or not the mirror actually led Brunelleschi to arrive at his rule has been
sufficiently discussed in the secondary literature.12 For our purposes it is of
interest to note that Leonardo may have used plane mirrors in his painting practice
which may account for paintings such as the Woman at her Toilet (fig. 53.1) by a
member of the school of Fontainebleau, which shows a face reflected in a mirror.
In any event, the idea remained, and at the turn of the seventeenth century the
mirror recurred as a perspectival aid in Stevin's treatise (1605):
The description of the image (which induced us herebefore to define a
glass) appeared so suitable to his Princely Grace, that he wanted not only to
imagine such an image in a glass, but also actually to draw it therein, and to
this end, he had a glass made in the way shown in the annexed figure,
where A denotes the glass (which was the glass of a large crystal mirror),
pivoting about the hinge B, so that it may be put as straight or inclined as
desired and fixed by means of the small screw C. The hole through which
one may look is D, which can be pushed nearer to or further away from the
glass and be fixed with the small screw E. The glass may also be set higher
or lower and then be fixed with the small screw F. It seems it may be said
in truth that postures of men cannot possibly be drawn so perfectly at sight,
without a glass.13
According to Stevin, all this was the idea of his prince (fig. 53.3). Was this
actually his invention or might not this reflect Brunelleschi's original instrument?
Mirrors continued to hold their fascination. Salomon de Caus (1612) entitled his
treatise, On perspective with the reason of shadows and mirrors. Hamilton (1738),
in his title, referred specifically to: reflections by polished planes. Philips
Jacobszoon (1775) entitled one work Introduction to the perspective of mirrors
and wrote another (1780), in order that, using the laws of perspective, one can
167
represent all objects in flat mirrors. At the end of the eighteenth century, Martius
(fig. 55.4) produced another descendent of Brunelleschi's device. Reflection
remained a theme in the titles of Dennis (1876, etc.), Heyn (1885), and Fuchs
(1902).
It is important to recall that not only plane mirrors were used. A fourteenth century
Boccaccio manuscript (fig. 52.1) showed a woman using a convex mirror in
painting her portrait. It is likely that the image depicted on a convex mirror by
Petrus Christus (fig. 53.2) was achieved by similar means. Indeed, it may well be
the case that the "curvilinear" perspective in Fouquet (fig. 53.30 and Witz (fig.
53.4) was also achieved with the help of convex mirrors. Rodler (1531, 1546) is
one of the few authors who specifically discussed the use of convex mirrors with
respect to perspective.
Window
The perspectival window (velo, rete, pariete), was by far the most popular of
perspectival instruments. Alberti (1434) claimed that it was indispensable for
perspectival construction.14 Piero della Francesca (c. 1480) described it, Leonardo
drew it (c. 1490), Dürer (1525) published it, and via Barbaro (1568), it
subsequently became known as Dürer's window in Italy. Dürer's student, Rodler
(1531) used the window for landscapes, an idea which found both military15 and
practical applications (fig. 58.1-2).
The window became much more than a simple mechanical aid. According to
Danti (1583), Tommaso Laureti produced a model window specifically to
demonstrate the principles of perspective, an idea subsequently taken up by the
French Academy of Sciences. As early as the 1490's Leonardo da Vinci devised
games which used the window principles to improve one's judgment of distance.16
Later authors such as Accolti (1625) and Bosse (1648) used the window to reveal
reciprocal relationships of size and distance and as a tool for imposing a
geometrical framework on nature. This made possible the equations between
optics, geometry and perspective, which were taken for granted until the
nineteenth century and have continued to the present (cf. above p. ).
Filarete described a variant of the window method involving a string, which Dürer
published, and which Danti (1583) again popularized in Italy (fig. 55.1). Pfintzing
(1598) took up this method and reported on improvements introduced by Hans
Haiden (c. 1590, figs. 54.5-6). This version of the window principle was adapted
by Marolois (1614, fig. 55.2), and remained popular throughout the eighteenth
century, as witnessed by Martius (1789, fig. 55.3-4). Dürer also published a third
version of the window principle (fig. 54.1), the military implications of which
were explored by Faulhaber (fig. 54.3). Such versions of the window principle
allowed one to take a foreshortened view of a fort and work backwards in
determining the layout of its ground-plan, thus illustrating practically the principle
168
of reversibility. The effects of geometrical transformations of images could now be
followed.
The window had other functions. It became a standard means of demonstrating the
principles of the legitimate construction to such an extent that Benedetti (1585)
could equate the two. Nor did this popularily diminish in the seventeenth century.
The window now served to demonstrate the complexities of intersecting planes:
not only the interplay between patterns on the floor and window, but also between
patterns on the ceiling and window, or what happens when the floor is tilted
upwards and downwards. Aleaume (1643) was among the first to study these
conditions systematically (figs. 30.1-4). The way had been prepared by Marolois
(figs. 31.1).
Desargues (1636, etc.) explored the consequences, for the implication was that all
these practical instances were concrete examples of some more universal principle
of interesting planes. This realization did not make the window obsolete. It
continued to be a standard item in the introductions to treatises on perspective.
Eighteenth century thinkers such as Hamilton (1764) produced ever more elegant
illustrations of practical examples of intersections (fig. 31.2). Monge's
breakthrough was, in a sense, a new way of relating the practical window to the
abstract principles underlying it (fig. 31.3). The window, then, was much more
than a simple tool for perspective. It was a means of visualizing mathematical
principles of planes and, it could be claimed, made possible a whole school of
visual geometry (anschauliche Geometrie) as later developed by Hilbert.17 As
such, the window proved as much a tool for abstraction, as it was an aid in
concrete representation.
Pantograph
The window also served for systematic alterations in scale. But for this purpose
another instrument was developed. Lencker (1571) designed a prototype which
involved rulers and compasses (fig. 56.1). Marolois (1604) designed a second
prototype (fig. 56.2), which was subsequently made famous by Scheiner (1631)
and appeared in ever more elegant versions in the eighteenth (fig. 56.3) and
nineteenth centuries (fig. 56.4).
Camera obscura
During the middle ages, the camera obscura was used to demonstrate optical
principles by Alkindi and Alhazen.18 In 1285 Guillaume de Saint Cloud used it in
observing a solar eclipse.19 In 1342 Levi ben Gerson, at the court of Avignon,
used a camera obscura in combination with a Jacob's staff in studying a solar
eclipse.20 By the end of the fifteenth century, the camera obscura was being used
for a variety of optical demonstrations. Leonardo da Vinci devoted over 270
diagrams to it.21 Cesariano, in his edition of Vitruvius, reported a device found
out and verified by the Benedictine monk and architect, Don Papnutio, which:
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if it be properly fixed in a leaf of a door or in front of a window shut, so
that no light may enter, and if you have a piece of white paper or other
material upon which everything passing through the aperture may be
represented, you will see everything contained in the earth or sky according
to the pyramid found through the aperture and with their colour and
forms.22
Beginning with Porta (1558, etc.), the camera obscura began to be recommended
specifically as an aid to representation.23 In the seventeenth century, this idea was
taken up by the Jesuits such as Leurechon (1626), Bettini (1642, fig. 57.2), Kircher
(1646, fig. 57.1), and Zahn (1665), and also attracted the attention of important
scientists such as Robert Hooke (1669) and Robert Boyle (1669). This continued
in the eighteenth century, when Brander (1764, 1767, 1769) developed camera
obscuras in combination with microscopes and telescopes, and Häseler (1779)
developed a version in keeping with the theories of Euler. The artistic applications
of the camera obscura also became ever more widespread. Gravesande (1711)
described a complex portable version in his treatise in perspective. Nollet (1735)
described another portable versions. The Encyclopédie listed a number of versions.
How widespread its use had become is suggested by a textbook in landscape
painting in 1796:
A good number of persons apparently believe that one can reproduce a
place most correctly using a camera obscura and it is no doubt true that I
achieve a proper representation of a place by this means. Even so, it is
much more beautiful and better when I draw from Nature directly and
without the help of a camera obscura....
The camera obscura is primarily a good tool for amateurs and those who
cannot draw from Nature directly or do not wish to learn how to do so.24
Camera Lucida
In the nineteenth century the camera obscura continued to be used but artists
turned increasingly to a new invention, the camera lucida invented by Wollaston
(1807) and developed by Amici (1823), Dollond (1830) and Chevalier (1830).
5. Mathematics and Proportion
Taken in isolation any one of these perspectival instruments might readily have
been dismissed as mere mechanical aids, simple technical shortcuts with no
relevance for high level theory and science. By the end of the fifteenth century,
however, a larger context was emerging. Luca Pacioli (1494) saw perspective as
intimately connected with matematical proportion, and saw instruments such as the
ruler and compass as a means of achieving this. With respect to proportion be
claimed:
170
Perspective, if one regards it properly would certainly be nothing if this did
not accompany it. Which is amply demonstrated by the monarch of
painting of our time, Master Piero della Francesca...Bellini, Malatini,
Botticelli, Luca and Pietro da Cortona and Melozzo da Forli who, always
proportioning with ruler and compasses bring their work to admirable
perfection in such a way that they represent themselves as divine rather
than human in our eye.25
He went on to claim that number, measure and proportion were basic to all the arts
and sciences. These ideas he pursued on 11 August 1508 when, in the church of
Saint Bartholomew in Venice he gave a sermon on proportion claiming that it
applied to philosophy, physics, natural philosophy, medicine, astronomy,
geography, painting, music, rhetoric, law, ethics and religion as well as
perspective. In his mind, proportion was a key to all human knowledge.26
Already in 1494 Pacioli had taken a further step in claiming that the eye on its own
was unreliable and that one needed instruments to achieve correct proportion and
perspective:
With the mechanical arts, considering all the exercises and trades, one does
not see faithfully by the eye alone. If you take from their hands the square
and compass with their proportion, they do not know what they are
doing.27
Nor was he alone in this view. Leonardo made similar claims.28 Caporali (1536),
in his edition of Vitruvius, also assumed a necessary link between instruments,
measurement and perspective. The compass, he claimed:
is more necessary for the measurements of geometry and perspective than
any other instrument because, with this, all lineal demonstrations are
measured and the angular things to which one extends the terminations of
lines and divisions...as is well known to the expert line makers who are
especially perspectivists.29
In this context we see in a new light Dürer's treatment of perspective in his
Instruction in measurement...using the ruler and compass (1525), and similar
works by Rodler (1531) and Lautensack (1567). Instrumentation and perspective
were now twin keys to universal measurement.
The compass and ruler remained important. In 1560, Tartaglia published the fifth
part of his General treatise of numbers and measures...in which is shown the way
to execute with the compass and ruler all the geometrical problems of Euclid and
other philosophers. The latter sixteenth century also saw the development of at
least three new kinds of compasses to deal with this bold task of universal
measurement.30 One of these was developed by Fabrizio Mordente in the 1550's,
while on a great journey which took him to India, Spain, Portugal, England,
171
Belgium, France, Germany, Czechoslovakia and Austria. It had four moveable
points along a two-pronged compass. In 1572, he presented a version of this
compass to the Emperor Maximilian. In 1575, with the accession to the throne of
the new emperor, Rudolph II, he presented a new version of the compass.31 In
1584, Mordente dedicated a book on this compass to the emperor, explaining that
it dealt with all the problems of Euclid.32 The book contained chapters on lines,
surfaces, bodies and distances and showed how the compass was intended to be
used in conjunction with a ruler on which were inscribed lines of various
proportions.
The fascination with proportion33 had led in the meantime to the discovery of
various kinds: arithmetical for the simple division of lines, geometrical (based on
square roots) for determining areas; stereometrical (based on cube roots) for
determining volumes,34 and still other types for determining relations between
different sizes of polygons or specific gravities of metals. In the first half of the
sixteenth century, these lines were usually discussed in isolation in specialized
treatises. In the latter sixteenth century, the growing quest for universal
measurement led to these various lines being combined on a single ruler, which
could then be used in conjunction with Mordente's compass or other instruments.
A second type of compass consisted of two adjustable rods which intersected to
form an X shape. Leonardo da Vinci termed this a proportional compass although
it was also known as a reduction compass because of its use in reducing circles to
different scales. By 1566, the Augsburg instrument maker, Christoph Schissler,
had designed a more complex version which served for the division of lines and
circles, as well as inscription of regular polygons.35 The various lines of
proportion were now being applied directly to the compass. The evidence of
Coignet, the town accountant and gauging master of Antwerp, attests that this was
not an isolated case; that there was widespread knowledge of a reduction compass
with as many as six basic functions.36 A manuscript attributed to Lencker, and
bound with a copy of that author's work on perspective, lends weight to this
view.37 An elegant version of this compass was developed by Jobst Bürgi in the
1590's,38 and became associated with his name following a publication by Hulsius
(1604).
Perspective continued to play a role in these developments. Besson (1571) outlined
an early version of a third type of compass, which consisted of two rulers joined by
a pivot in his Description and use of the Euclidean compass including most
operations made in geometry, perspective, astronomy and geometry. Danti (1583),
in his treatises on perspective described another early version for the inscription of
regular polygons and described the systematic transformation of geometrical forms
and solids as part of the perspectivists' task (see above p.
). The manuscript on
perspective, attributed to Lencker, described a more complex compass with six
functions.39 By 1597, Galileo had begun to develop his own version of such a
compass which he published in 1606.40 Coignet described a compass with as
many as twelve functions41 which may or may not have antedated Galileo's. Of
172
interest for our purposes is that Faulhaber (1610) illustrated the Galileo type and
Bürgi type compass along with a perspectival window on the title page of his New
geometrical and perspectival inventions. In France, the proportional compass was
described in treatises on perspective by Vaulezard (1630, etc.), H‚rigone (1634),
Bosse (1648), Huret (1670, etc.), Chales (1674). Elsewhere there were further
works by Leupold (1713), Lambert (1752), Taylor (edited by Kirby 1761) and
Phélippeaux (1819).
All three versions of the proportional compass were logical developments of
attempts at universal measuring instruments mentioned earlier, and hence
integrated the measurement of lines, areas and volumes. From the battlefield they
included a line of metals, which could be used to compute equivalences among
metals of different densities. Meanwhile, the early renaissance had seen the
development of geometrical play (de ludo geometrico), whereby regular shapes
were transformed. Alberti and Piero della Francesca explored these
transformations in two dimensional terms. Leonardo made this into a more serious
game of three-dimensional transformations involving both diagrams and models.
These became part of the perspective tradition and these too were incorporated into
the functions of the proportional compasses. These instruments thus served in
bridging abstract and concrete problems of mathematics as well as offering
solutions to problems in accounting, gauging, gunnery and surveying all of which
combined to create a sense of universal mastery, to which scientific theory
subsequently laid claim in the seventeenth century. Indeed, we would maintain that
this universality of practice made possible the very conception of a universally
applicable theory, and formed the basis of the mathematical sciences which
emerged in the seventeenth century (cf. p. ).
6. Mechanics and Physics
The nature of perspectival representation played its own role in the development of
a universal concept in science. In the thirty years between 1485-1515, Leonardo
da Vinci discovered that perspective was much more than a means for producing
three dimensional effects. It enabled representation of complex organic forms
such as the human body in methodical terms: from different viewpoints, as a
whole, and in relation to its parts, with a result that the functions thereof could be
made manifest. It offered the same possibilities with respect to machines, which
led to a catalogue of different mechanical functions. As Reti has shown, Leonardo
explored 21 of the 22 elements of machines later listed by Reuleaux: including
screws, keys, bearings, pins, axles, couplings, friction wheels, toothed wheels,
flywheels, ratchets, brakes, pipes, valves, cams and pulleys.42 These elements
provided him with a means of explaining different kinds of motion such as
hoisting, dragging and rolling. Not content to stop here, he wished to find the
principles underlying these elements, which led him to develop a concept of four
basic powers of nature: weight, force, percussion and motion.43 Convinced that
173
these same principles underlay human movement, he decided to preface his treatise
on human anatomy with a work on mechanics and the elements of mechanics.44
Proportion and perspective combined to make these insights of fundamental
importance. Leonardo believed that proportion underlay everything and therefore
set out on a quest to measure not only lines, areas and solids but all the forces of
nature in these terms: "Proportion is not only found in numbers and measures but
also in sound, weights, times and sites and whatever powers there be."45 He
became convinced that these powers of nature obeyed a proportion that was
pyramidal and perspectival.
At the same time, his studies of perspective led him to recognize that only the
visual was measureable, which forced him to redefine his goals. Traditionally
concepts such as motion had been ambiguous in that they included both mental
and physical change: i.e., growth and decay, disturbances of the mind and dreams,
as well as motions of balls and projectiles. Leonardo was aware of these, but
recognized that they could reasonably be reduced to two kinds: visible and
invisible.46 And he decided to limit his studies to visible motion, indeed, to make
the visible his standard, which explains why he rejected alchemists, astrologers
and others who based their claims on invisible things.
The decisions had basic implications for cosmology, which traditionally had
emphasized the four elements and used their tactile qualities of hot, cold, dry, wet
as basic characteristics of a world defined by substance which, although described
by organic metaphors of growth and decay was ultimately static, qualitative and
hierarchical. Thinkers such as Aristotle had discussed weight, force, percussion
and motion, but their function had remained incidental in a world view dominated
by the four elements.
Leonardo focussed his interest in the four elements on their visual rather than their
tactile qualities. He added tracers to air in order to make visible flow patterns
therein. He also added tracers to water and assumed that the flow patterns therein
were slow motion versions of what happened in air.47 He studied falling water and
found pyramidal, perspectival effects of percussion which paralleled the pyramidal
perspectival percussion of sand on a board.48 This attention to visible rather than
tactile qualities shifted concern away from their substance as elements, to their
function in terms of the four powers. The traditional quest for qualitative
descriptions, which were hierarchical was thereby replaced with a search for
quantitative dimensions which were a hierarchical. Leonardo insisted that the
universe was not at the centre of the universe, but at the centre of its elements.
Thereby he was able to argue that the moon was also at the centre of its elements
and that this principle, applied to all the planets and stars.49 Conceptually, this
breaking of the chain of being was of greatest importance although it would take
the writings of his contemporary, Copernicus, and subsequently, Galileo, to
explore the larger consequences thereof.
174
Leonardo introduced another change that was equally fundamental. For, while he
continued to discuss the four elements, he focussed attention in the four powers.
Hence, while he continued to pay lip service to organic metaphors, mechanical
metaphors now dominated his concerns.50 As Dijksterhuis51 has shown, such
metaphors were not new. They had been used since Antiquity. What was different
in Leonardo's case was a direct link with the visible world achieved through
proportion, perspective and instruments. This served to bridge theory and practice
and transformed what had traditionally been loose metaphors into visual
hypotheses about the nature of matter and motion which were open to quantatative
testing. Which set mechanics, physics, astronomy and cosmology on a new course
culminating in early modern science. The scientific revolution is often described as
if it occurred primarily in the realm of astronomy. It owed as much to disciplines
such as surveying and geography which, combined with perspective, established a
vision of universal measurability, which could be applied in the heavens as it is on
earth.
7. Centres
In an earlier chapter we have already emphasized the role of centres such as
Urbino, Nürnberg, Antwerp, Paris and London, in the development of perspective
and have mentioned some connections with science. It is useful to return to these
centres at this point, to note that they were also centres in the development of
instruments, for these combined activities help us to understand why these centres
played a special role in the emergence of early modern science.
At Urbino, (fig.38) already in the latter fifteenth century, Piero della Francesca,
was emphasizing not just an abstract mathematical approach to perspective, but
one which could be demonstrated using surveying methods and perspectival
windows. He also relied on compasses, as we know from the passage in Pacioli,
cited earlier. Francesco di Giorgio Martini also used both surveying instruments
and compasses in his perspectival demonstrations. In the sixteenth century these
connections became more significant. The same Commandino, who was active in
perspectival theory (1558), was
URBINO
Euclid
Apollonius
Archimedes
Francesco Lauranna
Ptolemy
Piero della Francesca
Diophantus
Luca Pacioli
Nicolo Tartaglia
175
Pappus Francesco di Giorgio Martini
Francesco Maurolyco
John Dee
Federico Comandino
Christopher Clavius
Giovanni Battista Benedetti
Guidobaldo del Monte
Paolo Gallucci
Paul
Guldin
Gregorius Saint Vincent
Galileo Galilei
Bonaventura Cavalieri
Fig. 38. Theoreticians on perspective, mathematicians and instrument makers in
Urbino (1450-1600).
FLORENCE
Oronce Fin‚
Bartolommeo Genga
Jacques Besson
Pierre de la Ram‚e
Baldassare Lanci
Cosimo Bartoli Silvio Belli
Fabrizio Mordente
Daniello Barbaro
Giorgio Vasari
Latino Orsini
Michel Coignet
Egnazio Danti
Agostino Ramelli
Giorgio Vasari, Jr.
Ostilio Ricci
Francesco Pifferi
Lorenzo Sirigatti
Galileo Galilei Lodovico Cardi
Fig. 39. Links between Florentine theoreticians of perspective and makers of
instruments for universal measurement leading to the proportional compass and
sector (1550-1610).
NÜRNBERG
Leonardo da Vinci
176
Bolognese or Venetian Source
Jean Pélerin
Gregor Reisch Joachim
Fortius
Albrecht Dürer
Hans Beham Erhard Schön
Hieronymus Rodler
Augustin Hirschvogel
John Dee
Heinrich Lautensack
Frederic Risner
Pierre de la Ramée
Wenzel Jamnitzer
Hans Lencker
Hans Haiden
Michael
Maestlin
Paul Pfintzing
Jobst
Bürgi
Tycho Brahe
Galileo Galilei
[Michel Coignet]
Levinus Hulsius
Benjamin Bramer
Johann Faulhaber
Fig. 40. Theoreticians in N rnberg (1500-1625).
also involved in the development of a new instrument, which was a forerunner of
the Galilean sector, while at the same time being at the centre of editing texts basic
for the mathematical foundations of science.52 Commandino's student,
Guidobaldo del Monte, was deeply involved with perspective, instruments and
science. So too was his student, Galileo, and his contemporary, Giovanni Battista
Benedetti.
There links are even more striking in the Florentine circles (fig.39), which
drew their inspiration partly from Parisian developments by Oronce Finé, Jacques
Besson and Pierre de la Ram‚e. Cosimo Bartoli (1564) used their work as a
177
starting point for his book on universal measurement, which influenced Silvio
Belli (1565). Meanwhile, Baldassare Lanci, an engineer, important for his
perspectival decorations for the theatre, also devised his own instruments intended
to serve both for surveying and perspective. Daniele Barbaro, active also in
Venice, drew directly on the work of these three contemporaries, was in contact
with Fabrizio Mordente concerning new universal instruments,53 and reported on
the use of instruments in his own treatise on perspective (1568). Latino Orsini,
inventor of another universal surveying device,
NÜRNBERG, ANTWERP, PARIS, LONDON
Georg Peurbach
Johannes Müller (Regiomontanus)
Martin Behaim
Martin Waldseemüller
Peter Apian
Sebastian Münster
Gemma Frisius
John Dee
Mercator
Leonard Digges
Walter Arsenius
Oronce Finé
Abraham Ortelius
Thomas Hood
Michel Coignet
Pierre de la Ramée
Jodocus I Hondius
Frederic
Risner
Jodocus II Hondius Abel Foullon
Fig. 41. Links between instrument makers, cartographers and geographers and
authors on perspective (1450-1600).
the latin staff (radio latino), cited the influence of Barbaro and, in turn, influenced
Egnatio Danti, important not only for his treatise on perspective (1583), but also
for his scientific instruments including a large astrolabe (now in the Museum for
the History of Science at Florence) and the sundial on Santa Maria Novella in the
same city. Danti was also important for Ostilio Ricci,54 author of treatises on
practical geometry and surveying, and teacher of Galileo. Among the most
interesting figures in this context was Giorgio Vasari Jr., nephew of the famous
author of Lives of the Artists, who wrote a manuscript recording all the scientific
178
surveying instruments in the collection of the Grand Duke of Tuscany55 and was
also author of a treatise on perspective, upon which Sirigatti based his work, ideas
of which were taken up a turn by Cigoli, the author on perspective who was friends
with Galileo. For artists, practitioners, and scientists in Nürnberg, instruments were
at least as important as we have shown earlier (see above p. and fig.40).
Hence, there were close links between authors of treatises on perspective, those
connected with new instruments and those at the frontiers of science. A list of titles
in a Treatise of mechanical instruments by Levinus Hulsius (fig. 42, 1603-1605) is
particularly interesting in this regard. Hulsius mentions Danti, Guidobaldo del
Monte and Simon Stevin, each of whom was active on all three fronts. Among the
German names we find individuals important for the rise of science such as
Peurbach, Apian, Ursus56 and Brahe, also notable for the development of
scientific instruments, alongside authors on perspective such as Dürer, Rodler,
Lautensack, Jamnitzer, Lencker, Specklin and Pfintzing. Jamnitzer, besides his
work on perspective, was responsible for new instruments for gauging and
surveying, and is recorded as having designed a whole chest of scientific
instruments.57
In this context, it is instructive to recall that a chief incentive for Regiomontanus'
move to Nürnberg in the 1470's was precisely because this city was the
Netherlands
Italy
France
Germany
Johannes Werner
1514
Georg
Peurbach
1516
Jakob Köbel
1522
Albrecht Dürer
1525
Peter Apian
1533
Hieronymus Rodler 1546
Sebastian Münster
1551
Johann Schöner
1551
Jacques Bassentin
1555
Jacques Androuet du Cerceau 1559
Abel Foullon 1564 Heinrich Lautensack 1565
Wenzel Jamnitzer
1568
Silvio Belli 1570 Oronce Fin‚ 1570 Hans Lencker 1571
Egnazio Danti 1579 Elie Vinet
1574
Michel Coignet
1581 Guidobaldo del Monte
1581 Agostino
Ramelli
1580
Latino Orsini 1583
Zacharias Lochner
1583
179
Girolamo Cataneo
1584
Simon Stevin 1586
Cosimo Bartoli
1589
Daniel
Specklin
1589
Giovanni Paolo Gallucci
1592
Andreas
Helmreich
1591
Gabriel Busca 1594 Errard de Bar le Duc 1594
Iodocus Hondius
1597
Philippe Danfrie
1597
Nicolaus Ursus
1597
Adrianus Romanus 1597
Henry de Suberville 1598 Tycho Brahe 1598
Paul Pfintzing 1598
Johan Sems/Jan Dou 1600 Fabrizio Padoani
1601
Andrea Palladio
1601 Jacques Perret 1601
Levinus Hulsius
Fig.42. List of titles cited by Levinus Hulsius in his Treatise of Mechanical
Instruments (1603-1605). The heading Netherlands includes Flanders, and
Germany includes Prague.
leading European centre for the construction of scientific instruments. In the
generations that followed, scientific instruments served to secure the cumulative
dimensions of scientific knowledge. Regiomontanus' work on science and
instruments had a direct impact on Waldseemüller, famous in cartography, Martin
Behaim, renowned for producing one of the first globes, Sebastian Münster, and
Peter Apian, whose compendium of surveying instruments and fascination with
astronomical instruments was a direct inspiration for his Antwerp collaborator,
Gemma Frisius, who proved a seminal figure on at least three fronts: at home,
through his students, Mercator and Arsenius, which led to the workshops of the
Coignet, Ortelius and Hondius families; secondly in England, via John Dee,
Digges, father and son and Thomas Hood, and thirdly in France, through Oronce
Fin‚, Pierre de la Ram‚e and Abel Foullon, individuals who, as we have noted
already, again had their impact on circles in Nürnberg and Florence.
The sixteenth century thus saw the emergence of networks between Florence,
Nürnberg, Antwerp, London and Paris (fig.41). These were due as much to the
development of standards in instrument making which transcended local
workshops, as to the spread of printing. Politics played its inevitable role. When
Rudolph II became the Holy Roman Emperor, Prague functioned as a catalyst in
this process. Hence Fabrizio Mordente, an Italian active in Venice, published in
Antwerp his treatise on a universal compass (1584), which he dedicated to the
experor at Prague. To Prague came famous instrument makers such as Schissler,
the scientist Kepler, and the astronomer Brahe. Prague drew on the developments
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at Kassel, where the Landgrave of Hesse established Europe's first astronomical
observatory, where Brahe's assistant Bürgi, developed instruments for perspective,
surveying, geography and astronomy, activities which were taken up by Hulsius
(1603-1605), Faulhaber (1610) and pursued by Bürgi's brother in law, Bramer
(1617, 1730). Albrecht (1673) developed this theme describing an instrument with
which "a building, landscape on some other object standing before the eyes can be
taken perspectivally and drawn in isolation," noting that the same instrument could
be used to "diminish or increase all geometrical and perspectival figures in any
size you wish as long as you change the foreshortened scale as desired."58
One of the subtle consequences of these developments was that geography and
astronomy became visual problems in a way that they had never been in Antiquity.
Ptolemy, for instance, in producing his map of the world relied on reports of
longitude and latitude for a number of cities. But these were based on shadow
projections, which left geography a branch of astronomy and ultimately the
determining factor was a conceptual grid, which remained unrelated to the visual
evidence of landscapes.
The twin developments of surveying and perspective in the fifteenth and sixteenth
centuries changed this by making it clear that recording a building, town,
landscape, region, province or country were all extensions of a single principle
involving changes in scale. What might be termed an inductive approach to map
making thus emerged, which began with local sites and led to more generalized
patterns with the result that geography now had its starting point in the visual
evidence of surveying and perspective. In this context Egnazio Danti's position as
cosmographer to the Medici Dukes (pl. 24.5) or the perspectival author, Cristoforo
Sorte's, role as a cartographer acquire greater significance.
The incentive to look more closely at the heavens arose from discrepancies
between Ptolemy's claims, which needed updating, and the actual evidence. It is
noteworthy that the individuals concerned with this task of reconciliation,
Peurbach, Regiomontanus, Werner, Apian, Copernicus, Bürgi, Brahe and Kepler,
were concerned with both terrestrial and celestial instruments. If a junction
between terrestrial and celestial measurement had been implicit ever since Ptolemy
wrote his Geography and Almagest as two facets of a single scheme, it now
became explicit, partly through the use of common instruments, and partly from
the recognition that the same perspectival principles applied to map and
planisphere projection.
As the sixteenth century progressed, the tandem production of terrestrial and
celestial globes became common practice. Cosmological considerations provided
another incentive to consider the heavens as a visual problem. Leonardo's
speculations about the nature of the moon, mentioned earlier, prompted him to
"make glasses to see the moon large"59 and we have several hints concerning his
attempts.60 We know, moreover, that his chief writings on vision were intended
to serve as an introduction to his great work on cosmology and astronomy.
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Whether Leonardo's early efforts in the direction of a telescope directly influenced
the subsequent attempts of Fracastoro and Digges remains uncertain.61 But such
evidence confirms that the stimulus for Galileo's breakthrough in 1609 was at least
a century in the making. And underlying this breakthrough was a shift from a
deductive to an inductive approach to astronomy.
When Galileo published his Assayer ( 16**), he included an engraved portrait
flanked by his two chief instruments the sector and the telescope. These are usually
discussed in isolation as if they represented unrelated aspects of his work. We
would argue otherwise and claim that their appearance together confirmed how
surveying, geography and astronomy had emerged as elements in a single
challenge of mapping the universe, a challenge to which perspective offered a key.
We have returned to the problem of scale considered earlier in chapter two. There
we were concerned with its importance in the so-called conquest of reality, in
leading artists to recognize that the representation of interiors, exteriors, birds' eye
views, landscapes, maps of the earth and the heavens (cf. figs. 20-27) were all the
same problem in different scales. Here we are concerned with its role in the
emergence of early modern science, and would suggest that scale might be seen as
the problem of proportion with a visual dimension added through perspective and
instruments. We would go further to suggest that a theory of perspective, and
practice of instruments, combined in introducing a visual approach to surveying,
geography and astronomy which led inevitably to a visual standard of truth.
Traditionally the shift from a deductive to an inductive method, and the shift from
a mental to an experimental approach have been described as abstract
philosophical problems. If we are right there were more concrete reasons for these
shifts, which depended on a more systematic, quantitative approach to concepts of
scale, brought into focus through perspective and instruments; concrete reasons
which also throw light on the shift from substance to function which Cassirer
sought to explain abstractly.62 For scale is seeing relations, functions.
It would be wrong to imagine, however, that the problem of scale was one of these
insights that came suddenly only then to be taken for granted. Leonardo could be
said to have introduced the problem and Galileo to have begun its serious study.
But the concept was so seminal that in a sense the whole of western science since
the sixteenth century could be seen as a continuing exploration of its dimensions.
The seventeenth century explored how one could increase the scales of visible
things in both the macrocosm and the microcosm through telescopes and
microscopes. The eighteenth and the nineteenth centuries extended these
principles.
8. Modern Developments
A whole as yet unwritten chapter would, for example, need to be written
concerning the implications of photographic perspective on concepts of scale. For
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what are lenses but systematic tools for changing scale? Such a chapter would
need include the role of photography in surveying and cartography as developed
say, by Deville (1895), and relate how World War I, which saw the first use of
cameras in airplanes, brought new questions of relating perspectival photographs
to scale maps on which accurate distances could be measured. Theoretically, these
problems had been broached by Brook Taylor (1715). Even so J. W. Gordon's
solution in Generalized linear perspective (1922) marked a breakthrough in using
perspective to simulate nature, and led to a new science of photogrammetry. This
made it possible to map unexplored country, lay out highways, locate bridges,
even provide contour surveys without the expenses of traditional surveying.
Deneux (1930) and Hildenbrandt (1759) introduced new photographic methods ,
since superceded anew with the advent of satellites.
Twentieth century architects have played a significant role in these continuing
explorations of scale. For example, Holmes (1937) showed that one could use a
photograph of a building, draw in its perspectival lines, and work backwards to
establish the measured ground plan of the original. These principles have proved
very important in the area of town planning. Danielowski (1968), for instance,
used a photograph of a street where a building had been torn down, drew in
perspectival lines and added a drawing of a proposed new building to show how it
would fit into the existing context. Müller (1979) invented an "endoscope", which
permitted one to photograph an architect's model from a viewpoint simulating a
model-pedestrian. In France, the Ministry of the environment (1980) developed
similar methods, using photo montage to demonstrate effects of a proposed
housing estate on a landscape. Jantzen (1963), developed a complex interplay
between architectural plans, models, photographs and perspectival views, which
permit one to simulate effects of replacing buildings in any given context. Hiss
(1985) explicitly related scales in photographic lenses with different scales in
architecture.
Meanwhile these questions of relating different scales have increasingly become
the domain of computers. In the early 1970's the Sutherland company, then at the
frontiers of computer graphics, simulated, in three point perspective, architect's
conceptions of buildings in various scales. A Cornell project led by Greenberg
extended this principle to simulation of a whole context of buildings, within which
a proposed new building could be moved at will.63 It also simulated different
viewpoints of an imaginary viewer within a planned context. Since then there has
been much attention to creating simulations at different levels of abstraction and
relating them to one another. The French Ministry of the environment, which also
worked with photo montages, created elaborate wire line simulations of sites
which could be viewed from various prints (1980).
Reynolds (1987), demonstrated how one could relate wire line, hidden line and
hidden surface versions of a same building. This method of providing perspectival
views of different layers of a proposed building, for which models and
photographs exist, has also been used in designing the new Museum of Man in
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Ottawa.64 A new method called radiosity developed at Cornell, enables one to
take a room with complex spatial elements and to recreate it from different
viewpoints under various lighting conditions.65 The latest methods of computer
aided design (CAD), explore combinations of real buildings and imaginary
conceptions of possible buildings. In future this could be given an historical
dimension such that computerized repertoires of ruins and monuments of the past
could inspire new representations and constructions, a systematic approach as it
were to the tendencies of post-modernism.
A full survey of twentieth century innovations with respect to perspective and
instruments would readily be a book in itself. Morgan (1950) was still able to limit
his list to nine significant methods: office, measuring points, direct projection,
Reile, perspectigraph, charts, calibron machine and photography.66 Since then
extraordinary developments in satellite photography, lasers and holography have
opened further horizons, marking new steps in systematic treatment of scale and
the automation of perspectival principles. Indeed these momentous developments
with cameras and computers may help explain renewed interest in perspectival
effects and the history thereof. And yet science is but one part of the story. As will
be seen in the chapters that follow, the impact of perspective on art, the
environment and imagination has been equally profound.
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6. ART AND REPRESENTATION
1. Introduction 2. Objects 3. Functions
6. Conclusions.
4. Narrative 5. Contexts
1. Introduction
Perspective is inevitably associated with Renaissance painting: with Masaccio's
Trinity, Leonardo's Last Supper and Raphael's School of Athens. However, if we
are to assess the implications of perspective for representation and art, it is
necessary, at the outset to emphasize how it affected both a variety of media,
notably, marquetry, fresco, sculpture, as well as painting and a variety of objects
including doors, altars, furniture, walls, ceilings as well as painted panels. It will
be useful also to explore connections between perspective and different goals or
functions of art to show that various goals essentially precluded the possibility of
perspective and thereby to suggest new reasons why perspective occurred so late in
the history of representation and specifically in a European context. We shall claim
that there were special links between perspective, literacy and the narrative
function in particular; that this interplay between perspective and narrative was by
no means straightforward; that it had consequences which inevitably undermined a
strict narrative sequence, leading to new contexts of art which we now associate
with high renaissance, mannerism and baroque art.
Ultimately perspective had artistic consequences which went far beyond this,
transforming the architecture of buildings, landscape gardens and indeed the whole
environment; changing the meaning of metaphor and illusion in ways that
provoked new avenues of artistic freedom and creativity. These will be the
concerns of the final two chapters. Here we shall limit ourselves to the
consequences of perspective on representation and art in a stricter sense.
2. Objects
In an earlier chapter we have already noted that the development of perspective in
painting was part of a larger movement in European culture which affected space
in architecture (pl. 4.1-3) and a whole variety of media, including bronze (pl. 4.4),
manuscript decoration (pl. 4.5), marble (pl. 5.2), stone (pl. 5.7), drawing (pl. 6.1-2,
4) as well on painting. Wood was another medium. Indeed, the art of marquetry
or intarsia was among the most important early contexts for perspective. Vasari
reported that "the method of joining small pieces of coloured wood together to
make perspectives"1 was introduced in the time of Brunelleschi and Uccello. In his
life of Paolo Uccello, Vasari described at further length:
When Paolo showed his intimate friend, Donatello the sculptor, mazzocchi
with projecting points and bosses, represented in perspective from different
points of view, spheres with seventy-two facettes like diamonds and on
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each facette shavings twisted round sticks with other oddities upon which
he wasted his time,the sculptor would say: "Ah, Paolo, this perspective of
yours leads you to abandon the certain for the uncertain, such things are
only useful for marquetry, in which chips and oddments, both round and
square and other like things, are necessary.2
Marquetry soon became much more than a play of chips and oddments in creating
regular and irregular solids. In rare cases, such as Urbino (pl. 74.1) or Gubbio
marquetry served as an elaborate wall decoration, simulating furniture, painted
emblems, instruments, windows and even squirrels. In Italy marquetry became
particularly popular in the choir stalls of churches such as Todi (pl. 74.2), Verona,
Bergamo, where the representation of man-made objects, books, chalices,
instruments (pl. 75.3-4) frequently alternated with man made scenes, usually
idealized views of cities. The practice also spread to furniture, which gained
importance in Germany and the Netherlands. In Augsburg, Lorenz Stoer (1567),
produced a book of perspectival examples specifically for craftsmen in wood (pl.
75.1-2), involving various semi-regular solids and ruins. Idealized ruins became a
significant theme in its own right (pl. 75.4).
In his Lives of the Artists, Vasari discussed the inlaid chests of Giuliano da Maiano
in the sacristy of S. Maria del Fiore and the marquetry portraits of Dante and
Petrarch by Benedetto da Maiano in the Palazzo Vecchio. He also mentioned the
marquetry of Giusto and Minore, Guido del Servellino, Domenico di Mariotto,
Battista del Cervelliera, Giovanni da Verona, Baccio D'Agnolo, Francesca de
Salviati and Fra Damiano.3 Even this was but a small sample of activity in the
field. The chronicler, Benedetto Dei, listed 84 workshops around 1470 devoted to
marquetry in Florence alone.4
Bronze was another medium. In the case of the doors of the Baptistery in
Florence, Vasari noted how Ghiberti "introduced a building in perspective with
great effect"5 (pl. 4.4). In the case of Donatello's bronze reliefs on the high altar of
San Petronio in Padua, Vasari recorded that they were:
executed with such judgment that masters of the art have been struct dumb
with admiration in beholding them when they have considered their
beautiful and varied composition comprising such a number of remarkable
figures placed in diminishing perspectives.6
Modern tourists tend to be slightly more blasé.
Marble was yet another medium. Donatello's famous sculptured relief of Saint
George and the Dragon on the facade of Or San Michele in Florence at once comes
to mind. Indeed perspectival images were used in different media for almost every
object. Uccello, according to Vasari, even made "a number of small pictures in
perspective for the sides of couches, beds and other things"7 in many houses in
Florence.
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Certain objects, particularly altars, played a special role in the development of
perspectival representation. In the Italian tradition, altars were typically dominated
by a central saint, often the Virgin Mary seated on a throne. By the late thirteenth
century artists became concerned with rendering these thrones spatially. In the
altars of Cimabue, Duccio and Giotto a clear progression can be traced which led,
via Daddi, Simone Martini and Fra Angelico to famous examples such as
Domenico Veneziano's Saint Lucy Altar or Mantegna's Saint Zeno Altar. The
throne, in turn, became an excuse for spatial treatment of an entire context as seen
in Piero della Francesca's Brera Altar (pl. 7.1) and altars by Bellini, Cima da
Conegliano, Cosme Tura and a host of others. As in the case of niches, vaults and
windows mentioned in our opening chapter (p. ), thrones were another of those
basic forms which became part of a cumulative heritage of spatial ingredients.
Meanwhile the Franciscan movement had focussed new attention or episodes in
the lives of Christ and the Saints which had various consequences for the history of
altarpieces. In rare cases, such as Duccio's Maestà (pl. 2.1), such episodes
dominated the back of an altar. In the case of the Master of Saint Cecilia, six
scenes from the life of the saint flanked a central panel with an enthroned
Madonna. As the fourteenth century progressed another alternative became
standard, namely, to continue having a dominant central figure flanked by two,
four or more saints, beneath which were small predellas or panels with scenes from
the life of Christ or a saint. These panels are of particular interest for our purposes
for they contain important cases of perspectival space. An early example was
Simone Martini's Saint Louis of Toulouse (Naples, Museo di Capodimonte,
c.1317), which includes five scenes from his life in these panels below the main
figure. A little over a century later there was Gentile da Fabriano's Altar of the
Adoration of the Magi (now Florence, Uffizi, 1423 with a predella now in Paris,
Louvre) and his Quaratesi polyptych (now Florence, Uffizi with its predellas in the
Vatican and Washington, National Gallery).
More dramatic were the predellas beneath Fra Angelico's Louvre Altar (14341435), Carlo Crivelli's Polyptych of Massa Fermana (1468), or the altar of Matteo
di Giovanni (San Sepolcro) which originally had Piero della Francesca's Baptism
(now London, National Gallery) as its central panel. Piero's own Polyptych of
Saint Anthony (Perugia, Galleria Nazionale dell 'Umbria, 1460) transformed this
tradition with three spatial scenes beneath and a subsequent perspectival
Annunciation (1470) above the three main panels.
In terms of perspectival effects, Renaissance altars are of special interest because
they highlight differences between approaches to space South and North of the
Alps. While the Italians were intent on representing space, artists in the North were
equally concerned with reconstructing space. In some cases, such as the
Mengelberg Altar in the cathedral at Cologne, this amounted to a three
dimensional sculpture of a scene. More often an extraordinarily detailed wooden
carving was involved, as in Tilman Riemenschneider's Altars, such as that in the
Hergottskirche at Creglingen (c. 1505-1510), the Agilophas Altar in the cathedral
187
at Cologne (c. 1520), Hans Bruggeman's Bordesholmer Altar in the cathedral at
Schleswig (1621), or the magnificent altars in Lübeck and Stockholm.
Art historians have frequently characterized the represented space of Italian altars
as Renaissance, while describing the constructed space of Northern altars as
Gothic, i.e., primitive and behind the times compared to Italy. To insist on the
contrast would lead us to overlook cases such as Michael Pacher, who was
involved in both sculptured and painted altarpieces and to ignore a whole series of
altars which combined sculpted and painted elements such as the Deocarus (14361437) and Saint Roch (c. 1490) altars, both in St. Lorenz in Nürnberg.
There is a further reason for seeing the fascination with reconstructed and
represented space as two facets of a single development, for it offers insight into a
phenomenon connected with Flemish painting, namely, the tendency to represent
figures in paint as if they had been reconstructed in sculpture, both with respect to
isolated individuals (e.g. pl. 76.1-3) and series of figures (e.g. pl. 8.1, 3-4). Had
there not been such sculptural masterpieces as precedents, the perspectival
breakthroughs in painting would have been virtually impossible. In this context
the whole paragone debate, which opposed the merits of painting and sculpture,
obscured an historical interplay which had been essential for the development of
painting.
There are striking parallels in the development of choirs South and North of the
alps, and it may well be that a similar revision of thought is necessary in this case.
Perhaps we need to see the intarsia representations of Dante and Petrarch by
Giovanni and Giuliano da Maiano in the Palazzo Vecchio, which Vasari attributed
to Botticelli, as closely related to the sculptured busts found in cathedrals such as
Ulm and Vienna. Perhaps Italian marquetry and Northern misericords should again
be seen as two facets of a single fascination with three dimensional space. If so, we
might be closer to understanding why Ghiberti, Donatello, and indeed so many of
the early perspectivists were both sculptors and artists. Sculpture provided the
reconstructions or models which made feasible their representation in space.
The full implications of these suggestions are more dramatic than may be
immediately apparent. We need to return to the claim made at the beginning of our
essay, where we drew attention to parallels between developments in Romanesque
constructed, architectural space and reconstructed space (pl. 4.1-2) which the
Gothic period developed (pl. 4.3) in cases such as the West facade of Notre Dame
in Paris, and which the Renaissance subsequently represented (pl. 4.4).
If we look more closely at the portals of Notre Dame we see that this constructed
spaced is peopled with realistic three-dimensional sculptures which,-- we are
tempted to say who--, are the direct ancestors of the sculpted portrait busts in the
choirs of Ulm and Vienna, as they are of the figures on the facade of Or San
Michele: Nanni di Banco's Martyrs, Ghiberti's St. John the Baptist and Donatello's
St. George. In short, attention to individual, sculptural realism, which Auerbach
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vividly characterized as creatural realism,8 went hand in hand with exploration of
constructed, reconstructed and ultimately represented space.
To state the problem in these terms may seem altogether obvious. Yet to accept the
proposition is to recognize the constructions and reconstructions of Northern
Gothic architecture and sculpture as essential ingredients for the representations
which the so-called Italian Renaissance made famous. From this many things
follow. Renaissance perspective would have been unthinkable without Gothic art.
The Gothic North was not behind Italy: it was exploring other dimensions of the
same spatial problems of creatural realism. Which is why perspective spread so
quickly to the North. As we have already mentioned, Van Eyck, Bellini and
Alberti were contemporaries, as were Filarete, Fouquet and Memling. So too were
Piero della Francesca and Dirk Bouts. Perspective was a European phenomenon,
and in this context it is neither mysterious or paradoxical that it very quickly
became as much, and soon, primarily a Northern affair.
Of course, some will argue that all such comparisons between North and South are
very misleading: that there is a world of difference between Van Eyck's paintings
where lines converge towards a central area and the mathematical precision of a
vanishing point as specified by the legitimate construction. Yes, the point is well
taken if early Northern practice is compared with early Italian theory. But the
opposition disappears if both regions are compared in terms of practice. For
instance, closer inspection of inlaid marquetry panels such as those at San
Sepolcro connected with the school of Piero della Francesca, reveals that their
perspectival constructions are imprecise from a strictly technical standpoint. Very
often the perspectival lines were drawn by hand rather than constructed by ruler.
This happened equally in other media. The foreshortened squares in the floor of
Raphael's School of Athens (cf. pl. 11.5) were hand drawn, and from a strictly
geometrical point of view were quite incorrect. The floor patterns further back
were grossly distorted. Such irregularities or so called errors were not simply due
to difficulties inherent in the medium. They were so universal that perspectivally
perfect works of art were virtually non-existent in the Renaissance.
Artists ignored technical perspective in its narrow sense because they obviously
soon discovered that they could achieve extraordinary spatial effects such as we
still experience in seeing the School of Athens (pl. 11.5), even if the lines were
slightly crooked and only approximately right. Which helps explain why Dürer,
who went to such trouble to learn perspective, only used it technically in two or
three of his hundreds of works.9 And this could explain why Van Eyck never even
bothered to try. What is important for our purposes is the slightly paradoxical fact
that, while perspective in its narrow technical sense was virtually ignored by
Renaissance artists,--Vasari even complains that Uccello was wasting his time in
trying to get it right,10--perspectival effects nonetheless had a seminal influence
on representation of the time.
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Thus far we have outlined these effects on a whole range of media including
marquetry, fresco, bronze marble and painting, as well as noting its significance in
the case of particular objects such as altars. The most remarkable examples of
Renaissance perspective have yet to be considered, namely, those on the walls of
churches. They were usually frescoes. Some dealt with a symbolic theme in
isolation as in the case of Masaccio's Trinity (Florence, Santa Maria Novella, c.
1427-1428). Some were portraits of famous individuals, such as Uccello's Sir John
Hawkwood (1436) or Castagno's Niccolo' da Tolentino (1456) both in the
Cathedral at Florence. Some presented events, as a single scene as did Uccello in
his Battle of San Romano (London, National Gallery, c. 1445), although in this
case he made two other versions (Paris, Louvre and Florence, Uffizi).
Yet, in a sense, all of these were exceptions for, as in the case of altars, the great
examples of perspectival wall frescoes involved story telling and cycles of images
and once again, the roots of this practice lay firmly in the mediaeval tradition. To
be sure, as Gombrich has shown,11 mural painting had its origins in early
Antiquity and elements thereof evolved in an almost unbroken tradition. Of
particular interest for our purposes, however, are developments of narrative
sequences evident as early as the ninth century in the Reichenau, and the ceiling at
Hildesheim in the eleventh which led, by the late twelfth century to that
remarkable seequence of 167 scenes from the Old and New Testaments in the
cathedral at Monreale.
It is this tradition which leads via Giotto in Assisi, Padua and Florence to the great
perspectival cycles of the Renaissance: Masaccio in the Brancacci Chapel
(Florence, Santa Croce); Mantegna in the Ovetari Chapel (Padua, Eremitani
Church, 1454-1457); Piero della Francesca in San Francesco in Arezzo (c. 14521457); Ghirlandaio in the Sassetti Chapel (Santa Trinita, 1483-1486) and the
Capella Magiore of Santa Maria Novella (1485-1490) and, of course, Raphael in
the Stanze of the Vatican (c. 1509-1516). We shall wish to examine more closely
the connections with narrative which generated these prime examples of
Renaissance perspective, but by way of context a detour is necessary.
3. Functions
One of the enduring contributions of Sir Ernst Gombrich has been to demonstrate
that the history of art cannot be seen as a single, simple line of development and
must be studied as a series of parallel and even conflicting goals: that the magical
function of so called primitive art, must be separated from that of ornament, and
mimesis. If this approach is taken in combination with the idea of different levels
of literacy it offers further distinctions between these goals of representation
which, we shall suggest, are useful in understanding why perspective occurred
when and where it did. Indeed of the six basic functions to be considered
(connecting, ordering, imitating, matching, mixing, exploring) we shall show how
three precluded, one discouraged and two functions encouraged the use of
perspective, and then only under special circumstances.
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Connecting
So called primitive art12 had a function of connecting a totem in a community
with a magical or sacred world beyond it. This connecting function meant that a
totem actually became a given deity rather than being a simple representative
thereof. A sculpture suited this function much better than a painted representation.
Because it served as a bridge between the everyday world of the tribe and a
magical world beyond, it had to be sufficiently life-like to be recognizable by its
viewers: i.e. anthropomorphism was an inherent part of the system. Yet a fully
realistic statue would have linked it too firmly to the present world and thrown into
jeopardy its connecting function with a world beyond: i.e. a restricted
anthropomorphism was also built into the system. In such a context perspectival
realism would have been more of a threat than a goal.
Since these tribal communities were pre-literate there were no canonical texts
concerning the shape and meaning of the statue. And in the absence of these sacred
texts to establish a sense of community, the sacred statues acquired protocanonical functions themselves and forged this sense of community directly.
Hence any serious deviation in outward appearance was a threat to its connecting
function because it introduced the risk that a specific god would not even be
recognized.
Since polytheism was the rule in pre-literate societies these principles usually
extended to a number of gods. As the number of gods increased, the powers which
could be attributed to a given god decreased. Such considerations meant that there
were natural controls to keep in check an indefinite extension of these sacred
images. In this context the pantheon of images which would have been possible
through perspective was necessarily a threat to be avoided rather than a goal to be
sought. The connecting function precluded an interest in this-worldly, perspectival
space, focussing attention instead on a totem which would ensure contact with a
world beyond.
Ordering
A second goal which emerged among primitive tribes involved ordering,
producing patterns and ornament beginning with simple regular lines and evolving
to ever more complex geometrical shapes. In pre-literate societies these patterns
were usually restricted in number and had sacred connotations such that they
shared partly in the connecting functions of totems. In some cases, these patterns
were applied directly to the totems, such that, both the connecting and ordering
functions were contained. A gradual distinction between the two functions was
inevitable, however. For whereas the connecting function effectively depended on
a pre-literate society, the ordering function did not. The advent of literacy simply
extended its repertoire as Sir Ernst Gombrich has so eloquently shown in a Sense
of Order.13
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Some patterns could even be given spatial characteristics. The menander fret
could, for instance, be given a three dimensional effect through a clever use of
light and shade. Yet although some sense of depth was possible, systematic
treatment of space was not. Hence ordering was another goal which discouraged
perspective in its full sense.
Imitating
The primitive mind which saw images as connecting with a magical world beyond,
believed in an identity of image and god. A next stage in civilization denied this
identity and recognized that the two were separate: that the image was at best an
imitation or representation of the god involved. If this distinction between the two
mentalities was logically simple, psychologically the distance between them was
enormous and occurred gradually during the period between c. 4000 and c. 500
BC.
The shift from connecting to imitating was closely linked with the emergence of
literacy in the cultures of Akkad, Babylon and Egypt. Thus far the connecting
function had been limited to sacred images. Now it spread to sacred texts and
those who controlled them. In Egypt, for instance, the Sacred Book of the Dead
became a repository of these magical connections as did the pharaoh. This posed
new problems for the production of images. On the one hand, if an image of the
pharaoh was to function as a (living) image rather than a representation, it had to
become fully realistic and lifelike.
On the other hand, this very realism undermined the statue's connecting function,
linking it with an other worldly realm. Instead of being recognized as an immortal
figure, it now risked being seen as representing an all too mortal figure. One
protection against this was to control viewing conditions: placing the statue in a
dark place, laden with other-worldly atmosphere under ambigous conditions.
Which is precisely what the Egyptians did. The statue in the doorway of the
Mastaba of Mereruka at Saqqara comes to mind.14
These principles, designed for a supposedly immortal pharaoh, were inevitably
extended to others in his midst. By c. 2580 B.C. these included members of the
royal household in the form of reserve heads at Giza (now Cairo, Egyptian
Museum). By c. 2400 B.C., they included mortals, such as seated scribe from
Saqqara (Paris, Louvre). As this repertoire of mortal images increased, the need to
recognize them a representations rather than (living) images became more acute.
The crisis or so called revolution came in Greece. In Sir Ernst Gombrich's
account:
when classical sculptors and painters discovered the character of Greek
narration they set up a chain reaction which transformed the methods of
representing the human body--and indeed more than that.... Narrative art is
bound to lead to space and the exploration of visual effects.
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For this reason he believes that it was:
surely no accident that the tricks of illusimistic art, perspective and
modelling in light and shade, were connected in classical antiquity with the
design of theatrical scenery. It is here, in the context of plays, based on the
ancient mythical tales, that the re-enactment of events according to the
poet's vision comes to its climax and is increasingly assisted by the
illusions of art.15
According to this account, an interplay between literature and art sparked the
Greek revolution in art, introducing a form of imitation which amounted to
matching objects in the visual world, i.e. perspectival representation. Thereafter
the Renaissance was little more than "the return to the classical ideal of the
convincing image."16 As will be clear from our opening chapter, in our view the
situation was more complex. Mimesis or imitation meant at least five different
things. We shall examine each in turn to show that none of them was synonymous
with matching in the perspectival sense.
A first meaning involved imitation of verbal narrative. If we accept Gombrich's
fundamental insight that narrative texts inspired much of Greek art, we must also
accept the consequences. Representations of verbal descriptions of visual objects
were not direct records of the visual world. They were imitations, via a verbal
filter, of Greek literature which, as Auerbach has shown, had no clear sense of
reality when compared to the Judaeo-Christian tradition. The resulting art may
have had visual effects or the appearance thereof, yet it remained non-visual in
terms of its sources. It never aimed at recording visual reality directly and as such
was never concerned with perspective.
A second meaning involved imitation of ideal concepts of objects and persons.
There is a well known story of the Greek sculptor commissioned to do a statue of
Venus who studied different virgins and the combined their features in producing
his ideal statue. Here again there was no interest in recording an individual visual
record. This was imitation via the filter of a mental visual image based on a
universal concept of Venus which, it will be noted, amounted to much the same
thing as a verbal filter. Both mental visual and verbal filters were universal and
ultimately opposed to the individuality of a perspectival record. Hence this second
kind of imitation was equally non visual.
A third meaning entailed imitation of objects in isolation. The same principles
which had led in Egypt to detailed images of the pharaoh and isolated members of
his court were extended in the second millenium B.C. to isolated animals and birds
such that we find in an otherwise primitive scene, a lion or some geese of striking
realism.17 This attempt to copy simple objects precisely continued in Greece but
usually in terms of statues rather than paintings. It was presumably to this end that
Polycleitus developed his famous canon, a statue which served as a model for
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others. Pliny also recounts the story of illusionistic grapes by Zeuxis which fooled
the birds and the illusory curtain by his competitor, Parrhasius, which in turn
fooled Zeuxis.18 These again involved isolated objects rather than contexts, and
not unlike similar effects in ornament, depended on some simple tricks of light and
shade rather than principles of perspective in order to achieve their results. More
significantly we are told that this type of realism represented an early stage: that
artists first represented objects as they were and later as they appeared.19 Had the
Greeks discovered perspective it would have been in the later period. But as will
be shown, this period also had goals inimical to perspective.
A fourth meaning involved imitation of objects using optical adjustments. This
was a possibility, against which Plato complained in his Sophist (see above pp. **
). It entailed adjusting the original proportions of statues in order that they appear
correct. Based on a theory of visual angles, this method imposed on an object a
mental concept of how it ought to appear. For it sought to integrate effects of size
and distance in the object and keep the image constant. This was a goal
fundamentally different from Renaissance perspective, which began with the
premise that objects remained constant and sought to record visually effects of size
and distance on images. For this reason the visual angles method was
paradoxically non-visual in the Renaissance sense of the image. It did not visually
record, but rather it physically adjusted objects, so that no change in the visual
appearances would be noticeable. As we have suggested, (pp. ) the same mentality
applied in astronomy. Saving the appearances was more important than the actual
causes governing them. Subjective appearances dominated over objective.
An important shift had begun. The primitive mind had projected magical qualities
onto its images. The semi-civilized mind projected its theory of appearances onto
images while the civilized mind has attempted20 to produce images devoid of
these psychological projections. And the domain of study shifted accordingly from
an unseen, magical world beyond to a conceptual world of appearances and finally
to a perceptual, visual world of objects. As long as psychological projection onto
images continued, study of their perspectival aspects could not yet begin in
earnest.
A fifth meaning of imitation involved illusionistic effects of stage scenery using
optical adjustments methods which were also affected by this problem of
psychological projection of a theory of appearances onto objects. But here there
was also a deeper problem on which we touched in our analysis of the famous
Vitruvian passage at the beginning of our essay (pp.** ). The stage settings were
illusionistic in a special sense. They involved hypothetical buildings which never
have existed in the physical world. Nor could the space they appeared to represent.
Unlike perspective which permits a measured relation between pictorial space and
real space, here the buildings and spaces produced a fictive world closed onto
itself.
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Hence mimesis was many things, and the Greek revolution introduced approaches
to art as representation which resembled matching. But ultimately these involved
imitating distorted by a mental21 visual or a verbal filter. There existed as yet no
systematic quest to record the visible world passively, rather than imposing
adjustments on it actively.
Matching
The subtle shift from imitating to matching became a conscious programme during
the Renaissance when, as Vasari noted, artists:
sought to reproduce what they saw in Nature and no more and thus they
came to consider more closely and understand more fully. This encouraged
them to make rules for perspective and to get their foreshortening in the
exact form of natural relief.22
It is important once more to stress how gradual was this process. If, for example,
we consider some of the chief themes open to artists we could list at least eight
basic visual themes in the natural world : portraits, human figures, persons at work,
persons at war, persons at play, animals, landscapes, man-made objects, and four
other verbal-visual sources deriving from literature ( myth, literature, religion,
history). Most images in the Renaissance and the chief instances of perspective
were inspired not by the visual themes (1-8), but by religion, and specifically, the
Bible, and a few books on lives of the saints. Or to put it slightly differently,
matching could involve the visual world; the visual world illustrating verbal
sources, i.e. manuscript illustration; and the visual world illustrating implicit
common verbal, as in books such as the Bible which were so much a part of a
general cultural heritage that their basic themes could be taken as implicit and
requiring no explanation. Of these, it was the final of these alternatives which
inspired the most striking cases of Renaissance perspective. To understand this we
must return to the problem of narrative.
4. Narrative
In terms of narrative, it was precisely the best known stories which generated the
classic examples of perspective. For instance, in the life of Christ, it was
particularly the Annunciation (e.g. pl. 83.1-4) or the Last Supper which became
topics of perspective, although other themes included the Birth, Adoration of the
Magi, Flight into Egypt, Preaching in the Temple, Marriage at Cana, Flagellation,
Crucifixion, Emmaus (pl. 85.2) and the Resurrection. Why should the best known
stories become the most perspectival ones?
A contrast with conditions of primitive connecting and Greek imitating is
instructive here. In pre-literate societies the statue of a god, as an object which
members of a tribe had in common, helped to define the group's communality. As
already mentioned, this limited potential variations since deviations from the norm
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involved risk that the statue would no longer be recognized. With the advent of
literacy, this changed. Texts recorded the characteristics of a given god or Deity,
thus providing a corpus of what persons knew and had in common, a sense of
communality, and since this burden no longer lay with the image, it could now be
varied. The more famous a story became through texts, the more liberties could be
taken with its representation. Perspective was a key to varying images. Hence the
best known themes also became the best examples of perspective.
With respect to the Greeks, it will seem that we have contradicted ourselves. For
if Greek narrative precluded perspective, why then should Biblical narrative
involve perspective? As Auerbach has shown23 the two traditions had
fundamentally different approaches to reality. The Homeric tales were fictions
guided by rhetorical ends of story telling, conflating myth and history, leaving no
clear relation to reality. The Biblical stories, by contrast, were based on a belief in
creatural realism, and were historical, such that their temporal and spatial
coordinates were usually clear. The interpretation of Biblical narrative given by the
Franciscan movement stressed this creatural realism. The birth of Christ was not
merely treated as a story: a real child was laid in a manger and local peasants reenacted the role of Mary, Joseph and the shepherds.
This was fundamentally different from the Greek theatre (cf. p. 2), which had
developed impossible spaces setting it apart from the physical spaces of real
architecture and everyday life. In the Franciscan movement, the story of life
became a direct extension of the story of Christ and the narrative space in Christ's
story could, and implicitly had to be extended into the space of real life. As
Christian artists of the latter middle ages explored this narrative space these
connections with physical space became ever more explicit until the possibility,
even the necessity of matching pictorial and physical space became explicit also.
Both primitive connecting and Greek imitating had been constrained by magical
and ideal considerations, which acted as filters limiting art to universals of
invisible and verbal worlds. The new concept of matching opened the horizons of
artistic representation to the particulars of the visible world, which expanded even
more through the prospect of varying.
Varying
In the case of the Annunciation, this process of varying has begun even before the
rules of perspective had been formally established, as is evidenced by Pietro
Cavallini's Annunciation (Rome, Santa Maria in Trastevere), or Ambrogio
Lorenzetti's version (Siena, Accademia, 1344), generally accepted to be the first
painting in which all the lines of the tiles converged to a single vanishing point.
After Alberti's first treatise (1434), and particularly after the advent of printing in
the 1450's, variation increased in scale. Some examples, such as the unknown
fifteenth century painter in Santa Maria Novella, continued to produce rough
empirical versions. Fra Angelico produced several variants using an open
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colonnaded space (e.g. Madrid, Prado), thus developing a form used earlier by
Nicolo di Pietro Gerini (New Haven, Yale University Collection, 1375); or another
with a portico opening into a garden (Florence, San Marco), a theme which
Domenico Veneziano (Cambridge, Fitzwilliam, pl. 7.5) also explored. Sometimes
the scene was inside on a regular pavement, as in the anonymous Annunciation in
the Gardner Collection. Sometimes it was outside on such a pavement, as in the
version by Francesco di Giorgio and Naroccio di Landini in the Yale Collection.
At other times it was outside in a green garden as in the versions by Filippo Lippi
(London, National Gallery) and Leonardo da Vinci (Florence, Uffizi).
Crivelli, by contrast, developed a spatial example from Bellini's Sketchbook (pl.
83.1-2) in his Annunciation (London, National Gallery, pl. 83.3) which was at
once symbolic of Christ's coming and at the same time a record of a papal grant by
Innocent III to the citizens of Ascoli Piceno concerning certain rights in self
government, which reached the town on the feast of the Annunciation, 25 March
1492. He thus combined information from a biblical text, a sketchbook and
historical record. More complex textual sources called for a more complex
picture, which required complex spatial arrangements made possible by
perspective.
Any attempt at classifying the full range of variants on the Annunciation would be
a large book in itself. For our purposes it will suffice to note how every region
developed its own variants on a subject. In Florence, Annunciations inside homes
were the exception (e.g. Pollaiuolo's version in Berlin, Staatliche Museum, pl.
13.1). By contrast, Flemish versions were normally indoors: sometimes in living
rooms, as in Robert Campin's version in the Metropolitan, sometimes in bedrooms,
as in Rogier van der Weyden's version in Munich, Alte Pinakothek (pl. 12.2), or in
the apses of churches, as in Jan van Eyck's version in Berlin, Staatliche Museum.
In Germany, Annunciations were also frequently in bedrooms, as in Dürer's
woodcut, and in churches as in Grünewald's Isenheim Altar (Colmar, Musée
d'Unterlinden, 1510-1515), but with very different uses of space. Meanwhile, other
Flemish versions had combined elements of the living room, bedroom and church
interior in a single, rather unlikely space as, for instance, in the Annunciation
attributed to Henri met de Bles (Cambridge, Fitzwilliam Museum). Variants of this
composite spatial arrangement became popular in Spain as witnessed by Alejo
Fernandez' version (Seville, Museo de Bellas Artes) or in Berreguete's
Annunciation (Burgos, Cartuja de Miraflores).
This tradition of using perspective to create unexpected variants of a familiar
theme was further developed in the seventeenth century, by which time varying
went hand in hand with explorations of scale. In the case of Saenredam, for
instance, nine of the eighteen construction drawings for his famous interiors
involved a single church, St. Bavo, in Haarlem (e.g. pl. 20.5) which was further
studied by De Witte (pl. 20.6), while Berckheydye depicted its exterior from
different points of view (pl. 22.1-23.1).
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In terms of narrative, varying had a two edged effect on the story-telling process.
On the one hand, it made a theme such as the Annunciation immensely rich in its
many representations. On the other hand, in focussing so much attention on a key
theme, it undermined, and even prevented interest in other elements of the story.
Perspective which grew out of narrative thus posed a threat to a story's continuity.
This was not only due to varying. It was caused also by a second feature of
perspective which we shall term emphasizing.
Emphasizing
Perspective emphasized scenes in particular ways. It exaggerated the geometry of
the man-made environment, thereby drawing a viewer's eye into a spatial scene,
while at the same time reducing individual figures therein to a diminutive size.
This was no problem in the case of idealized cities (e.g. pl. 96.3), but proved
inconvenient in a Christian tradition which focussed on Christ, Mary and various
saints. A compromise thus ensued. Individual figures continued to dominate the
main panels while perspectival scenes relating to their lives were relegated to the
predellas, as was seen in our discussion of altars (pp. ). Once the laws of
perspective began to be understood in the 1430's, artists gradually discovered
means of keeping figures in the foreground of perspectival settings. Domenico
Veneziano's Annunciation (Cambridge, Fitzwilliam, pl. 9.5) was an early example.
Piero della Francesca's Flagellation (Urbino, Galleria Nazionale dell Marche, c.
1460-1470) marked an important next step leading to the most famous cases of the
high Renaissance: Leonardo's Last Supper (Milan, Santa Maria delle Grazie, c.
1495-1497) and Raphael's School of Athens (Vatican, Stanze, 15-15, pl. 11.5).
In cases such as the Last Supper, there were psychological factors which combined
to augment this process of emphasizing. Just as in portraits where eyes looking out
of the picture continue to follow a viewer as they move to the side, perspectival
pictures with alleys, corridors, rooms or any regular spatial features also follow a
viewer as they move to the side.24 For this reason we can look at perspectival
settings in theatres and movies, which are an extension of perspectival principles,
from a number of seats. Michael Kubovy, who has explored this phenomenon, has
termed this the robustness of perspective.25
Artists such as Leonardo obviously realized that the Last Supper would work even
though its vanishing point was at a height above that of any ordinary observer.
Indeed, precisely because it could be looked at without undue distortion from
anywhere within the refectory of Santa Maria delle Grazie, was a major reason
why it was worth emphasizing this painting to the exclusion of others. The same
applied in the case of Bramante's fictive arch in Santa Maria presso San Satiro in
Milan (pl. 5.4), and Tullio Lombardo's scenes from the Life of St. Mark in Venice
(fig. 5.3). The fictive depth involved might be small, as in Piero della Francesca's
Brera altar (pl. 7.1), or large, as in Masolino's version of Herod's palace at
Castiglione d'Olona. The effects remained the same. And, as in the case of the
varying function, the emphasizing function of perspective focussed attention on
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key episodes of a narrative thus serving also to undermine the continuity of a story.
Yet a third factor contributed to this process.
Relating
In representing a story with many episodes painters were faced with a problem of
individuating scenes. Frames were of some help, but these could not give many
clues concerning the order in which scenes were to be read. Here perspectival
treatment of certain features helped to relate scenes while at the same time
separating them. We have already alluded to this problem in a quite different
context (pp. ) using the example of Duccio's Maestà (Siena, Museo del Duomo,
1288, pl. 2.1), but it will be useful to consider it again in more detail.
On the reverse side of the altar, the story begins in the bottom left hand corner with
Christ's entry into Jerusalem, moves in an up-down sequence towards the right,
then returns to the upper left hand corner again criss-crossing its way to the far
right. Three scenes with Christ and his Apostles (Washing of the Feet, Last Supper
and Meeting with Apostles) all share one type of spatial interior with beams of the
ceiling converging towards a central axis. Three scenes with Caiphais and the
priests occur in an interior with a type of oblique parallel projection. A similar
oblique parallel method applied to an awning supported by columns connects
scenes with Pontius Pilate in the bottom right and top left. These protoperspectival elements thus relate separate scenes and help us to follow their
sequence.
In the Scrovegni Chapel at Padua (1304-1307), Giotto uses the same principle. An
oblique view of an open fronted house serves for both the Annunciation to Saint
Anne and the Birth of the Virgin. Similarly, a temple with a niche serves as a
continuation between three scenes: the Ceremony of the Rods, Prayer for the
Miracle of the Rods and Marriage of the Virgin. This function of relating separate
scenes in a complex narrative explains why a few proto-perspectival elements
became stock images, which improved empirically, while other architectural
elements remained spatially awkward and unconvincing. And as we noted earlier
it was precisely these stock images which were consolidated and standardized by
the early perspective treatises (cf. pp. , pl. 2.2-3, 3.1-6).
Relating took on many forms. In his Profanation of the Host (Urbino, Galleria
Nazionale delle Marche, pl. 78.1), Paolo Uccello used two vanishing points going
in different directions in order both to separate and relate the two scenes. The same
principle was used in the Munich manuscript of Boccaccio (pl. 78.2), in the
organization of the Teatro Olimpico at Vincenza (pl. 78.3) and in the gardens at
Versailles (pl. 78.4). Hence scenes with different vanishing points could be
implicitly related by means of perspective. Scenes physically separated from one
another were also explicitly related by means of a single vanishing point. Giotto's
Annunciation in the Scrovegni Chapel in Padua (1304-1306) was an early attempt
in this direction. Masaccio--and Masolino?--developed this idea in the
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Annunciation in San Clemente in Rome, while Foppa used it dramatically in his
Annunciation in S. Eustorgio in Milan.26 Nor was the principle limited to
Annunciation scenes. Parronchi has suggested that Ghiberti used it on the doors of
the Baptistery at Florence27 and has shown convincingly that Masaccio employed
it a relating the Distribution of the Goods with Saint Peter Curing the Sick in the
Brancacci Chapel (Florence, Santa Croce, 1426-1427).28 Once familiar, the
method was used in more subtle ways. Spatially analogous scenes were related
without their sharing a common vanishing point as, for instance, in Piero della
Francesca's Annunciation and Dream of Constantine in Arezzo.
Raphael developed these principles of relating in his famous juxtapositions of
sacred and profane scenes in the Stanze. Here the situation was complicated by
typological and symbolic considerations. The mediaeval period had seen an
increasing fascination with parallels between the old and new testaments with
minor references to relevant pagan figures such as the sibyls. This inspired the
ceiling at Hildesheim in the eleventh and the great rose windows at Chartres, Paris
and York in the thirteenth. In the next centuries the pagan element29 gained in
significance to the point that Raphael in the Stanze was challenged with finding
parallels between Christian and Antique themes such as the Church fathers versus
the school of Athens. In these and other great cycles it was no longer a question of
telling complete stories, but rather of choosing key episodes in stories which could
be balanced by others.30
Hence all three basic functions (varying, emphasizing and relating), which made
perspective so powerful, had the same effects. While focussing attention on key
episodes in a narrative, they simultaneously undermined the continuity of the story
telling process. Indeed as perspective provided more complex frameworks for the
organization and comprehension of such scenes, their narrative order became less
significant and sometimes disappeared. This helps to explain what would
otherwise be two contradictory trends in the history of narrative cycles from the
time of the Bayeux Tapestry (Bayeux, Town Hall, 1073-1083) and the mosaics at
Monreale (1182), to the frescoes of Giotto in the Scrovegni Chapel (1304-1306)
and Raphael in the Stanze (1507-1513). As the treatment of space improved, the
number of scenes diminished. Monreale had 167, the Scrovegni had 53, the Sistine
Chapel had 23 scenes. The sequential order of the story telling process also
decreased in clarity. To attain a deeper understanding of these phenomena requires
examination of contexts and frames.
5. Contexts
Perspective brought with it a tendency to reduce a number of independent episodes
and include these with a single spatial context, as is strikingly illustrated in
Memling's Seven Joys of Mary (Munich, Alte Pinakothok, c. 1480), which
integrated no less than seventeen episodes beginning with the Annunciation and
ending with the Assumption of the Virgin. Similarly, in his Treatise of Painting,
Leonardo recommended that one:
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must place the first plane at the eye level of the beholder of the scene and
on that plane represent the first scene in large size and then, diminishing
the figures and buildings on various planes, as you go on, make the setting
for the whole story.31
These tendencies towards a single spatial context, containing several temporal
episodes are of particular interest because they call into question the oppositions
between painting and poetry articulated by Lessing. In his Laokoon, he suggested
that painting and poetry used completely different means and signs in achieving
imitation; that painting used figures and colours in space, while poetry used tones
in time.32 Lessing elaborated on these basic oppositions. Painting, he claimed, was
concerned with bodies, poetry with actions;33 painting with a totality, poetry with
parts;34 painting with space, poetry with time.35 It is instructive that his examples
drew constantly on Greek art and poetry and indeed might hold if restricted to a
comparison between Greek sculpture and poetry. But they do not hold for the
whole of art. Indeed, the many scenes integrated into a single spatial context as
practiced by Memling, and recommended by Leonardo, show that perspective
removed these oppositions and introduced different actions of a body, different
parts in a whole and different times in a single space as important new dimensions
of representation, which take us directly to some of the richest aspects of art in and
since the Renaissance.
For instance, the first of these, the ability to represent different actions of bodies
prompted Leonardo to make a list of eighteen basic actions which could be
painted36 and led him to explore kinematic sequences of men at work and play, a
principle which has since inspired the development of motion pictures, television
and video. The ability to represent different parts in a whole was equally
fundamental in its consequences. For it explains why photographic details of
Renaissance paintings can function as if they were photographs of complete
paintings. This principle also makes possible the game of imposing imaginary
frames in galleries and observing how each of these functions as independent
pictures. Art dealers, who sawed off sections of old masters, and then sold these
whole-sale were, of course, taking the game a bit too far.
The principle which makes these games possible is intimately connected with
problems of particulars and universals. A perspectival painting, i.e., a painting
which has a context, is based on particulars, is comprised of individual features
and has the astounding feature that its "parts" also function as wholes. Nature has
this same feature which is why we can take any scene, add different lenses to our
concern and each time come up with an independent picture. Note the connection
between particulars, individuals and independence. Note that these are also a key
to creating new frames, focussing on details and changing scales which are three
ways of describing this open process.
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It is rather important to realize that none of this is possible as long as universals
govern representation, as tended to be the case in Greece. Given universals, the
goal of representation is perfection, literally putting an end to, a totality, a perfect
totality. To remove any part of a totality is to destroy its perfection and to remove
its aesthetic potential. (Or at least in theory, although some art historians will
assure us that gods and goddesses are aesthetically the richer through amputation
of arms, legs and other parts.) Hence a commitment to universals generates only
parts dependent on a totality, which remain impersonal, static and without a
temporal dimension.
By contrast, a commitment to particulars leads to individuals independent of the
whole, which can be personal, dynamic and with a temporal dimension. Because
universals limit attention to the perfection of a totality, any change of frames
would leave out some important part of that totality; any focus on a detail would
leave the totality out of focus and any change of scale would make no difference:
which is why photographs or slides of a three inch statuette or a six foot classical
statue sometimes produce exactly the same effect. When the emphasis is on
totality there is no context and no way of inferring scale. Indeed universals, with
their commitment to perfection, produced an approach to representation which
effectively denied the importance of size, scale, context, frames and time, i.e.,
precisely those features which perspective made the central concerns of
Renaissance art and science.
Mention of time brings us to the third of Lessing's oppositions which we need to
consider briefly before returning to the connections between perspective and
frames. Lessing's claim that poetry dealt with time, while painting dealt with space
overlooked the ways in which perspective introduced spatio-temporal dimensions
into painting. The most obvious examples involved episodes in the lives of saints
as in the Memling painting mentioned above. But there were also much more
subtle examples as in Carpaccio's St. George and the Dragon in the cycle devoted
to that saint (Venice, Scuola di San Giorgio).
In the foreground of the painting, just left of centre, we see a scene with a snake
looking at a toad which looks in turn at a lizard. In a second scene, further back,
we do not see the toad, while the lizard looks at the decomposing body of a woman
obscuring most of the snake except for its tail, which forms an unexpected
necklace for the corpse. In scene three, the toad reappears just right of the centre
near the corpse of a man while the snake lurks beneath the corpse's left foot. In
scene four, the snake devours the toad, while the lizard looks on. The subject may
be unappetizing, but it suggests that Lessing's claims about time, parts and actions
in painting were undigested.
There were other subtle ways in which spatio-temporal dimensions came into play.
As we have shown the matching function led to a natural extension of the
represented space of the painting into the physical space of the environment where
it was painted. Hence, as was noted in an earlier chapter (p. 31, cf. pl. 13.1-4,
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26.1), local townscapes inevitably entered as backgrounds in religious paintings.
As these background townscapes became more pronounced they brought into
focus unexpected anachronisms, for events in the life of Christ which had occurred
fourteen or fifteen centuries earlier now stood in the foreground of a contemporary
scene. By the late fifteenth century, when Ghirlandaio did his cycle on the life of
Saint Francis (Florence, Sassetti Chapel, 1483-1486) ,he depicted the saint literally
in the squares and streets of Florence. Here, of course, the anachronism involved,
only a few centuries but even so Ghirlandaio did nothing to remove it.
Perhaps there were problems in learning to see spatio-temporal dimensions in
paintings, just as it took a long time before painters became aware of problems of
shadows caused by the sun at different times of day in their landscapes. We might
have expected the writings of Machiavelli, Guicciardini and other historians to
introduce a greater historical consciousness, which would remove such
anachronisms. Instead, the anachronisms persisted throughout the seventeenth,
eighteenth and into the nineteenth centuries, until first the camera, and then the
impressionists focussed attention on scenes limited to a specific place and time:
Paris on a rainy afternoon, Arles on a sunny morning, etc.
But long before this the anachronisms had taken on a subtler form. For as the
contemporary background slowly moved forward to dominate even the
foreground, the historical event retreated quietly into the background. By the mid
seventeenth century with Claude we (almost) need to be told that the four figures
standing in a landscape involve the story of Jacob and Laban (London, Dulwich
Art Gallery); a principle that applies equally to mythological scenes such as his
Coastal landscape with Apollo and the Cumean sibyl (Private collection, 1665).
These shifts introduced by perspective deserve much more attention. For it is
usually assumed that the development of secular art was largely due to a rejection
of the religious tradition. We are suggesting that the reverse was true: that it was
paradoxically the Christian tradition of creatural realism that combined with
perspective to create frameworks for matching which extended biblical narrative
into the physical world and made nature first a background topic and gradually a
dominant theme in the history of representation. We have shown how
contradictions between and combinations of spatial and temrporal dimensions
played a central role in these developments. And Lessing's desire to maintain the
simple polarities of painting-space versus poetry-time led him to overlook this, and
indeed other fundamental contributions of Renaissance art.
Frames
To understand this properly we need to return to the problem of frames. For the
whole phenomenon we have been describing of townscapes slowly coming into
the foregrounds of religious paintings is very much a question of frames and fully
analogous to a zoom lens which focusses on what had been a background detail,
frames it and then increases its scale until it dominates the entire scene. Which is
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also why perspectival representation leads ineluctably towards a photographic
image, where framing is almost the name of the game. We shall show that these
connections between a play of perspective and frames go back at least to the time
of Giotto in the Scrovegni Chapel at Padua (1304-106), but before doing so we
need to refine an earlier claim.
We have stressed that perspective applies not only to painting but to other arts such
as architecture and sculpture involving various media including bronze, marble
and wood. However, in another sense, perspective has special applications to
painting because in this medium it imitates effects also produced by sculpture and
architecture, and for this reason, Chastel,37 has justifiably opposed (painted)
perspective to sculpture and architecture, or perhaps more accurately, painted
perspective vies and equivocates with effects which sculpture and architecture
create, thus encroaching upon and/or playing with the frames they impose or
suggest.
This did not always happen. In the case of altars, for instance, it played only a
small role. As Heydenryk, in his history of frames has noted, Italian afterpieces
imitated architectural features and effectively became cross sections of Gothic
churches,38 while in the North "the elements of a frame were invariably
emulations of architectural elements but no effort was made to create a logical
architectural structure as had been done in Italy."39 The advent of perspective
affected the contents of altars (cf. above pp. ) and meant that various ornamental
patterns on their frames which had previously been sculpted, were now painted.
But it had little substantive impact on the function of altar frames. By contrast, in
the case of frames in the fresco cycles,40 perspective had an enormous impact.
In the Scrovegni Chapel at Padua, Giotto explored the potentials of using proto
perspectival effects to replace, or rather match (see below pp. ) architectural
structures in his concealed chapels or coretti on the east wall. But while there was
play of boundaries between architecture and painted architecture, there was
effectively none between architecture and painted narrative, where each scene was
neatly separated from the next by clear cut frames. Giotto experimented with both
problems separately in the same building. The early renaissance pursued both
experiments, discovered and formalized the perspectival principles underlying
them. The high renaissance integrated the two experiments into a new synthesis as
becomes clear if we turn to Michelangelo's Sistine Ceiling (1505-1508).
As in the Scrovegni Chapel, there is a narrative cycle. But whereas Giotto's scenes
maintained a certain uniformity in size, Michelangelo plays with their scale. In the
central portion four large scenes alternate with five smaller ones which are
flanked, in turn, by ten medallion-like scenes. In the corners there are four further
scenes making a total of twenty-three episodes from the Old Testament. Then there
are the forebears of Christ in the triangular niches and in the semi-circular niches
below these. But the complexity of the Sistine Ceiling begins, in a sense, with the
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six sibyls alternating with six prophets in painted architectural cubicles enclosed
by column-like painted sculptures and topped by painted nudes.
The cubicles function as if they were part of a wall, the orientation of which keeps
changing as we move through the chapel and constantly contradicts, or rather plays
with the curvature of the actual ceiling. The nude figures seated on top of the
columns require us to read the surface three dimensionally, while we remain aware
of the ceiling as a flat surface. If we look higher than the nudes our eyes are drawn
into an orientation 90 degrees to the side, and if we look higher still, we need to
shift our orientation a total of 180 degrees if we are not to read the second set of
nudes as falling down.
Perspective continues to play a role in the actual scenes, as in the dramatic
positioning of Haman on the cross. But its main function is now in the spaces
between scenes, in, with, amongst the frames, provoking a complex interplay
between painted, painted sculptural and painted architectural elements which,
while continuing to separate the scenes, also integrate them into a new kind of
systematic whole. Perspective now creates spatial illusions only seemingly to
subvert them, playing with and on them to increase the potential for polyvalent
readings of different scenes theoretically separated yet, systematically related.
These polyvalent readings are encouraged by the nudes and other figures whose
arms and feet continually reach and step into the neighbouring spaces. At the
same time they are held in check by the painted architectural features which
maintain some clear linear boundaries between the scenes.
The mannerist period worried less about keeping these boundaries fixed. Already
in the Gallery of Francis I at Fontainbleau, boundaries between painted, painted
sculptural and painted architectural spaces were rendered more ambiguous a) by
increasing the extent to which figures reach out beyond their given frame into
adjacent spaces and b) by deliberate introduction of actual sculptural and
architectural elements which overlap with their painted equivalents. This
encroachment of figures and overlapping of art forms and media went ever further
until it became difficult (e.g. pl. 77.1), and ultimately impossible (e.g. pl. 77.2), to
know where one stops and the other begins. Hence if the high renaissance
discovered frames and their media as realms of perspective, mannerism used
perspective to play with frameworks, anamorphically distorting them in the
process. Baroque art went further, playing with the whole distinction between the
forms of frames and their contents. By the late seventeenth century, as baroque art
moved towards rococo, the actual architectural spaces were manipulated and
integrated in order to intensify this playful destruction of distinctions between
frames and paintings, between form and content.
The experiments had begun with Giotto's concealed chapels which played with
distinctions between painted and real architecture. By the 1580's this play between
painted and architectural reality had become a major challenge for masters of
perspective, particularly in terms of di sotto in su paintings, which involved
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illusionistic ceilings such as that of Scamozzi and Sansovino in the Marciana
library in Venice (pl. 72.1). This soon found published equivalents in treatises
ranging from a single illustration in Danti's commentary (1583, pl. 72.2), to the 75
examples in a now almost forgotten collection by Has, which appeared in the same
year (1583, pl. 73.3), which provided a context for Pozzo's illusionism in Il Gesù
(1691-1694, pl. 73.1) and also prefigured uncannily the twentieth century work of
Escher (pl. 73.4, cf. 73.3).
6. Conclusions
Such examples bear witness to an extraordinary shift in the applications of
perspective, from the content of paintings to their form. For we have shown that
perspective had basic consequences for both the spaces in paintings and the spaces
of the frames between paintings. The first of these concerns led to shifts from
isolated objects to scenes in context, to scenes in the context of a secular
background and to secular scenes in a specific place and time and ultimately to
new distinctions between these realistic spatio-temporal scenes and other more
symbolic ones, where time and sometimes even space were not factors.
Meanwhile, the second of these concerns began with the varying, emphasizing and
relating functions of perspective, led renaissance artists to discover connections
between perspective and the framing process, and to focus attention on the spatial
forms of containers of paintings. As they did so, attention to the contents within
the containers dwindled, or rather it shifted from narrative episodes to symbolic
moments in the narrative which, in the next generations were reduced to symbols
almost without moment until, finally, the capacities of perspective were focussed
on form without content (e.g., pl. 73.1).
Together these two developments transformed the whole of representation. They
removed the oppositions between bodies and actions, totality and parts, space and
time which Lessing had seen as separating painting and poetry. Indeed they
revealed the limitations of Greek concepts of perfection and introduced new
horizons of aesthetics in terms of size, scale, focus and frameworks.
All this was only the beginning. By the mid-sixteenth century perspective had
spread beyond the spaces of paintings and their frames, outside the buildings that
contained them into the streets and gardens. In the seventeenth century perspective
gradually transformed the use of physical space partly so that this too could be
rendered more perspectivally, a process of transformation which gradually spread
to the whole environment. This will concern as in the next chapter before we turn
in the final section to show how perspective also transformed the landscapes of the
mind cultivating new concepts of freedom and imagination, inspiring new
developments in art which still continue.
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7. ARCHITECTURE AND ENVIRONMENT
1. Introduction 2. Italy 3. Netherlands 4. France
5. England 6. Conclusions.
1. Introduction
We have already emphasized that perspective was much more than a pictorial
revolution, that it involved other media such as wood, bronze and marble; that it
went hand in hand with the development of new man-made spatial environments,
i.e. the representation of spatial doors; was part of a larger phenomenon, which
included their architectural construction and sculptural reconstruction (pl. 4.1-2).
If the development of such spatial structures created a context for the discovery of
linear perspective, perspective in turn transformed the nature of these structures.
At the outset this was mainly by way of playful equivocations between real and
imaginary space as in the case of Bramante's Choir in Santa Maria presso San
Satiro (pl. 5.4), or Michelangelo's ceiling of the Sistine Chapel, which might be
seen as experiments in visual metaphor--see below 2.4.
As the sixteenth century progressed, what had begun in some respects as a
competition of perspectival painting versus architecture and sculpture, evolved into
a new alliance between the three media, which were coordinated in playing with
existing spaces and the creation of new ones. In the previous chapter, we showed
how this helped to explain developments in the interiors of mannerist and baroque
buildings. It soon spread to exteriors. Beginning in Italy, buildings were rearranged
to control the observer's viewpoint, in order to make things appear nearer or
further. Perspective was used to link interior spaces of villas and the exterior
spaces of gardens. However, the hilly landscapes, in which the villas were usually
constructed, imposed their own limitations on creating regular geometrical grids,
which could function perspectivally. In the North of Italy, and in the Netherlands,
where the flatness of the land imposed no such limitations, the idea of a
geometrical perspectival pattern was explored seriously. By the 1560's, Vredeman
de Vries had begun publishing books devoted specifically to perspectival fountains
and gardens.
There was great interest in these problems in France as a shown by Androuet Du
Cerceau's (1576) publications on the great chateaux of France, which included
views of gardens revealing many parallels with Netherlandish models and yet, with
a difference. Whereas the Netherlandish examples invariably spread over an area
of 100 or 200 feet, the French examples were many times larger. In 1587, when Du
Perac came to France, he brought with him many Italian trends. These combined
with existing methods to produce experiments on an ever greater scale: from the
Tuilieries, to Vaux le Vicomte, and culminating in Versailles, which became the
model for European cultural politics for over a century.
Meanwhile, in England, there emerged a very different pattern, which rejected the
geometrical regularity of the Netherlandish and French models, but nonetheless
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emphasized new aspects of perspective. Here, theories about the aesthetics of
Chinese landscape inspired fashions, which soon spread to the continent. The
nineteenth century saw new applications of perspective in terms of town planning
which continue to the present. Since then, illusionistic views, which were applied
to interiors in the sixteenth, have become increasingly popular on the exteriors of
buildings, creating new ambiguities between exterior and interior, in an
environment where perspective plays ever more subtle roles. Each of these topics
will e considered briefly in turn.
2. Italy
An awareness that images could be transformed, and/or controlled depending on a
viewpont, had come through the optical tradition, and particularly through the use
of camera obscuras (see above pp. ). The study of perspective brought with it
new attention to problems of controlled viewpoints. Brunelleschi's first
perspectival demonstration required a camera obscura like aperture. Alberti is also
reported to have made a perspectival box which required a fixed viewpoint. The
idea lingered. Marolois (1614) and Dubreuil (1642-1649) described their
construction and at least six perspectival boxes from the seventeenth century
remain in museums.2 Fixed viewoints were also important for anamorphic effects.
Leonardo (1513-1514) considered the possibility thereof and decided against it.3
But seventeenth century thinkers took up the idea and Nic‚ron, for instance, played
with the problem, in his anamorphic wall of Saint Francis de Paul, in San Trinità in
Monte,4 while another Jesuit, Father Pozzo, specifically marked a spot on the
floor, from which his fresco on the ceiling of Il Gesù was intended to be seen.5
Controlled viewpoints were also of interest in the theatre (see below pp. ).
Yet it was in the realm of architecture that this idea of controlled viewpoints
gained a wider and more dramatic significance. Michelangelo, for instance, used
the principle in designing the Piazza del Campidoglio on the Capitoline Hill
(Rome, 1538-1564, pl. 88.2), constructing the two, side palaces diverging
outwards with respect to the Senator's palace to give the impression that this is
closer than it is, as one first approaches it coming up the stairs,-- which
incidentally employ the same device --, from the Piazza d'Ara Celi, and conversely
that the stairs appear further away than they are, when one looks from the Senator's
palace back towards the city.6 The architect, Vignola, responsible for the book on
perspective edited by Danti (1583), used this principle of controlled viewpoints
even more dramatically at Caprarola, to give the impression that the fortress
shaped palace was closer and more domineering than it actually was (pl. 98.1).
Below the main house at Caprarola, he experimented with the spatial effects of a
long alleyway integrating architectural and natural features. He pursued these
experiments at the Villa Lante in Bagnaia, the Villa Giustiniani in Bassano, the
Villa at Bomarzo and the Farnese Gardens in Rome.7
Others explored a combination of these effects, i.e., making the long alleyways
converge in order to play with normal effects of perspective. Shepherd and Jellicoe
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have, for instance, analyzed three classic cases beginning with the Villa Dona dalle
Rose at Valzanzibio where:
the effect of distance is obtained by a gradual closing in of the elements,
variety of the subtle breaks in the hedges and their freedom as they merge
into the countryside, unity by the ribbon of grass, and a climax in the
gigantic stairway of the fir avenue climbing the hill beyond.... At Collodi,
the stunning widening of the cascade towards the top gives the effect of
added distance above, and from below exaggerates the steepness and
violence by bringing the top very much nearer. At the Villa Aldobrandini
(pl. 88.3-4), at Frascati, both the lines and the levels of the cascade
converge to a point in the topmost loggia. Here sits my lord, enjoying the
apparent spectacle of the water tumbling dizzily in one vertical plane
between the columns. Other views of the same cascade have very little
drama.8
The Aldobrandini garden is of particular interest because it links a controlled
viewpoint inside a building with a complex view outside which functions,
ultimately as an extension of the architecture.
Such deliberate manipulation of perspective to create spatial effects was
subsequently exploited in baroque architecture. For instance, in Rome, the rows of
columns which join the oval arcades with St. Peter's diverge in the direction of the
Church, such that the great cathedral appears closer than it is as one approaches.
Conversely, as one leaves, the distance of the square is exaggerated. As if to play
with these effects, Bernini reversed them in his famous staircase, the Scala Regia.
Here the columns converge in order to increase apparent distance as one climbs the
stairs, and telescope distance as one leaves.9 As Sinisgalli has shown, Borromini's
experiments in the Palazzo Spada (pl. 5.5) stood in a long tradition.10
Indeed, by way of context, it is important to recall that no less than four different
traditions lay behind the approaches of the Renaissance. The most immediate of
these was the mediaeval enclosed garden (hortus conclusus), which relied on
certain geometrical regularities for symbolic and religious ends.11 A second
tradition, also cosmological, was linked with ideal cities, such as Plato's Atlantis,
or idealized landscapes, such as Dante's vision of Inferno (c. 1314), or Francesco
Colonna's description of Cythera in the Hypnerotomachia Pamphili (1499). A
third, involved the Roman tradition of gardening which had involved complex
extensions of domestic space, with fountains, regular alleys of colonnades and
works of art. Renaissance thinkers were inspired by this tradition. Androuet Du
Cerceau, for instance, published reconstructions of the gardens of Antoninus (pl.
92.1), Ovid and others as examples of perspective in his books of Roman
monuments. The resemblance between the secret garden of Pope Paul III,12
constructed behind the Vatican (1534), and such reconstructions, can hardly have
been a coincidence.
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A fourth tradition involved theatre. Already in the fifteenth century, there were
important connections between Brunelleschi's perspectival interests in
representation and his spatial reconstructions for sacred plays.13 In the sixteenth
century, these connections evolved greatly with Buontalenti's activities at the
amphitheatre that joined with the Pitti palace in one direction, and the Boboli
gardens in another. His perspectival scenery linked the space of the palace and
countryside, and in the amphitheatre, literally played on distinctions between
interior and exterior, thus extending artifice and play directly into nature.14
Nor was this limited to the stage. For the same Buontalenti worked with
Bernardino Poccetti on the ceiling of the large grotto at the Boboli (1583-1588),
which was simultaneously a construction integrating architectural and sculptural
elements, and a representation involving perspectival frescoes, all in the context of
a natural grotto, with hydraulic automats as an added feature.15 Buontalenti was
also the teacher of Salomon de Caus, who spread to France and England the idea
of grottoes, which were so shaped by artifice that they invited one to reflect on the
meaning of natural (pl. 99.1). The same De Caus wrote both on perspective (1611)
and on hydraulic devices16 of the kind which helped to inspire Descartes'
mechanistic model of reality (see above p. ).
Buontalenti's play between interior and exterior space may call to mind earlier
discussions concerning the window principle (see above p. ), and the function of
perspective in linking narrative and physical space (see above p. ). Yet there are
important differences. There it was a question of linking a fictive and a real space.
Here a real interior space is being linked with a real exterior space. Mantegna had
moved in this direction with his painted perspectival aperture or oculus in the
Camera degli Sposi in Mantua (pl. 70.2), which linked a real interior with
potentially real clouds outside. Leonardo pursued, it when he used perspective in
the Sala della Asse (Milan, Castello Sforzesco, c. 1497) to simulate an open
canopy of interlacing branches and knots, through which one can see the sky
beyond--a theme upon which Vignola played in the portico of the grand court in
the Villa of Pope Julius III in Rome.17 Peruzzi took up the problem more directly
in his Hall of Perspectives in the Villa Farnesina in Rome (c. 1516) which linked
the interior space with a view of the city outside. Veronese took it further in the
Villa Maser, where his perspectival frescoes linked the interior space with vistas
down pathways which simulated actual views out of other windows elsewhere in
the building.
These examples bring to light an essential difference betweeen ancient spatial
effects and those of perspective. At Pompeii, Herculaneum, the Villa at Oplontis
and elsewhere the ancients invariably produced spatial effects by a closure of
space. By contrast, as artists explored the implications of perspective they
increasingly created spatial effects which opened space beyond a given interior
into exterior landscapes. This was matching in a new sense, and a next logical step
was to use painted perspectives as substitutes from real landscapes in gardens
which, as we shall see, is precisely what happened in France. Before considering
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these developments, however, it will be useful, by way of context, to mention the
Netherlands, which took up another strand of the Italian tradition, that France
subsequently developed further.
3. Netherlands
The secret garden of Paul III (1534) behind the Vatican had been constructed as an
independent space, enclosed by walls with galleries crossing at right angles
dividing the gardens into quarters. In the next generation, the nearby gardens of
Julius III (1550) were again constructed in independent spaces,18 while the
gardens of the Villa d'Este (1550) were carefully planned as a series of neatly
defined adjacent spaces. This principle of gardens, clearly framed by a gallery or a
wall, appears to have held a particular fascination for Vredemen de Vries, who
produced what was probably the first collection of perspectival views of gardens
(1583 etc., pl. 92.2-3). For our purposes, it is fascinating to note how, as an
architect, Jan Vredeman de Vries, treated gardens as if they were simply
extensions of his buildings, such that his main task became one of imposing
regular geometrical patterns on the greenery. Indeed, he went so far as to adapt the
principle of the five architectural orders (doric, ionic, corinthian, tuscan and
composite), as a means of distinguishing gardens of lesser and greater complexity
(e.g., pl. 92.3). The most developed of these, could show a group of four or five
adjacent gardens, but even so the scale of the entire space remained limited to a
maximum of a few hundred feet.
His son, Paul, maintained this framework. He linked the five orders to the five
senses, and again showed differing gardens in the background. The distance to the
gate at the end of the garden might be a hundred feet further. There might even be
a hint of space beyond, yet this was so hazily treated as if to show it was out of
bounds. The focus of Vredeman senior and junior, as well as his student Hondius,
was on a small enclosed perspectival space, which functioned, curiously, as if it
were a secular version of the mediaeval walled garden (hortus conclusus).
Elsewhere in the North a more ample concept of natural space was emerging. As
early as 1511-1513, Wolf Huber, had, for instance, sketched a view of Urfahr near
Linz, on which he superimposed perspectival lines (pl. 91.2). He also made a
preparatory sketch showing Christ on the Mount of Olives (1526, pl. 91.1), in
which perspectival lines were again imposed on a landscape stretching into the
distance.19 In the text attributed to Rodler (1531) there were also illustrations to
show how the principle of a perspectival window could be applied to landscapes.
Yet it was particularly in France where the larger horizons of perspective were first
thoroughly explored.
4. France
The reasons were partly political. At a time when the Netherlands were still stifled
by Spanish control, and Germany remained a series of isolated states, France was
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already a country where enormous power was centralized in the hands of a few
influential families. Even a cursory glance at the gardens in Androuet Du
Cerceau's collection of great French houses (1576) reveals a new sense of scale.
The palace at Gaillon, for instance, has connected with it, a walled garden with a
geometrical layout reminiscent of individual gardens at the Vatican, or those of
Vredemen de Vries. But beyond this is a so-called park, which consists of a
regularly spaced orchard, plus at least a dozen geometrically organized rectangular
gardens. Italian gardens such as the Boboli may in fact have been larger, but being
spread out over several hills, they did not produce the same cumulative effect.
Spread out on flat land, the park at Gaillon, might still nominally be contained
within low walls, but even so they conveyed a sense of stretching much further.
The sense of space ending after a few hundred feet as in Vredeman de Vries does
not apply here.
The same book also contains a ground plan to the chateau at Charleval, which
offers a preview of the new aesthetic that is evolving. The chateau is on a quadratic
island, bounded by a moat rather than a wall, i.e., interrupting physical contacts
without interfering with visual links between interior and exterior. Directly behind
it, and connected to it by means of a small bridge, is a second island containing a
garden comprising twelve square, ten rectangular, two angular and one oval
compartments. From the chateau, across the bridge, there is a view which goes
straight down the path, across the moat and into the open. How such a view could
be extended, not just another few hundred feet, but to the limits of the horizon
became a major concern a seventeenth century France.20
As the idea evolved, it became clear that much more was involved then producing
a straight road that continues to the limits of vision. More and more elements
needed to be controlled in order to create the desired effect. It was not just a case
of aligning a few bushes and trees to create alleyways. The irregularities of nature
had to be systematized. This process may have been stimulated by the sojourns in
France of both Leonardo and Serlio. The works of Androuet Du Cerceau attest that
the process was well under way by the 1570's. The arrival from Italy of Du P‚rac
(1587) and De Caus (c. 1600) must have brought new incentives. By 1600 Olivier
de Serres was convinced that the gardens of France were the finest anywhere. As
examples he cited Fontainebleau, Saint-Germain-en-Laye, the Tuileries, Monceaux
and Blois adding:
It cannot be without a sense of wonder that one beholds plants speaking in
the form of letters, mottoes, numbers, coats of arms, clocks, gestures of
men and animals, dispositions of buildings, ships, merchant vessels and
other things imitated in plants and bushes with marvelous industry and
patience.21
The Jesuits published the shape of things to come. For example, Dubreuil (16421649), demonstrated how trees were effectively reducible to rows of geometrical
lines (pl. 90.1-2) and how bushes could be fashioned into rectangular bodies,
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bringing to gardens all the regularities of a geometrical ground plan (pl. 90.3-6).
Vredeman de Vries had imposed architectural orders on the curious shapes in his
gardens (pl. 92.3). Dubreuil went further. He explicitly compared the principle of
the vanishing point in an architectural construction with that of a row of trees (pl.
91.3). His contemporary, Bosse (1648) took this regimentation of nature to a
logical conclusion, transforming nature into avenues of regular or near regular
green solids (pl. 91.4), reducing nature, in fact, to simple architectural forms.
Morel in his Theory of Gardens (1776) described these tendencies, accusing the
architect of confusing the principles of architecture and gardening:
and being too accustomed to regular forms,...he tried to link by mutual
correspondence a building, which he made his principle object to a garden,
which seemed to him only an accessory. He arranged a garden like a house;
organized it into halls, rooms, corridors, made divisions with walls of
hedges, pierced by doors, windows, arcades, and their piers were filled
with all the ornaments destined for buildings.
As a result of this false analogy, architects gave these rooms, round, square and
octagonal forms, like those in their buildings; they decorated them like an
apartment, with vases, niches, openings in which they put statues as lodgers,
insensible inhabitants, well suited to so dismal an abode. They furnished them like
rooms with carpets of greenery, of trellis work, painted perspectives, beds and
seats of earth covered by grass. They went as far as building theatre rooms,
dormitories and ultimately even devised a miniature labyrinth. Always architects
when they should have been gardiners, they cut a tree like a stone, as a vault, a
cube or a pyramid and reduced even water, if mobile, to their forms.22
Once reconstructed with such regularity, nature could be represented
perspectivally and accordingly gardening treatises recorded the increasing
significance of perspective. For example, Olivier de Serres, in his Theatre of
agriculture (1600) observed:
It is worth noting that in looking at compartments from a distance, as far as
the bedding of a garden is concerned, it is useful to make more distant rows
further from one another, than the ones one sees from nearby. One will see
them as being closer together the further away the eye is, for the good
reason that the object diminishes in accordance with its distance as a result
of perspective. For this same reason, the rows of compartments occlude
one another, when one looks at them from the level of the garden itself,
walking along the alleys, because, since the viewpoint from which one
looks is low, the view is taken up by the first rows of plants which it
encounters, which do not permit it to extend as far as the others. For this
reason, it is desirable that gardens be viewed from on high, be it from
neighbouring buildings, be it from terraces around the confines of the
garden, as the King had had done by artifice at the Tuileries with his fine
alley of mulberry bushes, and also at Saint-Germain-en-Laye, where nature
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has contributed a great deal of her own through the altogether favourable
lay of the land.23
Claude Mollet, in his Theatre of plants and gardens, (also written c. 1600 but not
published until 1652), drew attention to another perspectival problem:
The largest alleys you will plant are the noblest ones. In any case, it is
necessary to proportion them in keeping with the length that you are able to
give them. Hence, those which will be one hundred and fifty fathoms long,
must be made five fathoms wide, because perspective foreshortens them.24
His son, André Mollet, in his Pleasure garden (1651) returned summarily to the
problem, which De Serres had considered: “ First, it is to be noted, that the
parterres which are more distant from the eye, need to be made larger than those
which are nearby, in order to appear more pleasing to the eye and better
proportioned.”25 This amounted to looking at immense gardens as potential
anamorphic games requiring subtle adjustments to create desired effects. At
Chantilly, for instance, the ponds were constructed in oval shapes such that, when
seen from the terrace, they appeared to be foreshortened circular basins.
In baroque interiors there was an increasing fascination with the ambiguities of
perspectival space. Gardens now became the exterior equivalents of these
concerns. Hence, it was no longer enough to reconstruct nature geometrically, so
that it could function perspectivally. Playing with these effects became a new
source of optical entertainment. For example, Michelangelo's technique of making
buildings diverge in order that they look closer (pl. 88.2), was adapted by Le Nôtre
to affect the layout of the entire property at Dampierre, with the added feature that
the space at the end of the garden was made to converge in a V shape in order that
it appear further.26 The french landscape gardener Dezallier d'Argenville used
such a divergent space, specifically referring to it as an Italian esplanade.27 It was
used again at Luneville and became a familiar feature in French gardens.
The reverse effect of converging space was equally popular. It was used to
increase the apparent length of an avenue of grass beyond the main pond at
Chantilly and developed at Rydorp (pl. 89.1) and Würzburg (pl. 89.2) to make
gardens look much larger than they actually were. At Chenonceau (pl. 89.3), the
principle was applied to increase grandeur by exaggerating apparent distance to the
entrance of the chateau, an idea subsequently exploited on a grand scale at
Versailles (pl. 89.4). At the Olympic Theatre in Vicenza, Scamozzi had used this
principle for interior stage sets (pl. 78.3). At Versailles, it was adapted for the socalled water theatre in the garden (pl. 78.4). At the Hannoverian court of
Herrenhausen, it was used to increase effects of distance on an open air stage.28
These playful uses of perspective went hand in hand with other developments
involving painting, as it became clear that, if perspective could be extended to
paintings of nature, such paintings could in turn be used to extend effects of nature.
214
Once again the roots of this idea lay in Antiquity. Vitruvius reported how in their
covered walks the Romans:
painted landscapes representing different sites; some showing ports,
promontories, shores, rivers, fountains, streams; others temples, graves,
flocks, shepherds. And in some places they painted large pictures
representing the gods as they are described in fables.29
As in the case of Roman scene paintings (see above p. ), the emphasis was on
imaginary situations, mythological scenes and different sites, rather than a
commitment to extend the space of the surrounding countryside. The idea of
paintings in gardens was revived in the Renaissance. In the Hyperotomachia
Pamphili (1490), for instance, Francesco Colonna spoke of painted scenes in the
garden at Cythera.30 Erasmus, also broached the problem in his Colloquies, when
the guest Timothy discovered that the marble column he saw was actually painted:
Timothy: An artistic deception indeed. I'd have sworn they were marble.
Eusebius: Let that be a warning to you not to believe or swear to anything
rashly: appearances often deceive. We make up for lack of wealth by
ingenuity.
[They turn now to the frescoes on the walls of the galleries]...
Eusebius: Our garden wasn't enough to hold all kinds of plants. Moreover,
we are twice pleased when we see a painted flower competing with a real
one. In one we admire the cleverness of nature, in the other the
inventiveness of the painter; in each the goodness of God, who gives all
things for our use and is equally wonderful and kind in everything....
This painted grove you observe, covering the entire wall, presents a varied
spectacle. In the first place, you see as many varieties of trees as you do
trees, each one represented with no little accuracy....31
Yet there were important differences between these paintings and, those of the
Vitruvian tradition. These paintings were of real objects in nature, not imaginary
ones. Moreover, part of the delight stemmed directly from comparing real flowers
with painted ones, using painting as an extension of real particulars of nature
surrounding one, rather than as evocations of imaginary universal scenes of nature
outside of place and time. A little over a century later, the Italian author, Bisagno,
in his Treatise on Painting (1642), included a special section on "what sort of
paintings are to be painted in fountains, gardens, in rooms and other places of
pleasure," where he explained that one could use:
various perspectives which have the effect of extending the gates and walls
of the garden and besides, the columns in the intervals, landscapes which
accompany them in such a way that they appear to follow those of nature,
adding some stories which are appropriate to such places.32
215
Here a lingering Vitruvian tradition produced combinations of natural and
mythological scenes. By contrast, in France, perspectival paintings became literal
extensions of landscapes. For example, André Mollet, in his Pleasure Garden
(1652) described the use of bushes and trees to create long alleyways at the end of
which "one will place beautiful perspectives painted on canvas in order that one
can remove them from the injuries of weather when one wishes."33 At Reuil, there
was a grotto decorated with shells, stalactites and columns in a niche offering: "a
perspective of which the sky is painted with colours so natural that one is assured
that birds were deceived and thinking they were flying in the open air they killed
themselves".34 Unlike the famous story of Zeuxis and Parrhasius, cited earlier (p.
), which involved isolated objects, this involved a whole context. At Rueil, there
was also a "perspective" in the form of a trompe-l'oeil arch in the middle of a real
park (pl. 99.1). Nor were such methods limited to France, as we learn from the
following description of the "perspective" at Schwetzingen:
Ahead of us lies a dark pathway, and in the far distance a pleasing
landscape appears, stretching out before our eyes, a landscape based on a
drawing by the court painter Ferdinand Kobell and painted so deceptively
on an oval-shaped wall by a common house painter in Mannheim by the
name of Truckenm ller, that one truly believes, at first glance, that a broad
natural landscape is unfolding before one. What gives rise to this beautiful
effect is, in part the approach by means of a heavily shaded pathway three
hundred and seventy feet long, in part the fact that the landscape is painted
on an oval form [i.e. a concave surface] and just before coming to this, one
finds oneself at a small grotto broken up by an artificial cliff, where the
water that runs off the walls and the ceiling collects in the basin.35
That the view at Schwetzingen was called "The perspective", reflected more than
local usage. The French term "perspective" had literally come to mean: "a painting
which represents gardens or buildings at a distance and which one places at the end
of a gallery or alleyway in a garden, in order to deceive the eye pleasantly."36 If
artists had begun by matching paintings with nature, a complex process of
matching nature to paintings was now emerging. Hence, De Serres (1600)
recommended that a garden should resemble "a panel of an exquisite painting
which has come from the hand of a good master"37 just before discussing
perspective. Elsewhere, he suggested that gardiners should base their work on the
drawings of painters.38 Nor were such remarks limited to France, Shenstone
(1765), in England made related, albeit more critical, comments:
I have used the word landscape-gardeners; because, in pursuance of our
present taste in gardening, every good painter of landscape appears to me
the most proper designer. The misfortune of this is, that these painters are
apt to regard the execution of their work, much more than the choice of
subject.39
216
A generation later, Medikus (1783), in Germany, pursued the analogy in a more
subtle vein :
Just as a landscape painter, by a juxtaposition or combination of individual
natural beauties, has an unlimited material for the most beautiful paintings,
which he uses and orders with an inventive spirit, so too must the gardiner
first study these beauties of nature and make himself familiar with them,
before he dares to set up such a nature painting in the garden that he has to
construct, all the more so, in order that one will not tend to get rid of his
efforts in the way that one removes the painting of a bad landscape artist
from the walls of its owner.40
By the late nineteenth century, there analogies between painting and landscape had
become sufficiently commonplace that artists could treat them satirically. When,
for example, a lady mentioned that a landscape reminded her of his work, Whistler
quipped: "Yes, Madam, nature is catching up."41
A closer reading of the above passages reminds us that etymologically "painted
landscapes" existed before the concept of landscapes in the modern sense emerged.
Perusal of the Oxford English Dictionary, for instance, confirms that the term
landscape first appeared as "painted landskips" in Haydocke's translation of
Lomazzo (1595) and soon led to Du Bartas (1605) reference to "the cunning
painter limning a landscape" and Howell's (1642) report: "how some have used to
get on the top of the highest steeple, where one may view all the country
circumjacent and so take a landskip of it." Such turns of phrase offer insights into
the complexities and paradoxes which the perspectival matching principle had set
in motion. If painting copied nature, nature also copied painting. To represent
nature perspectivally, required that it be reconstructed artificially, and the artifice
of painted landscapes then made possible the discovery of natural landscapes.
At a practical level, all this led to experiments on an ever greater scale. The
Tuileries led to Richelieu and Rosny, and pointed the way to Vaux le Vicomte and
Versailles.42 To create the view at Vaux le Vicomte, two villages had to be
removed. To create Versailles, a whole countryside had to be adjusted, which is
one reason why the plan took nearly a century to complete (1664-1758). But then
Versailles was much more than a house or a garden. It was a grand demonstration
how geometry and perspective were matrices for the organization of nature. And,
in a sense, it was an encyclopaedia of all the optical and perspectival experiments
of the past two centuries. It contained views to the limits of the horizon, and others
which were cut short to produce special effects, spaces which converged to
exaggerate a sense of distance, others which diverged to telescope effects of
distance; terraces and slopes which played on one's estimates of distance.
Androuet Du Cerceau had once produced a book on all the famous houses of
France. Pérelle (1722) could devote an entire book to the wonderful views of éthis
one complex.
217
Versailles has often been called a symbol of absolute power. This is misleading.
For at a certain level the assertion of power involved was absolutely literal. To
approach the King's premises, required experiencing how every view reaching to
the horizon had been transformed and was now in his control. Moreover, just as
individual figures had shrunk to an insignificant size in the early perspectival
paintings, visitors to Versailles experienced this in real life, when confronted by
the grand scale of buildings and gardens. And these demonstrations of power
already exercised, were the real power behind a so called absolute throne.
Versailles had many consequences. At Salzdahlum, the Duke of Lower Saxony,
literally made a wooden replica.43 In Augsburg, Decker (1711), adopted its
principles with teutonic thoroughness to show how they could be extended to
every nook and cranny of the horizon (pl. 93.2). The Nymphenburg in Munich
(1701) and Schönbrunn in Vienna (1759-1760), were important imitations. Sans
Souci (1745) and Würzburg (1770) were interesting variants, yet they basically
added little that was new.44 They confirmed that if one extended the principles of
perspective to transform the whole environment, it came with the price of
regularity, which could be surprisingly predictable, and sometimes even monotous.
5. England
One country developed conscious alternatives to this regimentation of nature. But
this came slowly. For a long time, England remained much influenced by the
continent. Witness the gardens at Wilton House (1630's), Longleat (1675, 1678),
Petworth (1695), Blenheim (1704-1764) and Hampton Court Palace (1702-1710).
For a time, the influence had been Netherlandish, as Dennis remarked:
While architectural vistos were imitated by planted avenues, the charge of
inconsistency could not be advanced against disposition of a flower garden,
into beds of unnatural figures, not infrequently assimilated with the
unnatural shape of, what is termed, a Pope Joan table. Happily this Dutch
style was for some years superseded.45
As late as the 1760's, there remained a fascination with formal effects of loss of
distinctness perspective, and linear perspective, as witnessed, for instance by
Shenstone's (1765) recommendations
A straight-lined avenue that is widened in front, and planted there with
yew-trees, then firs, then with trees more and more fady, they end in the
almond-willow, or silver osier; will produce a very remarkable deception
of the former kind; which deception will be increased if the nearer dark
trees are proportionable and truly larger than those at the end of the avenue
that are more s[h]ady.46
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But this was the generation of Stourhead (1740-1785), and the atmosphere was
changing,47 as is also reflected in Chambers (1772) description of continental
developments which was as damning as it was colourful:
The gardens of Italy, France, Germany, Spain, and of all the other countries
where the ancient style still prevails, are in general mere cities of verdure;
he walks are like streets conducted in strait lines, regularly diverging from
different large open spaces, resembling public squares; and the hedges with
which they are bordered, are raised, in imitation of walls, adorned with
pilafters, niches, windows and doors, or cut into colonnades, arcades and
porticos; all the detached trees are shaped into obelisks, pyramids and
vases; and all the recesses in the thickets bear the names and forms of
theatres, amphitheatres, temples, banqueting halls, ball rooms, cabinets and
saloons. The streets and squares are well manned with statues of marble or
lead, ranged in regular lines, like soldiers at a procession; which, to make
them more natural, are sometimes painted in proper colours, and finely gilt.
The lakes and rivers are confined by quais of hewn stone, and taught to
flow in geometrick order; and the cascades glide from the heights by many
a succession of marble steps: not a twig if suffered to grow as nature
directs; nor is a form admitted but what is scientific, and determinable by
the line or compass.48
To leave no doubt concerning his views Chambers added that this European style
was "held in detestation." His respect for typical English gardens was not much
higher, which brought him to the topic announced in the title of his work: A
Dissertation on Oriental Gardening. Among the extraordinary features which he
attributed to Chinese gardens, was a complex use of space involving multiple
viewpoints of an object:
Where the ground is extensive, and many scenes can be introduced, they
generally adapt each to one single point of view; but where it is confined,
and affords no room for variety, they dispofe their objects so, that being
viewed from different points, they produce different re-presentations; and
often such as bear no refemblance to each other. They likewife endeavour
to place the separate scenes of their compositions in such directions as to
unite, and be seen all together, from one or more particular points of view,
whence the eye may be delighted with an extensive, rich and variegated
prospect. They take all possible advantage of exterior objects; hiding
carefully the boundaries of their own grounds; and endeavouring to make
an apparent union between them and the distant woods, fields and rivers:
and where towns, castles, towers, or any other considerable objects are in
sight, they artfully contrive to have them seen from as many points, and in
as many directions as possible. The same they do with regard to navigable
rivers, high roads, foot-paths, mills, and all other moving objects, which
animate and add variety to the landscape.49
219
Chambers went on to relate this aesthetic of mutliple viewpoints to advanced uses
of linear perspective, anamorphosis, and colour perspective among the Chinese:
All sorts of optical deceptions are also made use of; such as paintings on
prepared surfaces, contrived to vary the representations as often as the
spectator changes place: exhibiting, in one view, groupes of men; in
another, combats of animals; in a third, rocks, cascades, trees and
mountains; in a fourth, temples and colonades; and a variety of other
pleasing subjects. They likewise contrive pavements and incrustations for
the walls of their apartments, of Mosaic work, composed of many pieces of
marble, seemingly thrown together without order or design; which, when
seen from certain points of view, unite in forming lively and exact
representations of men, animals, buildings and landscapes: and they
frequently introduce pieces of architecture, and even whole prospects in
perspective; which are formed by introducing temples, bridges, vessels, and
ther fixed objects, lessened as they are more diftant from the points of
view, by giving greyish tints to the distant parts of the composition; and by
lanting there trees of a fainter colour, and smaller growth, than those that
ppear in the fore ground: thus rendering considerable in appearance, what
in reality is trifling.50
Sir William Chambers was also involved with Kew gardens, which accounts for
the pagoda and other oriental features which still remain there today. But his text
is of interest to us for other reasons. Two years before this, Thomas Whately had
published his own Observations on modern gardening (1770). Unhappy with the
frontal methods of perspective dominant in Europe, Whately proposed alternatives
which bore an uncanny resemblance to Chambers' so called oriental methods:
Buidlings, in general, do not appear so large, and are not so beautiful, when
looked at in front, as when they are seen from an angular station, which
commands two sides at once and throws them into perspective: but a
winding lateral approach is free from these objections, it may besides be
brought up to the house without disturbing any of the views from it; but an
avenue cuts the scenery directly in two, and reduces all the prospect to a
narrow vista. A mere line of perspective, be the extent what it may, will
seldom compensate for the loss of that space which it divides and of the
parts which it conceals.51
Whately illustrated his point with a long description of the approach to Caversham,
the seat of Lord Cadogan, near Reading. The following year (1771) there appeared
in French a work entitled The art of forming modern gardens, or the art of English
gardens. Translated from the English to which the translator has added a
preliminary discourse on the origin of the art. The preface began with what was
rare praise for a Frenchman: “Without pretending that their gardens are exempt of
faults, I believe that those who have seen them and who sense the extent to which
220
noble simplicity is superior to all the symmetrical refinements of art, will prefer
their gardens to ours.”52
There followed the preliminary discourse, which was a translation of Chambers'
Dissertation on Oriental gardening53 and served as an introduction to a
translation of Whately's Observations on modern gardening. Obviously the
translator had also been struck by the parallels between the two. In one of his notes
the translator dealt with a perspectival problem omitted by Whately. We shall
quote it for, if it may betray how little the translator actually understood the details
of English aesthetics, it also reveals how far the consequences of perspective had
gone:
Animated objects are a genre of beauty so interesting and so particular to
English gardens that it would be desirable that the author would have
dedicated a section to them. Thereby, it seems to me, he would have made
his work more complete. Not every species of animal is appropriate for
every perspective, and even through everyone knows that goats enliven a
rocky scene and that sheep spread across the bottom of a valley, form a
most pleasing pastoral picture, it is, nonetheless, in this branch of art,
which involves the manner of distributing animals, that there exist fine
nuances, known to the English, and which the author might perfectly well
have explained to us in his manner had he so wished.54
The English response to this French enthusiasm concerning their methods was
mixed. For example, the anonymous author of Planting and Ornamental
gardening (1785), set out to prove that claims about English gardens being
founded on those of the Chinese was "founded in Gallic envy rather than in
truth."55 The same author launched a vigorous attack on the whole complex
interplay between painting and landscape which perspective had stimulated:
In a picture bounded by its frame, a perfect landscape is looked for: it is of
itself a whole, and the frame must be filled. But it is not so in ornamented
Nature.... Suppose a room to be hung with one continued representation, would pretty pictures be expected? would correct landscapes be looked
for? Nature scarcely knows the thing mankind call a landscape.... Let the
ingenious artist call from Nature her choicest beauties...but do not let us
carry his production back again to Nature and contract her unbounded
beauties within the limits of a picture-frame.56
In spite of such protests, the Anglo-Chinese style, exerted considerable influence,
and the analogies between painting and nature continued. In Italy, Silva (1801), in
his book On the art of English gardens (1801) repeated Chamber's theories
concerning oriental gardening and also emphasized the importance of colour
perspective in a manner reminiscent of Shenstone:
221
The expert gardiner will take care that the distribution of his greens obtains
the effect of perspective of colours, called aerial perspective by painters....
If he has a small space, and wishes to have his wood, valley, or bush
disappear rapidly from a given point of view, he should be encouraged to
place up front, trees and bushes which have a deeper green, larger and
more detailed leaves; trunks, with rougher and darker bark, putting at the
limits of the horizon, the paler greens, the smoother trunks, the whiter
leaves, which produce such a brilliant effect when dominated by the sun.
Thus he will obtain the marvelous effect of enlarging the place by reducing
colours with the same rules, that linear perspective has established for the
landscape painter.57
In England, Humphrey Repton (1805), one of the greatest Engtlish authors on
gardening reasserted links between painting, perspective and gardening:
The art of landscape gardening is in no instance more intimately connected
with that of painting than in whatever relates to perspective, or the
difference between the real and apparent magnitude of objects, arising from
their relative situations, for without some attention to perspective, both the
dimensions and the distances of objects will be both changed and
confounded.58
Repton devoted an entire chapter on optics or vision59 and included an appendix
with his theory of colours and shadows.60 His chief concern was how optical and
perspectival principles of occlusion could be used in planning improvements to
landscapes as seen from a specific viewpoint: how, for instance, a careful
positioning of trees and shrubs could hide an industrial suburb of Bath from a
nearby park, or how removal of certain trees could open up a beautiful vista of a
lake. Repton provided beautiful flap up pictures showing before and after effects to
illustrate his examples. Perspective, which had helped to create an awareness of
context, was now being applied to isolated parts deemed to need adjustment in that
context. In the English tradition, these adjustments became associated with
deception. Perspective belonged to the category of special effects. Dennis (1835),
mentioned an example:
At Corsham, in this vicinity, where the exclusive object is to produce
pictoresque effect on view from the picture gallery, a grand river appears
flowing through the park by a complete deceptio visus,the eye not
perceiving sunk spaces intervening between successive sheets of water.61
Given these associations, perspective was no longer an essential instrument for
organizing the environment. It became an emergency measure, a technique to be
applied only in exceptional cases: “But when absolutely necessary to conceal an
object, to break a line to foreshorten an ill-proportioned area, or sometimes to give
perspective, a parterre should received irregular form and be composed of
incurvated lines.”62
222
And so perspective, which had moved to the foreground of all spatial orientation in
France, moved into the background and seemed to lose its integrating significance
in England. Or to put it differently: the English tradition focussed attention on the
occlusion principle of perspective. As such, it could be used as a means, without
necessarily being visible in the end result: e.g. perspective could be used in
deciding how to occlude an ugly view with a clump of trees, without these trees
needing in any way to be perspectivally arranged to create special effects of
depth.63 As the nineteenth century progressed, this was perfected into a technique
which allowed one to see what effect a new building or complex would have on a
skyline or popular view.
Essentially, this is the same method which has since been mechanized in the
methods of photo-montage which authors such as Jantzen (1983) have recently
made popular (see above p. ). It applies perspectival principles of occlusion
specifically to a building or complex of buildings and is usually not concerned
with context as a whole. And in a curious way, this relates to another fashion of
our times, which plays on the occlusion principle of perspective, to create spatial
views on the exteriors of buildings, which frequently bear no connection with their
context, and function rather as surprise snapshots or frames into other imaginary
spaces.64 But whereas the nineteenth century used the occlusion principle literally
to close views and spaces, the twentieth century method plays with the possibilities
of physically closing and yet optically opening the same spaces by making careful
use of perspective, using the frame principle in a new way.
6. Conclusions
In the previous chapter dealing with interiors, we showed that perspective affected
both the contents and the forms of pictures. The first of these concerns led to
emphasis on spatial context; the second led to emphasis on their frames, and
ultimately to geometrical plays of form, at the expense of content. In this chapter,
we have shown that perspective had equally profound consequences for exteriors,
for spaces outside buildings, and have found that there were again two different
strands of influence, with certain parallels to the different concerns affecting
interior space. In terms of exteriors, one tradition explored the consequences of
perspective for the contents of nature.
This tradition began in Italy, received certain impulses in the Netherlands, and was
taken to its logical consequences in France. It was concerned with, what might be
termed the opening principle of perspective, i.e. the converse of the occlusion
principle. Its effects were extraordinary. It approached nature as an extension, first
of architecture, and ultimately of geometry, transforming and reducing its myriad
irregularities to the predictable contours of regular and semi-regular solids. In the
process, the content of nature was subordinated to context, and emerged as a
pattern of geometrical matrices. And as in the painted ideal cities, the scale of the
geometry was such, that it rendered the individual seemingly insignificant, making
223
it attractive to absolutist monarchs such as Louis XIV, and various totalitarian
minds since.
In interiors, the study of perspectival contents had led to contexts, but there being
many of these within the frames, these contents had remained isolated spaces, and
it was the study of frames that brought a more universal context. In exteriors the
reverse happened. Here study of contents affected one universal context within
which, by contrast, frames functioned as isolating features, snapshots which, even
though they assumed a greater whole, nonetheless, focussed on parts, leading
towards a fragmentation of space. The English aesthetic, which concentrated on
the occlusion principle of perspective and its framing functions, led in this
direction.
We have shown that perspective affected not only the representation of space in
painting, but also the reconstruction of space in the environment, and that, from the
outset, there were complex interactions between the two activities. In this chapter,
we have deliberately cited some extreme examples to focus attention on
unexpected applications of perspective. It must be emphasized, however, that
perspective was much more than a Hobson's choice between these two extremes:
one leading to the impersonal uniformity of geometrical matrices artificially
imposed upon nature; the other, involving isolated applications out of context, and
a fragmentation of space.
True, there was a choice between two elementary alternatives: an opening
principle, which generated alleyways leading as far as the horizon, and an
occlusion principle, which generated walls controlling the distance of the horizons.
And it was possible to apply either principle absolutely, But this choice had
nothing to do with the principles. The principles could be contained at will.
Indeed, an unending combination of the principles was possible. For this reason,
there was much more to Versailles than a single path to the horizon, and
considerably more than walls to occlude views in great English gardens at
Blenheim, Castle Howard, Stourhead and elsewhere. And thus gardiners,
architects, artists and others very gradually realized that, while the laws of
perspective were fixed, their applications were not. As they did so, they
discovered that perspective was a new key to imagination and freedom, as will be
seen in the final chapter.
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8. IMAGINATION AND FREEDOM
1. Introduction 2. Illusion and Metaphor 3. Theatre and Spectacle 4. Trompe
l'Oeil
5. Old and New
6. Real and Imaginary
7. Literacy and Levels of
Distance 8. New Functions of Art 9. Conclusions
1. Introduction
Perspective brought with it a new kind of matching, which enabled a quantitative
fit between representation and object. We have already shown that this was
extremely important for the development of early modern science (see above 2.1).
In the case of art, this was potentially disastrous, because it threatened to reduce a
work of art to a mere copy, constraining the artist with instruments and
construction lines. The reverse proved to be true. Perspective was an
unprecedented stimulus the creativity, freedom and the imagination.
By way of introduction we shall return to our earlier discussion (see above p. ) of
Greek mimesis to suggest why this led to a negative concept of illusion, affected
their concept of verbal metaphor and prompted goals of art in terms of a closed
system. We shall then show how Renaissance perspective was fundamentally
different: that it introduced positive dimensions to illusion, visual metaphor and
new goals of art in terms of an open system. Links between Renaissance theatre,
perspective and play will be explored us will problems of trompe l'oeil, old and
new, real and imaginary. This will take use back to the theme of literacy and art
and to outline further branches of matching and two new goals of art involving
perspective which have emerged since the Renaissance.
2. Illusion and Metaphor
In our earlier analysis of mimesis with respect to the visual arts (see above p. ),
we identified five different meanings of the term. Each of these involved imitation
in some form, yet none of them involved matching in our more technical sense of
the term: i.e. none of them established a quantitative relationship between a
painted representation and an object; none of them involved a concept of
reversibility, whereby one could work backwards from a painted representation to
reconstruct the original object. Because the Greeks made no distinction between
mental visual image and actual (physical) visual image - as Kepler later did when
he distinguished between imagines rerum and pictura rerum -, subjective and
objective dimensions remained undifferentiated, which meant that there was no
testable standard for the accuracy of an imitation. Indeed, although there was
much verbal discussion about truth, there was no standard to establish visual truth.
As a result, images could be rhetorically convincing, even illusionistically
persuasive, but in each case the illusionism remained a trick, at once negative and
deceptive, as Plato repeatedly insisted.
225
It is instructive to examine the Greek concept of metaphor in this context.
Aristotle tells us that the word, metaphorein, literally means to carry over,
transfer.1 Yet it is striking that all his examples involve approximations: i.e.
imitations, not matches. Ten thousand, he claims, is a metaphor for "the many."2
This is a connection or comparison which is likely, convincing even, but not one
that is visually testable. As such Greek metaphor is like the illusion in Greek
painting, based on a comparison for which a real fit or match is not possible. It is
therefore the more significant that Aristotle himself speaks of likely
impossibilities.3 Both Greek painting and verbal metaphor are universal
likelihoods, not particular truths; universal imitations of space, not particular
spaces; universal indications of chronology, not particular times; mythic, not
historical. The famous dictum ut pictura poesis now emerges in a new light.4
Both poetry and painting were guided by rhetorical truth of words (universals)
rather than the visual truth of pictures (individuals). Which is why Auerbach's
claims about mimesis in literature5 have parallels in ancient paintings.
In the absence of a true, visual standard, physical copies, sculptural duplicates,
were as close as Myron and his contemporaries could come to a standard.
Copying remained the highest to which art could attain. Literal identity or
equivalence triumphed over metaphor. Sculpture dominated over painting,6 as it
was better suited to a metaphysical system based on essence, emphasizing
universals, totality, perfection; leading to a closed prescriptive system. Hence
Aristotle wanted to limit poetry and painting:
The poet being an imitator just like the painter or other maker of likenesses,
he must necessarily in all instances represent things in one or other of three
aspects, either as they were or are, or as they are said or thought to be or to
have been, or as they ought to be.7
Note that Aristotle did not consider possible things as an alternative. Similarly,
Vitruvius sought to limit painting to what is or what is possible.8 Ironically since
an unclear imitation could never produce a clear match, both the Greeks and
Romans were doomed to keep producing representations which were impossible
when seen from a standard of visual truth.
The Renaissance may well have been inspired by Antiquity, but perspective
challenged it to go in fundamentally new directions. Perspective introduced a
visual standard for checking quantitatively to what extent a match was involved
between an individual object or context and its representation. Matches were now
testable. If this transformed the nature of representation (see above p. ), it also
transformed the nature of illusion. Giotto's illusionistic paintings of concealed
chapels in the Scrovegni Chapel offer an early case in point. Unlike the impossible
scenes of the Greek stage, this is possible architecture: a physical construction
which could readily exist. So we check and discover that the chapels are not real
architecture. The paintings thus make visual statements that something is,
assuming we will know that it is not. As such they function as visual metaphors.
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Whereas Greek illusions were based on universal concepts, Renaissance illusions
were based on particular elements: Giotto's chapel, Bramante's choir (pl. 5.4),
Pozzo's cupola (pl. 73.1), each of which could be tested in terms of a one to one
match. As a result, while Greek illusions were designed to deceive the eye,
Renaissance illusions were planned for us to see through them, thus transforming
the very concept of illusion from a negative trick to a positive game: challenging
us to look more closely, to play with change in focus, scale, and framework (see
above p. ); teaching us to expand our sense of what is and what is possible rather
than trying to limit these as had Aristotle and Vitruvius.
These links between perspective and visual metaphor deserve closer attention. The
development of perspective involved ever closer matches between object and
representation, resulting in more realistic representation, and an ever finer play on
the distinction is - is not, which lies at the heart of visual metaphor. When
perspective is at its best, the distinction is-is not is at its height. This intimate
connection between the rise of perspective and visual metaphor is important for at
least two reasons. First, it suggests that perspective transformed the very meaning
of metaphor: from a general comparison without a specific match, to a particular
comparison with a -potentially- specific match, from a verbal concept to a visual
metaphor. Secondly, perspective changed its function. In Aristotle's scheme,
metaphor remained an ornamental frill with respect to the structure of language, an
extra of no real importance.9 Perspective implicitly made metaphor central to the
whole aesthetic experience, for now the effect of a painting turned on how well it
could play upon the distinction is - is not.
In Padua, Giotto explored these problems in terms of painting (1304-1306). In
Verona, a decade later Dante explored them in terms of language with respect to
sculpture, when he wrote in his Divine Comedy (c. 1314) of the angel that:
Appeared to us, with such a lively ease
Carved, and so gracious there in act to move,
It seemed not one of your dumb images,
You'd swear an Ave from his lips breathed off,
For she was shownthere too, who turned the key
To unlock the treasure of the most high dove;
And in her mien those words stood plain to see:
Ecce ancilla Dei, stamped by art.
Express as any seal on wax could be.10
Dante went on to describe pictured smoke,11 stories in stone narrated,12 complete
with visible speech.13 We must at this point resist the temptation of a Dante
commentary and only mention in passing that there are clearly parallels between
these developments in literary narrative and those in pictorial narrative considered
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above (p. ). It is of interest that literary historians of the period have provided a
more ample context for understanding Auerbach's concept of creatural realism
arising out of the Judaeo-Christian biblical tradition. Indeed, they now speak of a
development of perspective in literature: in terms of stories based on individuals in
specific times and places, rather than eternal heroes in universal landscapes.14 We
have seen pictorial parallels, as the townscapes of Florence and other towns
entered into the backgrounds of paintings showing the lives of Christ and the saints
(pp. , cf. pl. 13.1-4).
It is important to note that the problem of visual metaphor, which plays on the is-is
not distinction, involves both spatial and temporal dimensions. To continue with
our Florentine example (pl. 13.2), at a spatial level the distinction plays on whether
this is Florence or is not Florence (i.e. only a representation of Florence). The
more difficult it is to make this spatial distinction, the more necessary it becomes
to make a temporal one: i.e. the more we are convinced that this is actually
Florence in the background, the more we have to insist that although this be a
contemporary scene, the story in it is not. To put it differently, the more
realistically we paint the space of a religious story, the more allegorically we need
to see its contents if we are not to fall into crass anachronism. Use of visual
metaphor in space thus leads to use of visual allegory in time. Two years after
Giotto painted the Scrovegni Chapel (1304-1305) in Padua, Dante in his Convivio
(1307), distinguished between literal and allegorical as well as moral and
anagogical senses.15 Such parallels suggest new fields of study: exploring the
extent to which the development of visual metaphor in painting went hand in hand
with a growing importance of metaphor in language to a point where, in the United
States, there is even discussion of metaphors we live by.16
These developments are so central to European civilization that they take us at
once into many controversies which still rage. Here our role is not to take sides but
simply to report on different viewpoints. The development in perspective, which
led to visual metaphor and positive dimensions of illusion17 began in Italy and
continued in France. In other countries they evoked very different responses.
While we have stressed the interplay of North and South, differences between the
two cannot be overlooked. The South tended to be more abstract and ideal, the
North more concrete and realistic. Hence, in terms of art, Italy explored paintings
with perspectival space, while a tradition in the North continued to explore
sculpture with physical space. In terms of language, Italy was more interested in
the spirit than the letter and thus welcomed metaphorical and allegorical
interpretation. The North took words far more seriously, stressed the literal and
worried about allegorical and metaphorical interpretations.
In England, for example, there were two very different approaches to metaphor.
One, based on the biblical tradition was positive. Hence, Bonner in his Homilies
(1555) noted "that Chryste always in his speakynge dyd use figures, metaphors and
tropes," while Addison (1712) referred to "those beautiful metaphors in Scripture
where life is termed a pilgrimage." Another, more widespread tradition,
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approached metaphor as something negative. For instance, Wilson in his Rhetoric
(1533) defined it as "an alteration of a woorde from the proper and natural
meanynge to that which is not proper and natural thereunto, by some lykness that
appeareth to be in it." A little over a century later the Earl of Moumouth (1560)
was even less equivocal: "The Metaphora, which is so frequent with them...is it
not an imposture?"18
This concrete, realistic strand of the North, which emphasized literalism over
metaphor had profound consequences. It inspired a particular kind of dead pan
humour epitomized by Till Eulenspiegel which laughed at itself for taking things
so literally.19 But there were also less humourous consequences. One extreme
form of this approach read sculptures and all visual images of God as idols,
revived the iconoclastic tradition and wishing to exclude visual images from
sacred matters altogether, sought to limit religion to words.
The complex interplay between North and South inspired almost every region to
develop their own solutions in these debates concerning the primacy of words over
pictures or conversely. Luther's friend, Cranach, inadvertently pointed to the
dilemmas of applying literalism to painting. Wishing to avoid painting a symbolic
Last Supper, Cranach used Luther's portrait as his model for Christ and added
Luther's friends as apostles in the Dessauer Altar. Similarly, in order to avoid
allegorical or symbolic buildings in another religious painting, Cranach literally
added the contemporary Wartburg in the background of his scene.20 We note that
the Wartburg functions precisely as does Florence in the background in the Italian
paintings considered earlier (p.
). Both are effectively visual metaphors. But,
ironically, those in Northern culture, who tried to emphasize words to the
exclusion of visual images, found themselves using literally when they meant
metaphorically. Which may be why the North, which made such great efforts at
literalism produced such unexpected volumes of allegory, emblems and other
visual metaphorical expressions. The efforts of the Fruit Bearing Society come to
mind.
3. Theatre and Spectacle
In this context, it is not surprising that theatre, which took perspective's
dimensions of metaphor and illusion to new limits, evoked two fundamentally
different responses. The most extreme forms of the northern approach tried to ban
theatre and indeed all art from human affairs. Hence, in England, twenty-two years
after the first complete edition of Shakespeare, performances of his plays were
forbidden. Visual images of the stage and painting were now held as false illusions
in contrast to the truth of texts. So Shakespeare was read but not seen. Hence the
dramatic visual imagery of plays intended for the stage embedded itself in the
domain of words and language. A century later an extraordinary series of German
readers, Lessing, Herder, Goethe, Tiecke and Schlegel saw the larger implications
of this process when they found in Shakespeare's writings the origins of dramatic
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perspectivism,21 thus starting a visual trend in criticism which has led via
Lubbock22 and Ortega y Gasset23 to Guillen24 and Weimann25 in our day.
Meanwhile, the Puritan stand which suspected metaphor,26 read illusion as only
negative, and sought to ban painting and theatre had enduring results. To this day
expressions in English connected with the stage very often have a negative tone:
e.g. He made a scene. He made a (big) Spiel. Don't make such a show. (German
has an equivalent phrase: Mach kein Theater.) The very words theatrical and
spectacle have something dubious about them because they are too strong, while
the word play often has a suspicious ring far removed from the elevated
connotations of homo ludens. Spectacular, is an interesting example of a word,
which remained negative in England, later to become positive in North America,
due largely to Hollywood. Even so, phrases such as Shakespeare's "all the world's
a stage" reflect another tradition, which saw the positive side of illusion and was
much more developed in Italy (cf. the meanings of spettacolo) and France (cf.
spectacle),27 where mise en scene became a basic dimension of life. And it is this
tradition which we shall examine more closely, keeping in mind that it was but one
of a complex series of responses within Europe.
Renaissance commentators interpreted Vitruvius' reference to scaenographia as
perspective (see above p. ), and saw their own efforts as a revival of his ancient
methods. Hence it is no coincidence that there are parallels between the
engravings in Cesariano's Vitruvian commentary (1521) and Renaissance stage
designs (cf. fig. 80.2 - 80.1, 81.1; fig. 82.1-8). Nor is it surprising that Barbaro,
author of a treatise on perspective (1568), should have written a Vitruvian
commentary (1556) with the ancient theatre reconstruction on which Palladio's
Teatro Olimpico was based.
Once again, however, it is necessary to stress the differences between GrecoRoman scene painting and the perspectival stage sets of the Renaissance. The
ancient stage settings, as we have shown (above p. ) involved impossible images,
buildings which could not exist in real architecture. By contrast, Renaissance stage
sets were curious interplays between fiction and reality with the important
difference that they could be real. Serlio, for instance, had a stage set which
recalled St. Mark's Square in Venice (pl. 80.1), with the Tower of the Clocks in the
background (pl. 80.3), and was the more interesting because it related to his later
version of the comic scene in his second book on architecture (1544, 1545, etc.).
Similarly, one of Peruzzi's drawings (pl. 81.1), recorded sights in Rome such as the
Colisseum and the Castel San Angelo. Another of his drawings (pl. 81.2) showed
the Pantheon and the Column of Trojan. Meanwhile, others such as Baldassare
Lanci's scene (1569), now in the Uffizi, involved a playful combination of
contemporary Florentine buildings notably the Palazzo Vecchio and the Duomo.
Closer examination of these drawings for stage set reveals another important
element: play with basic motifs, which could be real. The colonnaded arcade is an
excellent example. Cesariano used it in his Vitruvian commentary (1521, pl. 80.2,
230
82.1). Serlio used it (pl. 80.1), as did Peruzzi (81.1,82.2). Serlio then published this
motif in the perspectival section of his book on architecture, a theme upon which
Danti played in his treatise on perspective (1583, pl. 82.4-5). A stage design
attributed to Donato Brumante (Florence, Uffizi, pl. 82.6), was closer to Serlio's
version (pl. 82.3). Another stage design by Gozzoli (pl. 82.7) offered a variation on
the theme. In painting practice, the Master of the Barberini Panels, in his Birth of
the Virgin (New York, Metropolitan Museum, pl. 82.8) adapted the colonnaded
arcade for his purpose. Meanwhile, Bellini in his Sketchbooks had explored
variants of this theme for drawings of the Annunciation (pl. 83.1-2) which, bear
comparison with Crivelli's later painting (London, National Gallery, pl. 83.3) and
an intarsia version of the Annuncation by Fra Damiano da Bergamo (Birmingham,
Museum and Art Gallery, pl. 83.4). Masolino had, of course, used such colonnaded
arcades at Castiglione d'Olona.
Many more examples of this theme could be cited and a full catalogue and a
chronology thereof, would one day establish whether the uses of this motif went
from painting to the stage, or conversely. What interests us here is how arcades
were another of those basis spatial building blocks crucial for the development of
perspective (see above p. ). For the examples we have cited (pl. 80-83), suggest
how these building blocks could be combined in their component parts, much in
the way children play with mini-bricks, meccano, and other toy sets in creating
other, new structures. In other words, once there was a commitment to
verisimilitude and visual metaphor, i.e. a visual standard of truth, elements which
were potentially real followed as a consequence which could then be constructed
and reconstructed in an open ended system. By contrast, Greek stage settings had
relied on elements which were not architecturally valid, could not be recombined
at will, and led to a closed system, as well as closed space. And whereas the
Greeks produced scenes with impossible architectural spaces, mainly in the
context of their tragedies, Renaissance stage designs became new explorations of
possible spaces in the context of play, not only on stage but everywhere. The great
debate about whether or not the Baltimore, Urbino (pl. 96.7) and Berlin panels
represent stage settings is an expression of this ambiguity.28
For there was an extraordinary way in which play extended from the stage into
everyday life, just as perspective extended from paintings and the stage into the
environment. Hence triumphal arches were subjects for representation (eg. pl.
59.1-2), stage-sets, settings for triumphal entries acted as if in play, or later, even
garden ornaments (pl. 99.1), as well as real objects. The rise of pageants and
carnivals and a whole body of literature epitomized by Castiglione's Courtier
contributed their part in making a life of acting, a metaphor for the act of life,
Shakespeare's all the world's a stage, which had its Dutch equivalent with Vondel
(De wereld als speel-toneel).29
By the eighteenth century, the interplay of scenography and architecture had led to
remarkable imaginary stage sets, such as those in Bibiena's Architectures and
perspectives (1740, pl. 79.2). To a Puritan eye these would be negative illusions in
231
the worst sense. To French and Italian eyes, who knew how to see them as play,
they were illusions in a positive sense, and it is not surprising, therefore, that the
real quality of Bibiena's and Piranesi's fictive spaces inspired the fictive quality of
real spaces such as Vanvitelli's Palazzo Reale at Caserta (pl. 79.1), and various
palaces in Genoa, the dramatic staircases of which could be stage exits, as easily as
entrances into private domains.
Such examples reveal in new ways how the perspectival window principle did
much more than link interior and exterior space: it made the two interdependent.
If, as we have shown earlier (p. ), it extended pictorial space of interiors into
exterior environments, it also extended theatrical space of interiors into exterior
environments, thus making the is-is not distinction, which we have termed visual
metaphor, a part of everyday life. Perspective was not just some handy trick for
painters. It was a fundamentally new approach, which transformed western man's
approaches to illusion and reality.
4. Trompe L’Oeil
The spatializing functions of perspective which transformed paintings, walls, stage
sets and even the environment, need to be seen in direct connection with the
development of trompe l'oeil,30 which became another of the major expressions of
illusion in its new, positive dimensions. And here linear perspective in turn became
part of a larger context involving colour perspective, aerial perspective and
chiaroscuro.
Once again, Giotto's activities in the Cappella degli Scrovigni in Padua, bear
witness to the early stages of these developments. In addition to his concealed
chapels (see above p. ), there are fourteen allegories of virtues and vices on the
side walls below the narrative series. These monochrome figures, set against the
dark background of doors, which function partly as frames, were evidently
experiments in creating relief. Beneath the figures of Justice and Injustice there
are scenes where the frescoes are clearly representing three dimensional effects of
sculpture.31 Indeed, when seen in context all the figures look as if they were
dramatic trompe l'oeil sculptures rather than paintings, and Luzzatto has rightly
praised the "statuesque quality" of Hope in particular.32
By the fifteenth century, the creation of relief for purposes of trompe l'oeil, had
become an important goal in painting both in the North and the South. For
example, Rogier van der Weyden and Van Eyck each pursued the challenge of
using painting to create sculptural effects, as if the painted biblical figure were
actually a statue (pl. 76.1-3), and as if a painted figure portrait were a living statue
(pl. 76.4). In Italy, these ideas were taken up by Antonello da Messina, Bellini and
Mantegna who, in the Camera degli Sposi painted busts of emperors on the ceiling
as if they were sculptures, and in his monochrome works, simulated marble and
stone as in his Samson and Delilah (London, National Gallery, 1495). His
contemporary, Leonardo, made these effects of relief and chiaroscuro into the
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chief goals of painting.33 Positive illusions created through combinations of
perspective and chiaroscuro now became fundamental to art.
There were many combinations. Sometimes perspective was used as much in the
frames as in the paintings (see above p. ). Frequently perspective was used for
spatial effects inside the paintings while chiaroscuro served to extend these spatial
effects in the frames and ancilliary areas. In Raphael's Stanze, we can witness the
process evolving. In the Stanza della Segnatura (1509-1511), the area beneath the
School of Athens has two figures painted with chiaroscuro as if they were
sculptured caryatids. In the Stanza dell'Eliodoro (1551-1514) each wall has four
such figures and various frames which look to be real architecture thanks to
chiaroscuro. The ceilings have more complex interplays of painting, architecture,
sculpture and ornament. Perspective and chiaroscuro now have a systematizing
function, integrating different media such that a whole room functions as one
spatial context evoking various positive dimensions of illusion.
In Venice, the play of frames borrowed from contemporary architecture to produce
a particular kind of scroll work known as the Sansovino type.34 In the latter half of
the sixteenth century, these became the starting point for engravings of threedimensional cartouches (pl. 94.5) and other ornaments (pl. 94.6), which functioned
as visual metaphors of sculpture. The authors of these books on cartouches,
notably Cock and Vredeman de Vries, were also authors of treatises on
perspective, in which these elements recurred as fancy borders (pl. 94.3), or as
decorative motifs on wells (pl. 94.4). This latter case had physical equivalents in
wells and fountains in town squares. Hence as these grotesque representations
inspired new objects in physical space, play with spatial form affected spatial
content. Such play with grotesques sometimes became an end in itself and indeed
inspired Montaigne's literary style as we learn from the introductory paragraph of
his essay On Friendship:
As I was considering the way a painter I employ went about his work, I had
a mind to imitate him. He chooses the best spot, the middle of each wall,
to put a picture laboured over with all his skill, and the empty space all
around it he fills with grotesques, which are fantastic paintings whose only
charm lies in their variety and strangeness. And what are these things of
mine, in truth, but grotesques and monstrous bodies, pieced together of
diverse members, without definite shape, having no order, sequence, or
proportion other than accidental?35
As art began to explore possible worlds systematically, literature began a similar
journey into possible worlds, a theme which Bolzoni has recently studied in
another context.36 The trompe l'oeil illusions of perspective and chiaroscuro thus
led in two different directions. In the case of Vredeman de Vries, it led to a
dispersal of effects among various media, engraving, painting, architecture,
sculpture, etc., with elements from one being adapted elsewhere in unexpected
contexts. Ortelius, for example, adapted these cartouches for the purpose of
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cartography.37 On the other hand, it led to a new integration of media and created
systematic, united effects as in Raphael's Stanze. The Palazzo Borghese (pl. 77.1)
was a further development of these integrating effects of perspective and
chiaroscuro in transforming the entire context into a positive trompe l'oeil illusion.
If we look up we see a real architectural vault, to which are added painted
architectural features such as cornices and architectural features, perched on which
are painted three-dimensional figures, which look like living statues.
In the Palazzo Pitti (pl. 77.2) the situation is at least as complex. Effects of
perspective and chiaroscuro are now inseparable in creating such compelling
effects of relief that architecture, painting and sculpture combine in a single
integrated illusion. Are the supporting figures, the atlantes, sculptured or painted?
Which balconies belong to architectural space and which belong to painted space?
Which parts are physical, architectural room and which are painted room? Here
the is-is not distinction of visual metaphor has been taken to such a level that the
game is worth playing for its own sake. Mannerism was tempted in this
direction.38 The baroque turned temptation into a challenge and made art for
illusion's sake, which is a deeper reason why it tended toward form without
content (see above p. , pl. 72-73), and why, inevitably, reactions such as neoclassicism and romanticism set in to bring content back into focus.
If we interpret such reactions as proof that the baroque was somehow an hiatus, an
intermission in the serious play of art, we overlook the deeper significance of the
positive illusions of trompe-l'oeil introduced by perspective and chiaroscuro. For
the breaking down of oppositions between form and content was part of a larger
pattern of removing what had seemed key oppositions between old and new, real
and imaginary, leading out from a prescriptive closed system of Antiquity to a
descriptive open vision of art.
5. Old and New
We have already noted that those who studied Roman ruins in the fifteenth and
sixteenth centuries were also leading architects (see above p.
). It is not
surprising, therefore, that techniques of visualization developed with respect to
these old buildings, were applied equally to new ones, as was the case with
architectural cross-sections (pl. 84.1-3). Donato Bramante developed these
methods in terms of both ruins (pl. 84.4), and churches (pl. 84.5) with a result that
his cut-away of a new church looked more like an ancient ruin than a modern
edifice. Serlio's books on architecture codified this tradition and included hundreds
of ancient and modern buildings together as ground-plans, elevations, interiors in
section (pl. 84.1), as well as details of architectural elements. Although weak in
theoretical principles, Serlio greatly increased the repertoire of forms. Hence,
whereas Piero della Francesca had drawn only one archway in his treatise on
perspective (pl. 7.3), Serlio provided six (e.g. pl. 7.4), thus illustrating the variation
possible on a given theme. And while many of Serlio's drawings represented real
234
buildings, some were architect's conceptions of possible constructions. Hence there
was an interplay between old and new in two senses.
Nor was he alone in this. Almost from the outset, the study of ruins had involved
imaginative interpretation, leading both to new ruins and new buildings.
Mantegna's ruins, put in the context of contemporary houses, in the background of
his Saint Sebastian (Paris, Louvre, pl. 86.1), were a case in point. Jacques
Androuet Du Cerceau took this approach considerably further. Many of his ruins
were idealized interpretations of ancient buildings. Occasionally we can trace how
a motif such as two broken arches at the entrance to a barrel vault in one drawing
(pl. 86.2) was developed elsewhere (pl. 86.3), or how the motif of such a vault
framing a gateway recurred in another engraving (pl. 86.4).
In this and other collections of his engravings a play element is evident: slight
variations of elements produce a series of different structures. This process of
creative archeology becomes the more fascinating when we learn from one of his
titles that Androuet Du Cerceau did so consciously when he referred to: "twenty
five arches partly invented by me and partly taken from monuments both in Rome
and elsewhere as well as now existing as the inscription to each arch indicates."39
A generation later, Vincenzo Scamozzi, was even more articulate about this
process in his Discourses on antiquity (1582):
It may be that this plate was drawn from some antique thing and that I do
not remember having seen it, but it is much more likely that it was made as
a fine capriccio, since the only person who would not tire in drawing every
ancient object precisely, would be he who does not know how to make any
beautiful invention [of his own].40
Such statements provide a valuable context for understanding Vredeman de
Vries,41 who took this principle of idealizing ruins further to create modern
versions of ancient cities (pl. 87.1-2), inspiring the idealized cities of Steenwyck
(pl. 87.3) and Van Delen. Hence study of ancient ruins involved creative play with
basic architectural forms, which inspired new early modern buildings.
The engravings of Vredeman de Vries were integrated by his student Marolois, as
part of a larger corpus which included a series by Stevens. Here we find Roman
ruins such as the baths of Antonine (pl. 85.1), as well as his version of Emmaus
(pl. 85.2), the place where Christ dined shortly after he rose from the dead. It does
not require the world expert in middle eastern architecture for the year 33 A.D. to
recognize that this restaurant has experienced certained archaeological liberties.
Indeed, we can safely leave to such an expert a full analysis of anachronistic
details in this Chenonceaux of the North stationed in the Holy Land. What
concerns us is that even if the Israelites did not build such an Emmaus, even if it
was historically infeasible, it was architecturally possible. The same principles
used to represent ruins, helped to visualize structures for which no archaeological
model existed. If the perspectival principle of visual metaphor introduced a
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standard whereby the visual truth of image could be tested, it also inspired a whole
genre of images which failed the test, and yet were fully valid spatially.
Study of the past thus became a creative enterprise, as is well illustrated by the
roof-top decorations in one of Vredeman de Vries' engravings (pl. 87.1). At first
sight we are likely to dismiss these as imaginary while accepting them as spatially
coherent. A closer look (pl. 94.1), and comparison with the facade of the Armoury
at Wolfenbüttel, built a few decades after his sorjourn there (pl. 94.2), reveals how
ruins and interpretations of ancient buildings provided a vocabulary for mannerist
architectural forms. Vredeman de Vries' perspectival engravings of wells (pl. 94.4)
and caryatids (pl. 94.6), mentioned earlier, added to this vocabulary. This process
continued into the baroque period when Scamozzi's term capriccio became
indicative of a whole genre of paintings,42 including playful combinations of real
buildings, as epitomized by Panizzi, and fully imaginary constructions as in the
case of Desiderio di Monsu. Old and new, imaginary and real were now combined
in creating new structures, and if perspective removed the opposition between old
and new, it did the same in the case of real and imaginary.
6. Real and Imaginary
Here again we find a distinction between Antiquity and the Renaissance. For as we
have shown, Vitruvius' description of ancient scenography involved imaginary
spaces, which had no physical counterparts, and in this sense, were opposed to
reality. Plato saw the opposition of real-imaginary in other terms but the effect was
the same. Renaissance perspective changed this. Brunelleschi's experiments
involved the rerpesentation of an actual building, the Baptistery in Florence. But
the result was hardly an opposition between real-imaginary. Indeed, Brunelleschi's
decision to have the real sky mirrored in the upper portion of his picture increased
the ambiguity between real and imaginary, or to return to our earlier phrase, it
sharpened the is-is not distinction of visual metaphor.
The opposition between real-ideal also faded, for a fascination with idealized
buildings, which had grown out of a study of ancient ruins, led to interaction
among various kinds of images, including records of real ruins as they were
imagined to have been, architect's conceptions of possible buildings, real
contemporary buildings, reconstructions thereof in books of ancient ruins, and
imaginative versions of historical and legendary buildings, as is illustrated by the
case of a round temple surrounded with columns. Francesco di Giorgio Martini
included at least two ancient examples of such a building in his sketchbooks: a
temple near the theatre of Pompeo in Siena (pl. 96.1), and the temple of Vesta.
Leonardo da Vinci used such a round temple in his design for a mausoleum (pl.
96.2).
The form recurred as the central building in the famous Urbino panel (pl. 96.3).
Bramante constructed such a temple: San Pietro in Montorio, the so-called
Tempietto (pl. 96.4), which reappeared in modified form as an engraving among
236
Androuet Du Cerceau's ancient ruins (pl. 96.5), in a treatise where it became a
close relative of a Temple of Jupiter (pl. 97.1), a pagan edifice which had its
Christian equivalent in a temple in the background of Raphael's Marriage of the
Virgin (Milan, Brera, pl. 97.2). A complex interplay of architecture, drawing,
engraving, and painting thus transformed art into a vocabulary of images in
different media pre- and representing possible realities and possible extensions of
reality. These interplays between old and new, real and imaginary, help us to
understand unexpected parallels between a building which Androuet Du Cerceau
associated with Troy (pl. 97.3) and Bramante's plan for the new St. Peter's (pl.
97.4); or between Androuet Du Cerceau's imaginary Roman architecture (pl. 97.6)
and the Palazzo del Te in Mantua (pl. 97.5).
More complex interplays between real, represented and theatrical space ensued. In
the case of the Uffizi (pl. 95.1), Vasari used a parallel arrangement of the galleries
to create its perspectival effects, with the arcade at the end functioning as a
window to reopen the space and to frame new views. His son used the same
principle in his treatise on perspective (pl. 95.4), and it became almost a
convention in seventeenth century stage sets (pl. 95.3). The framing device of the
arcade functioned equally well when looked at from the Arno side, as is illustrated
by an eighteenth century engraving, in which the galleries, with the Palazzo
Vecchio and Piazza di Signoria in the background, look like a stage set (pl. 95.2), a
possibility which Baldassare Lanci had put in practice in his perspectival scenery
for Cini's The Widow (1569). In other words, architectural space which had been
reconstructed consciously lent itself to being represented perspectivally and invited
life therein to be re-enacted theatrically.
These effects were augmented by links between intervention and representation:
adding automatons to create special natural effects. Such treatment of nature as
artifice made it apt for both theatrical play and artistic representation. Bernardo
Buontalenti and Alfonso Parigi, who completed the Uffizi, were both active in
stage design, and this same Buontalenti (cf. above p. ), was active in creating the
Boboli gardens behind the Pitti palace, with their amazing grottoes, a word which
may well be linked etymologically with grotesques. Buontalenti's student,
Salomon de Caus, developed these principles (pl. 98.1) to a point where nature and
artifice became one, where grottoes became stage sets, which lent themselves to
perspectival representation, where wild animals were tame stuffings, where forces
of water were transformed into dramatic fountains on a stage within a stage,
artifically thrown into relief by controlled, natural light.43
If nature with artifice created new stage settings (pl. 98.1), painted stage-settings
(pl. 98.2), and painted representations (pl. 98.3), extended natural artifice to create
plays of reality in various senses. It was this context which inspired the trompe
l'oeil facade at the home of the Marquis de Dangeau in Paris44 and the trompe
l'oeil arch at Rueil (pl. 99.1), where the garden was real and only the arch was
painted. The same context inspired Bibiena, in his stage settings to paint both
garden and architecture perspectivally (pl. 99.2). As a result real and imaginary,
237
everyday act and theatrical re-enactment could and often did become one, which
inspired as many sources of delight in Italy, France and isolated courts, as it posed
serious threats in other parts of Europe, where perspective, metaphor and illusion
remained a negative trinity.
It is possible to identify at least four stages in these developments from 1300-1700:
imaginary extension of real, imaginary play with real, imaginary, and real
extension of imaginary. If Giotto's concealed chapels in Padua were a forerunner
of the first stage, some of the most important examples thereof occurred in the late
fifteenth century: Mantegna's oculus, the illusionistic round opening on the ceiling
of the Camera degli 'Sposi (pl. 70.2), Bramante's choir in Santa Maria presso San
Satiro (pl. 5.4), Leonardo's Last Supper and Pietro Lombardo's facade in Venice
(pl. 5.3). Our examples of the second stage, imaginary play with the real, have
included stage sets of Serlio und Peruzzi (pl. 80.1, 81.1), paintings of Mantegna
(pl. 86.1), and early ruins of Androuet Du Cerceau (pl. 86.2).
This stage, where play is implicit, is distinguished from a third stage where play
continues, but the distinction between imaginary and real is either explicit, as in
the later ruins of Androuet Du Cerceau (pl. 86.3-4) and Scamozzi, or taken to such
extremes, that it is apparent as with Stevens (pl. 85.2) and Steenwyck (pl. 85.3).
The fourth stage, real extension of imaginary, involves direct intervention in
nature, and includes Michelangelo's Campidoglio (pl. 88.2), Bernini's Scala Regia,
Borromini's Palazzo Spada (pl. 5.5) and Le Nostre's Versailles (pl. 93.1).
Examination of fig. 44, which summarizes these developments, reveals that, in the
first stage, effects of trompe l'oeil, illusion and visual metaphor, involve either
interiors (first four examples) or exteriors (fifth example). By the fourth stage,
these examples initially involve exteriors, and later, in the Palazzo Spada and
Versailles, involve such an interplay between exteriors and interiors spaces that the
opposition no longer applies.
DATE IMAGINARY IMAGINARY IMAGINARY REAL EXTENSION PLAY
IMAGINARY
EXTENSION
OF
OF REAL
WITH REAL
IMAGINARY
1300-1349
Giotto
1400-1450
1450-1499
Mantegna
Bramante
Leonardo
P.Lombardo
1500-1549
Serlio
Michelangelo
Peruzzi
1550-1599
Androuet
Androuet
Vignola
238
Vredeman
Scamozzi
1600-1649
Steenwyck
Bernini
Stevens
1650-1700
Borromini
Le Nostre
Fig. 44. Shifts in the role of the imagination in early modern art and architecture.
On the surface, as these oppositions disappeared, distinctions between terms such
as interior-exterior, subject-object, real-imaginary became blurred, which accounts
for apprehensions of the North. Yet at another level, they gained new meaning,
because the matching mechanism of perspective created ever subtler visual
metaphors, i.e. finer distinctions between is-is not by means of a visual standard of
truth. Hence the closer they come to seeming to blur, the more subtly we learn to
see their differences, or as the North would say, tell them apart. Thus perspective,
which literally involves seeing through (per-spicio), also teaches us to see through
the illusions it creates. In Antiquity, when optical adjustments methods produced
illusions to deceive the eye, Plato understandably railed against these methods of
representation, which separated appearances from reality. In the Renaissance,
when perspective created illusions to instruct the eye in seeing beyond deception,
illusion was transformed into a positive force in cultural development.
Something much deeper than getting beyond deception was also involved. For the
matching mechanisms of perspective inspired an interplay of art and science
unique to the west. The artist engineers of the Renaissance, epitomized by
Leonardo da Vinci, were an early manifestation. In the eighteenth century it led
Lambert, who studied Leonardo closely, to write On the photometric part of the art
of the painter (1768),45 in which he attempted to analyse scientifically, in
quantitative terms, differences between images in paintings, mirrors, and camera
obscuras -the theme of instruments once more. In the nineteenth century, this
tradition led scientists such as Helmholtz46 and Brücke47 to study painting, and
convinced Fechner48 that one could quantify aesthetics, a temptation that still
lingers at M.I.T. Ironically, although our universities have faculties of arts and
sciences, the history of what brought art and science into their unique western
relationship has not yet been studied in detail.
7. Literacy and Levels of Aesthetic Distance
As for the cultural dimensions, we understand these more clearly when the
development of art as visual metaphor is seen in relation to literacy and levels of
aesthetic distance. In primitive societies, when connecting was the goal of art (see
239
above p. and fig. ), and there were no texts, a statue was a god. It presented
rather than represented, such that art asserted the equivalence of god and image. In
Greco-Roman culture, as imitation became a goal of art, and as isolated
manuscripts recorded the names, characteristics and deeds of the gods, the function
of statues changed from presentation to representation, such that what had
functioned as equivalents, now functioned as substitutes of the original. As the use
of texts spread from descriptions of divinity to include learned interpretations
thereof, the thinker Euhemerus suggested that statues and paintings represented
men as if they were gods. This theory of Euhemerism, named after him, thus
introduced a new level of distance between original and image.49
The rise of Christianity, with its focus on the Bible, meant that the images in this
text could be cited or even be alluded to indirectly.50 A statue of a painting could
now represent a but mean b: it could, for example, show a good shepherd and
mean Christ. Symbolism thus introduced a further level of distance between
original and image. The development of textual communities51 led to refinement
of these principles in the form, as we have seen, of Dante's distinction between
four levels of interpretation: literal, allegorical, moral and anagogical (see above p.
). The advent of printing expanded the range of books common to textual
communities, and what had begun as parallels between Old and New Testaments,
were extended to relate pagan and Christian themes, as in the Sistine Ceiling and
the Stanze.
The spread of printing went hand in hand with more subtle levels of literary and
visual interpretation. Mediaeval symbolism had involved representing a while
meaning b (the good shepherd meaning Christ), with the assumption that one
believed in the reality of both a and b. The Renaissance introduced a play element
into this formula: a painting now represented a in the guise of a1 without requiring
that one actually believed in a1. Honthorst's painting of the Princess of Orange as
Diana (Utrecht, Centraal Museum, 1643), offers a case in point. At one level, it is
a portrait of Louise Henriette of Nassau, Princess of Orange. At another level we
recognize the dogs, bow and arrows as attributes of Diana, through literary culture.
So we see the princess playing the part of Diana without needing to believe
literally in the pagan goddess or her powers.
The increasing tendency to push topics into the backgrounds of landscapes in the
seventeenth century, as in the case of Claude considered above (p. ), increased
distance in two senses. When subsequent mythological figures stayed in the
foreground, the play element was frequently extended to their attributes to indicate
that one was not expected to believe in them, as in Boucher's Venus, Mercury and
Amor (Berlin, Schloss Charlottenburg, 1742). We recognize the man as Mercury
by his winged feet. But the wings have been tied on with a ribbon, to help us see
through his guise, and to leave no doubt that this is a Frenchman playing the part
of a god. Sir Peter Lely went further still in his Nell Gwynn and the Duke of St.
Alban's as Venus and Cupid (Chiddingstone Castle), where he relied on the topos
of a reclining female nude with standing child without attributes to indicate Venus
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and Cupid, and by making these figures portraits of two well known and notorious
personalities, he transformed a purportedly classical scene into a social statement
about a contemporary relationship. These developments are summarized in fig. 45.
DATE
-1000
1000-200 B.C.
. 200-300
300-1200
1200-1450
1450-1560
1650-1800
PROCESS
TERM
statue equals god
equivalence
statue represents god
substitution
statue,painting represents
euhemerism
man as if god
statue,painting represents
symbolism
a but means b
painting represents a
and means a
literal
O.T. and means N.T.
allegorical
Christ's actions in relation to man
moral
Christ's actions in relation to. Eternity anagogical
painting represents a in guise of a1 ---painting represents a in playful guise of a1 ----
Fig. 45. Links between art and levels of abstraction.
Since then there have been many further developments: Salvador Dali's treatment
of Millet's Angelus comes to mind.52 However, a detailed map of all these levels
of distance is not our concern here. We are interested rather in pointing to the
larger context of perspective: that there were important connections between
literacy, more complex uses of space, and more subtle levels of interpretation; that
perspective, which on the surface involved literal realism, played an important role
in associating art with levels beyond the literal. Perspective and symbolism went
hand in hand. Perspectival realism made it possible, for instance, to represent
Roman soldiers in Turkish costumes in Renaissance versions of the Crucifixion,
such that this scene reflected both an historical event and contemporary religious
problems. Instead of pinning the image down, perspective made it polyvalent, and
if it made serious matching possible, perspective also introduced playful matching.
Hence instead of dooming art to a closed system of copying, perspective
transformed it into a creative act, open to new themes and new goals.
8. New Functions of Art
Thus far we have considered four goals of art: connecting, ordering, imitating and
matching, and with respect to the latter have focussed on matching the visual
world illustrating implicit common verbal sources, such as the Bible, which were
so well known that knowledge of their stories could be taken for granted.
Perspective had its greatest impact in visualizing such texts. Nonetheless, there
were no less than nine other types of matching and two other goals of art, mixing
and exploring, which require brief mention, even if detailed consideration thereof
is beyond the scope of this introduction.
241
Matching
The most obvious type of matching, involving a simple record of the visual world,
was implicit in Brunelleschi's first experiment involving the Baptistery. It became
more common, as use of the window principle was extended from individual
objects to views of towns and landscapes (pl. 58.1-2). Perhaps because it was so
obvious, this type of art remained of less interest to art than the military until the
advent of the camera, which effectively mechanized the perspectival window
principle, awakened new interest in its creative potential.53 Matching could also
involve illustrating a text directly, an approach which was applied to the Bible,
classical authors such as Ovid, mediaeval literature such as Boccacio (pl. 78.2)
cited earlier, and chronicles such as Froissart (e.g. B.M. Harley 4380, fol. 23b).
Thirdly, matching was used to illustrate recurring events, particularly the four
seasons and topoi, which could be based on classical sources, such as the three
graces, or be of a more general character: old age, the fool, the land of cockaigne
etc.
In some cases, matching involved an implicit verbal source, which was either so
uncommon that most persons would not recognize it, (or alternatively so common
that everyone at the time took its meaning for granted and we in retrospect find it
mysterious). Three famous examples immediately come to mind: Botticelli's
Primavera,54 Giorgione's Tempest55 and Bronzino's Allegory56 (London,
National Gallery). In other cases, matching involved well known verbal sources,
which remained difficult to recognize because the scene was set as a part of every
day life or in the background of a landscape. In early examples, such as
Carpaccio's Calling of St. Matthew (Venice, Scuola di San Giorgio degli
Schiavoni, 1525-1526), where Matthew was shown simply as a tax-collector, the
surrounding pictures provided a context for understanding its meaning. In
Caravaggio's treatment of the same theme (Rome, San Luigi dei Francesi,
Contarelli Chapel, 1597-1598), only a ray of light revealed that this was a sacred
rather than a secular scene. By the time of Tenier's Seven acts of mercy (Dulwich,
Picture Gallery), we need to recognize that passing a loaf of bread is a visual
metaphor for feeding the poor. We need even more discerning to recognize
classical scenes set in the context of landscapes, as in the Claude mentioned above
(pl. ).
The twentieth century has shown a fascination for treating the matching function in
a playful and/or ironic manner, as, for instance, in Magritte's Treachery of Images
(New York, Private Collection, 1928-1929), which shows a meticulously painted
briar pipe with the caption: This is not a pipe. Magritte's Promenades of Euclid
(Minneapolis, Institute of Arts, 1955), offers a more subtle example by
demonstrating how a flat road going into the distance and a three dimensional
tower both project triangular shapes on a perspectival window. Some of Escher's
work might also be mentioned in this context, although he is more complex in that
242
he has different perspectival viewpoints for separate parts of a picture, which are
then carefully integrated to function as a single context (e.g. pl. 73.4).
There have, in fact, been a number of movements which have played with the
matching principle mainly by overemphasizing certain aspects of reality, including
the Precisionists, (e.g. Charles Demuth, Ralston Crawford); Pop Art (Richard
Hamilton, Edward Ruscke); New Realism (Mel Ramos) and Photo Realism
(Richard Ester, Ralph Goings, Chuck Close).57 In all of these movements,
perspective continues to play a central role. The revival of interest in trompe l'oeil
is another manifestation of this play with matching principles as, for instance, at
the American embassy in Paris (pl. 100 ). Here the oblique walls are carefully
painted illusions, with doors that reveal clouds beyond. The left wall, itself a
trompe l'oeil, opens into a trompe l'oeil of the second degree, showing a
colonnaded arcade. In front of this stands a trompe l'oeil officer representing a
country which until recently had a former actor as its president.
Anamorphosis was an unlikely form of matching, which involved distorting shapes
in such a way that, when seen from a specific viewpoint, their original form
returned. This alternative, developed by Piero della Francesca, received particular
attention in the seventeenth century (see above p. ), and was then ignored until
an historical study by Baltrusaitis (1956) inspired new interest therein.58
Meanwhile, the twentieth century has introduced another kind of matching
involving distortions: it abandons a rigid geometry of straight lines, involves a
simplification of spatial features, yet nonetheless remains committed to
representing familiar objects in every day life. Sometimes, as in Henri Matisse's
painting of A Girl Reading (Edinburgh, Scottish National Gallery of Modern Art,
1919), the results are close to those of parallel perspective. At other times the
departure from Renaissance perspective is striking: as in Picasso's Woman Reading
(Paris, Musées Nationaux, 1935).
The twentieth century has introduced yet another type of matching involving
occlusion. Renaissance painting had concentrated on the opening function of
perspective, treating the picture as a window into a world beyond. By contrast, the
occluding function concentrates attention on the picture as a surface. The opening
function had led painting to match architectural and sculptural effects. Yet, even
when painting created effects indistinguishable from those of architecture and
sculpture, it ironically upheld an underlying assumption that the three media were
distinct from one another. The occluding function of perspective, which
emphasized painting as surface, meant that painting was no longer a medium
which could match the effects of the other two, such that painting, architecture and
sculpture now emerged as equals, and what had been a focus on pictorial space,
shifted to a new interplay of pictorial with physical sculptural and architectural
space. One reflection of this basic change in orientation was a trend of important
painters, who also practiced sculpture: including Daumier, Gauguin, Degas,
Renoir, Bonnard, Picasso, Matisse, Modigliano, Braque, Derain and Leger.59
243
Aspects of cubism were also linked with this change in orientation, which
emphasized occlusion rather than transparency, and which relied on perspective
more than might be expected. Gleizes, for example, in his basic work On Cubism
(1921) retained respect for perspective:
In the beginning the framework created the perspectival principles was
robust, but it was reversed by the follies of realism, and it was
impressionism which threw itself hopelessly into atmospheric
inconsistencies.60
In his chapter on realism Gleizes admitted:
If an artist whose specialty is in painting still life academically suddenly
renounced all his favourite subjects for subjects composed of bricks,
cylinders, and boards he would paint them with optical perspective and
conventional lighting.
Many cubist paintings are simply a product of this substitution.61 Fernand Léger's
Nudes in the Forest (Otterlo, Kröller-Müller Museum, 1909-1910) comes to mind.
Gleize's aim, however, was to reduce painting to two-dimensional surfaces
To pretend to endow it with a third dimension is to wish to denaturalize it
in its own essence.
The results obtained will become only the trompe l'oeil of our threedimensional material reality, through the deceptions of linear perspective
and conventions of lighting.62
Mixing
Ultimately, Gleizes wanted to escape matching. The result was a new goal for
painting. As he wrote in his manifesto:
Painting therefore is not an imitation of objects. The reality of the exterior
world serves as its point of departure. But it strips away the world of this
reality to touch upon the spirit.63
Hence the trend in matching, which focussed on the surface of painting, led to a
new goal within cubism, which involved mixing visual and mental world. While
this re-opened the way for non-perspectival paintings, it also produced complex
new combinations of perspective. Three examples must suffice here. In Juan Gris',
La Place Ravignan. Still Life in Front of an Open Window (Philadelphia, Museum
of Art, 1915), the still life in the foreground was composed of a series of
intersecting planes, partly transparent, partly roccluding. In the background, both
wall and window were transparent. Hence the perspectival principles of
transparency and occlusion became a matter of play, while its spatial effects
continued to be important. Robert Delaunay, in his St. Severin (New York,
244
Guggenheim Museum, 1909), went back to the Renaissance theme of Church
interiors (e.g. pl. 8, 10, 16-20), introducing into the straight lines of the
architecture subjective curvatures. By contrast, Jacques Villon, in Abstraction
(Philadelphia, Museum of Art, 1932), used a room with very sharply defined
perspectival lines as in a Renaissance interior, but then removed details and played
with colour to create unexpected effects. Other movements in modern art, which
shared this goal of mixing outer and inner worlds, led to further experiments with
perspective: constructivism (Kasimir Malevich, El Lissitzky, Josef Alpers);64
surrealism (Max Ernst, Yves Tanguy, Salvador Dali),65 neo-romanticism (Eugene
Berman) and magic-realism (Pierre Roy, Paul Delvaux).66
Implicit verbal sources remained important. It would, for example, be difficult to
understand the symbolism of Salvador Dali or Paul Delvaux without some
biographical context. But a new dilemma now loomed. For the more these
paintings entered into the inner life of the individuals concerned and became
personal expressions, the more they required autobiographical knowledge, which
could not be expected of a general public. In the Renaissance, the emergence of
universally known texts such as the Bible had led to visualizations of implicit
verbal sources becoming more important than direct illustrations of texts. In the
twentieth century, as the concept of such universally known texts receded, a
reversion occurred: direct illustrations of verbal sources once again became more
important than visualizations of implicit verbal sources, whence the extraordinary
rise of a whole new genre of deluxe art books (Les livres d'art, Malerbücher)
which involved most major artists of the twentieth century ranging from Braque
and Eluard to Hockney.67 Picasso alone produced over 150 of such books.68
This renewed concern with a verbal filter detracted attention from perspectival
visualization.
Exploring
Meanwhile, another new goal involved exploring three further horizons of arts:
chance, the inner world and the perceptual world. The first of these, emphasizing
intuition, and relying largely on accidental actions and chance patterns, involved
abstract expressionism (Hans Hofmann, Sebastian Antonio Matta Echauren,
Willem de Kooning, Jackson Pollack).69 The second of these explored the inner
world: phantasy and the irrational. In the nineteenth century, romanticism had led
to the creation of dream worlds (Gustave Moreau, Rodolphe Bresden, Odilon
Redon).70 These continued into the twentieth century with the naive painters
(Henri Rousseau),71 and the metaphysical school (notably Giorgio di Chirico),72
which led to further explorations into the irrational through dadaism,73
surrealism74 and conceptualism.75 Striking is the extent to which these inner
visions emphasize perspectival space. Even in the art of mentally disturbed
persons, despite distortions, a basic spatial pattern is usually still recognizable and
sometimes has a compelling coherence of its own (e.g. William Kurelek).76
245
A third area of exploring has involved the perceptual world. It could be argued that
this was effectively an extension of the detailed attention to visual effects initiated
by the impressionists. In Antonio Lopez Garcia's drawing of Antonio Lopez
Torres (London, Marlborough Fine Arts Ltd., 1971-1973), for example, which
Arnason77 cites simply as part of the revival of representational painting in the
1970's, we note curvilinear effects on the floor reminiscent of those found in
Cezanne78 and Van Gogh.79 Inspired by nineteenth and twentieth century optical
theorists (Helmholtz, Hillebrand, Ames, Luneburg),80 a number of painters (see
above p. ) have claimed that spherical perspective more closely approximates the
effects of vision than does linear perspective. In the nineteenth century, thinkers
such as Hauck had considered spherical projections as subjective perspective.81
Panofsky followed this approach.82 However, recent thinkers such as Barre and
Flocon or Hansen claim83 that spherical projections exemplify objective
perspective.
In terms of strictly scientific principles of vision, the most succinct challenge to
these views remains Pirenne,84 whose work also poses problems for Termes'
experiments85 with one, two, three, four, five, and six point perspective (fig. ), or
Blotti's explorations86 of alternative projection methods (figs.
). To enter into
great polemics as to who is right, would be to assume that both sides are concerned
with the same thing, which they are not. Impressionists such as Pirenne's father,
and Pirenne himself, were concerned with information available to one eye, from a
given station point, at a given time and place. These contemporary artists, by
contrast, would argue that no single viewpoint does justice to the complexities of
visual experience and that the challenge lies, therefore, in incorporating,
combining, integrating different viewpoints simultaneously in achieving
panoramic effects, such as we experience when we walk around in every day life.
Certainly no eye from a single viewpoint could see all the images on the 360o
spherical surfaces of Albert Flocon's Tableau spherique (Paris, Grand Palais) or of
Dick Termes' Termespheres. Yet a painting, which does not stop with the artificial
boundaries of a frame and which continues to unfold as we walk around it, comes
closer, they would argue, to our experience of the visual environment of every day
life.
This quest to incorporate various viewpoints simultaneously has led artists such as
Lucien Day to renew interest in cylindrical projection planes, not as a rejection of
linear perspective, but rather as an attempt to go beyond its limitations. In Day's
own words:
My work is an attempt to incorporate more than one angle of vision in a
picture plane. I want to expand the means of academic perspective to
include more of what we see and how we see it.... Working with a camera,
I am able to freeze these changed peripheral elements and use them as part
of the picture. Instead of a fixed viewing eye, which is the basis of
academic perspective, I make two angles of vision work together.87
246
As Marcia Clark has demonstrated in an important exhibition, Day's concerns are
part of a new trend which includes Susan Crile's multiple perspectives, and Clark's
own conbination paintings in which, as she explains:
Though the painting is seen in three parts these connect in the mind's eye.
Both the shifting perspectives and the serial nature of the painting bring a
dimension of time into the visual experience. Within this, a process of
discovery can unfold, reflecting not only the view but also the experience
of seeing.88
In the context of our analysis three aspects of this trend are of particular interest.
One is how artists such as Clark, Crile and Lima consciously speak of their work
as metaphor.89 Second, is the way in which artists such as David Hockney, David
McGlynn and Richard McKown use photography, with its objective perspectivalimages, as a starting point for their subjective explorations of perceptual spaces.90
Whereas an earlier generation would have perceived oppositions between art and
science, subjective and objective methods, this generation is exploring how they
can be integrated in new ways. Related to this is a third phenomenon: for the quest
to integrate different spaces has focussed attention on the challenge of relating
different times. Clark referred to this in the passage cited above. Hockney has
drawn attention to it:
It's a different time in each square and as I went I found, suddenly at times,
incredible spatial effects happening, which made one realize that time was
deeply related to space - maybe they were the same thing - and
immediately I noticed its connection with cubism.91
McKown has been even more conscious of this process:
...each image in my work starts out as a separate exposure in the camera. I
want the viewer to experience the time element by looking at the individual
images before looking out at the illusion of the whole composition.... I'm
working with the aspects of cubism. However, by my use of photography,
there is a reference to reality that pulls the image into a whole instead of
fragments, so that the concept of time is slowed down and expanded.92
In emphasizing such temporal-spatial problems, these painters were, in a sense,
pursuing themes which Carpaccio had explored nearly five centuries earlier (see
above p. ) and demonstrating in a new way the limitations of Lessing's aesthetics,
which opposed painting and poetry in terms of space and time. Indeed, it could be
argued that the full implications of perspective for temporal-spatial dimensions of
painting are only now coming into focus.
In moving from pre-literate to literate society, imitating replaced connecting as a
goal. What is striking about these recent developments, however, is that they have
not replaced existing goals such that ordering, matching, mixing and exploring,
247
with their various subcategories: all exist together. At a certain level, evolution is
embracing, not replacing. The full significance of this phenomenon has yet to be
assessed. It is instructive to recall, for instance, that just over a half century ago
Novotny wrote an influential work entitled, Cezanne and the end of scientific
perspective (1938).93 He was by no means alone. Many of his contemporaries
were fully convinced that exploring chance and abstraction had become the only
goal of modern art, and even today, some scholars still assume artistic progress
occurred in terms of one goal at a time.94 In these minds, art history since 1500
could be reduced to a simple story of how artists gradually rejected perspectival
principles, and the twentieth century became a final chapter in a move from
perceptual to conceptual art.95
Our all two brief outline has shown a rather different story. For if perspective was
rejected by those exploring chance and abstraction, it has proved essential in
exploring both the perceptual world and the inner world (naive and metaphysical
art), in new goals of mixing outer and inner world (cubism, constructivism,
surrealism, neo-romanticism and magic realism) and new branches of matching
(precisionism, pop art, new realism, photo realism, hyper realism). All of which
helps to explain the pattern of publication revealed in fig. 47:
1400-1499
1500-1599
1600-1699
1700-1799
1800-1899
1900-1989
1
456
732
849
2714
2801
Fig. 47. Books on perspective printed since 1400.
Perspective did not die: it did not even experience a serious decline. Since 1500 its
story has been one of continuous development. What began as a mechanical means
of recording the outer world objectively in quantitative terms, has become a
fundamental method for exploring the inner world with its subjective dimensions.
Perspective has led the west to create more images than any other culture. In the
process it has given us a concept of visual metaphor, leading to ever subtler plays
on is-is not, teaching us that seeing is also seeing through, revealing positive
dimensions of illusion, opening our image-ination, asserting in unexpected ways
our freedom as individuals.
9. Conclusions
Two generations ago, the greatest scholar in the field, Erwin Panofsky, could
plausibly claim that perspective was a symbolic form,96 that a given culture was
bound to a particular method of spatial representation: that spherical perspective
belonged to antiquity and linear perspective specifically to the Renaissance. This
tantalizing hypothesis unfortunately raised more problems than it answered: what
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evidence was there that the Greeks had developed a coherent method of spherical
perspective? Why did some scholars insist that the Greeks had linear perspective?
If linear perspective truly belonged to the Renaissance, why was it that this period
also offered the first serious evidence of spherical (Fouquet), cylindrical
(Mavolois) and conical (Vaulezard, Niceron, Dubreuil) perspective? Why should
spherical perspective have found new exponents in the nineteenth century (Hauck,
Ware)? Indeed what happened to culture after the Renaissance?
Panofsky,97 his colleague Cassirer, and Aby Warburg, at whose institute they both
worked, had been inspired by neo-Kantian theories of culture (e.g. Cohen),98
which began with a premise that there was progress, that each stage in cultural
evolution brought a new world view, and that each world view determined
perception and representation, in both theory and practice. This implied that any
given culture was limited to a single method of representation, and progress would,
therefore, be a simple linear development. Ironically Panofsky's own studies
suggested, and Warburg's meticulous research showed conclusively, that the
details of Renaissance art involved so many particulars and contradictions, that
they could not be reduced to one goal of representation determined by a single,
universal world view.
Warburg's biographer,99 who later became director of his institute, pursued these
problems in three studies in the art of the Renaissance (Norm and Form, Symbolic
Images, The Heritage of Apelles),100 in which he examined the climate that made
different artistic expressions possible, as a direct challenge to deterministic claims.
But he devoted his main energies "to study some of the fundamental functions of
the visual arts in their psychological implications."101 While insisting that art has
a number of different goals or functions including narrative, caricature and
symbolism, Sir Ernst Gombrich focussed attention on two major functions:
ornament (A Sense of Order)102 and illusion (Art and Illusion, Illusion in Nature
and Art, Image and the Eye).103 He saw the problem of illusion as relatively well
defined:
It basically concerns the process by which the rendering of the visible
world was seen to change from schematic to naturalistic styles - a process
which can be observed twice in the history of art - in classical antiquity and
again in the Renaissance.104
This suggested, however, that the Renaissance brought nothing new, that it was
literally a rebirth,105 and simply involved a repetition of ancient illusionistic
tricks. Underlying this approach was an important assumption: that concepts of
progress and determinism were necessarily linked, and that in order to escape the
totalitarian perils of the latter, it was wiser to forego entirely the very idea of the
former.106
This essay points beyond these problems of either-or. The six goals of art outlined
above are not deterministic in a narrow sense. We have shown that Antiquity tried
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at least five different versions of imitation; that the Renaissance practiced linear,
conic, cylindrical, spherical and parallel perspective, and that there has been an
even greater diversity in the modern period as a simple glance at Blotti's
alternatives (fig.
) reveals. Therefore simplistic equations between one worldview, one theory of vision and one practice of representation can be rejected
outright. Nonetheless, certain goals favoured some methods, and actually
precluded others. We have shown, for instance, that connecting, ordering and even
imitating precluded perspective, whereas matching, mixing, and most branches of
exploring required perspective.
The climates which precluded or favoured perspectival representation were more
than a question of theory. They involved architectural construction, such that
building spaces with perspectival effects was an important prerequisite for
perspectival representation. They were also bound up with levels of literacy:
connecting and ordering requiring none, imitating needing some, matching
requiring a textual community, mixing and exploring requiring complex textual
communities with a heritage of both visual and verbal images.
1. Connecting
2. Ordering
3.
4.
Imitating
1.
2.
3.
4.
5.
Narrative
Ideal world
Isolated objects
Isolated objects-using optical adjustments
Imaginary scenes-using optical adjustments
1.
2.
3.
4.
Directly
Verbal sources
Implicit common verbal sources
Implicit common verbal sources-as everyday
life,landscape
Implicit common verbal sources-as play, irony
Implicit uncommon verbal sources
Recurring events, topoi
Distortion (Anamorphosis)
Distortion through simplification
Surface
Matching
5.
6.
7.
8.
9.
10.
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5.
6.
Mixing
1.
2.
3.
Directly
Verbal sources
Implicit verbal sources
1.
2.
3.
Mental world
Perceptual world
Chance
Exploring
Fig. 43. Six basic goals of art
Seen in this way both Antiquity and the Renaissance emerge as distinct phases,
and a cumulative dimension of culture comes into focus. The Renaissance could
never have attempted its synthesis of Christian and pagan images had there not
been these two traditions, had these not been a well established culture which
made this heritage accessible. Whereas Ancient imitation limited itself to
representation of universals, Renaissance matching opened art to representation of
individuals and took art in at least ten new directions (fig. 48). Some of these
evolved simultaneously: e.g. the visual world, illustrating verbal sources directly,
implicitly, recurring events and topoi. Others, such as illustrating verbal sources as
every day life, with play, irony or distortion were only possible when new levels of
distance had been reached, and these levels, once attained, rendered difficult return
to a more naive level. Hence the process was not only cumulative: it tended at a
certain point to become irreversible.
Earlier goals of art linked visible and invisible worlds: connecting, for example,
linked a visible statue with an invisible god; imitating linked visible statues with
invisible gods and concepts, thus leaving only one side of the equation testable,
and keeping object and subject conflated. By contrast, in the Renaissance,
perspectival matching established links between visible objects and visible
representations, thus making both sides of the equation testable and, at least a
theory, separating subject from object. Cassirer, in his Individual and the Cosmos
in Renaissance philosophy (1928) described the subject-object distinction as a
static event, brought about by a shift from a finite to infinite world view.107 In our
analysis, the subject-object distinction grew out of an interplay of perspective, new
levels of literacy, and interpretation, was dynamic, and should be seen as part of a
larger process involving increasing levels of distance (fig. ).
Perspective thus emerges as something much more profound than an early copying
tool. It led to a systematic exploration of interiors and exteriors, of inside and
outside space in the natural world, and pointed to new distinctions between inner
and outer at a psychological level. If its matching function brought the natural
world into closer focus for study, it was simultaneously a distancer. Hence there
was a two-fold way in which perspective brought a new power over images: first,
251
it introduced systematic combination and play in the representation of basic spatial
forms. Second, it led to representation being recognized as something separate
from the observer, at levels of greater aesthetic distance, such that playful
treatment of images in another sense became possible also.
There remained a serious side to this playfulness, however. For the method which
rendered nature visible for man, and liberated man from nature, also threatened to
separate him in the negative sense, to alienate him. Connecting had assured a
feeling of being at one with nature through communal rituals involving a
totem.108 With matching this communal assurance was gone, and reassurance
was at an individual level, using representations in galleries to reestablish
relationships with nature. Seen in this way the art galleries of our cities are by no
means luxuries. Even the visual metaphors and puns on billboards in major cities
are more than advertising gimmicks: they are a part of a process helping us to see
through illusion and gain more distance from nature and ourselves without
becoming alienated: teaching us to see our relationships.
Perspective is therefore much more than an instrument of art. It is an instrument of
civilization, creating representations convincing enough that we can accept them
as substitutes for the most threatening dimensions of reality: such that pictures,
movies and videos, become substitutes for war, violence, rape and other forces of
destruction, while at the same time threatening to stimulate the very things they
were aimed to prevent. At the limit, a life of action in the field risks becoming a
life of reaction to a camera or a screen. But this may be the price for a method,
which transformed the closed, prescriptive rules of representation to an open,
descriptive approach, which encourages new images, challenges creativity and
imagination, and asserts our fundamental freedom.
252
III. EPILOGUE
1.Introduction. 2.Vision, Representation and Culture. 3.Ambiguities. 4.Price of
Vision. 5.Scale. 6.Fractals and Scale. 7.Passive Recording and Active
Intervention. 8.Objectivity and Subjectivity Reconsidered. 9.Scales and Samples.
1.Introduction
The discovery of perspective has been ranked with the discovery of the new world
as one of the great events of western culture. Its advent has been described as a day
the world changed. Indeed some popular accounts could lead us to believe that
Brunelleschi woke up one morning and decided that he would change the western
concept of space. We have shown that there was no sudden revolution. A gradual
evolution in spatial representation was part of a larger phenomenon involving
changes in the construction and reconstruction of space.
Awareness of these changes came more slowly. A generation passed before
Manetti and Filarete even mentioned Brunelleschi's demonstration. Another
generation passed before Pacioli (1494) mentioned by name some of the early
Italian practitioners and theorists. Vasari (1560) widened the scope considerably
mentioning a number of individuals, some specific paintings and several treatises
but usually without specific titles or dates. Lomazzo (1590) alluded to at least
seven treatises which can be identified. Thirty four subsequent bibliographies have
increased the number of sources to 1284 (Index at V.1). The present bibliography
contains 7,900 sources. With respect to perspective in a strict sense we have
attempted to be comprehensive. But under more general headings such as
geometry there is more to be found and with respect to related topics such as
sundial projection or cartography there is a vast amount of material that has yet to
be examined.
Hence although 450 years have passed since the advent of perspective, awareness
of even the basic sources remains incomplete. Of these only a tiny sample has, in
turn, been used in considering the history of perspective in particular and
projection methods in general. Poudra's (1864) standard history cites 167 sources.
Panofsky (1927), the most famous single study in the field, cites 24 sources. It is
not surprising, therefore, that the claims made by these authors need revision. We
shall begin with changing relations of vision, representation and culture. We shall
then show that vision, as used in the West since the Renaissance, is complex and
comes at a considerable price but nonetheless brings enormous advantages largely
through concepts of scale. Recent developments with fractals challenge us to
reconsider basic assumptions of perspective in terms of scale, whether the process
is passive or active, objective or subjective, and indeed, the very foundations of
scientific method. We shall suggest that this offers new ways of understanding the
unique characteristics of western culture.
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2.Vision, Representation and Culture.
Panofsky's most famous claim was that perspective is not something absolute, that
is can be seen as a symbolic form in Cassirer's sense, that each culture has its own
world view, particular theory of vision and corresponding theory of representation.
According to Panofsky a finite world view of the Greeks led to a spherical theory
of vision and perspective, while the emergence of an infinite world view in the late
middle ages led to linear perspective and a corresponding adjustment in Euclidean
optics. As we have shown (p.202), this model is too simple.
We have shown that these changing relationships of vision, representation and
world view are better understood if we see them in the context of texts and
literacy. In pre-literate societies, for instance, individual artists might reflect on
these questions but, because they did not write them down, no fixed theory could
be identified with their particular culture. The absence of texts meant absence of a
defined standard. This allowed freedom with respect to loosely defined boundaries
of a given style, yet imposed constraints in that such societies were usually limited
to one style with which to identify themselves. The advent of manuscripts was a
necessary but not sufficient condition for texts on vision and representation. India
developed a complex culture without texts on optics or representation. China
produced texts on representation without reference to theories of vision. Islam
produced texts on optics without reference to representation. Greece, which
produced texts on both vision and representation was an exception. These texts
were more ambiguous than Panofsky assumed. Euclid's theory of vision could be
taken to imply spherical, cylindrical or even flat projection planes. Hence Greece
did not establish a given projection method for optics and art. Its contribution lay,
rather, in using geometry for vision and representation, but geometry without
reference to measured size and distance, i.e. without a defined scale.
During the Renaissance, which saw the advent of printing, written theories of
vision and representation became more widespread. Geometry was applied
increasingly in conjunction with measured size and distance. But it was again the
case that no single projection method was used exclusively for vision and art.
Explorations of planar projection methods in linear perspective went hand in hand
with study of angular, pyramidal, conic, cylindrical and spherical projection
methods. Hence the important characteristic of the period 1400-1600 was not
simply the use of linear perspective but rather a recognition that, depending on the
surface used, representation involved a number of projection methods governed by
mathematical laws: i.e. that projection depended on geometry rather than optics.
This raised further questions which came into focus in the period 1600-1800:
whether there might be different projection methods in everyday vision and
representation and whether there could be conflicts between these methods. One
reaction was to concentrate on representation. Another was to consider only cases
where there was no conflict. Since 1800 there has been increasing interest in what
the precise nature of these conflicts might be and has led, more recently, to
renewed study of cylindrical, spherical, hyperbolic and other complex planes
254
which frequently reflect personal theories of vision rather than claiming to embody
universal optical laws.
Panofsky claimed that each society develops a specific theory of vision and
corresponding theory of representation. Our claim is that articulate theories of
vision and representation do not emerge in pre-literate societies; that such theories
require manuscripts and only begin to thrive when there are printed texts and that,
paradoxically, the advent of print culture, instead of establishing one specific
method to the exclusion of others, proliferates the number of methods. Advances
within such cultures cannot therefore be seen as a simple choice of a new method
and are better understood in terms of increasing distinctions between vision and
representation and attention to personal solutions for bridging these distinctions.
So it is not really a question of which kind of perspective is used in a society, but
rather a more basic problem of the ways in which mathematics, and particularly
geometry are used in explaining vision and representation. If Panofsky were
writing today he might have discussed mathematics in optics and representation as
a symbolic form.
3.Ambiguities of Vision
It is so difficult to discuss these changing relationships largely because vision,
which is often assumed to be constant, varies culturally and historically. A
paleolithic tribesman, an Athenian Greek, a Renaissance Florentine, an eighteenth
century Parisian and a modern New Yorker all have two eyes. Yet what each of
them could see varies tremendously. A contemporary native of the Amazon rain
forests sees all kinds of dangers which we as casual tourists would never notice:
dangerous animals, deadly snakes, poisonous plants, and at the same time is only
aware of a small percentage of the 1700 species of birds which fly around him. An
ornithologist will see the species, but may not see the trees for the birds. Someone
who grows up driving automobiles at 200 kilometers per hour on German
highways sees very different things.
Every occupation and profession focuses on certain visual skills at the expense of
others: a hunter, a goldsmith, tool and die maker, geologist, detective, botanist and
an artist each see different dimensions of what is theoretically one world. Most?
cultural history is frequently approached in terms of isolated representations of
artists which are then taken as typical of the way in which a culture "saw." Sir
Ernst Gombrich has explored other reasons why one might wish to avoid speaking
of what persons "saw" altogether. Strictly speaking we can, at best, only attempt a
history of what persons recorded in the form of words and pictures as having seen:
a second-hand history of sight, as it were. Even in this we have scarcely begun.
Histories of graphic methods such as Dubery and Willats are strikingly summary.
A comprehensive history of projection methods has yet to be written. A history of
how different trades and professions changed the boundaries of the visible has yet
to be attempted.
255
4.The Price of Vision
There are also more subtle problems. We have shown that perspective owed much
to a late mediaeval commitment to transform storytelling into painting, and we
have emphasized the positive dimensions of this process. It exploded the
boundaries of representation. It introduced spatio-temporal dimensions. But all this
also came at a price. For it reduced the dynamic act of storytelling to static
moments. It took away the performance aspect, the spontaneity, the uniqueness of
the process, replacing this with something fixed, motionless, but capable of being
reproduced almost exactly. Cultures such as China, India and Africa chose another
path. They frequently avoided pictures and even words altogether, preferring to
translate their stories into dance. In this form each version of a story was unique,
spontaneous, full of motion and life, yet incapable of being repeated exactly. The
west wanted repeatability and gradually found it, but again at a price. Each step
closer to repeatability meant more mechanical aids, first compasses, then
pantographs, gradually cameras, photo copy machines and CAD graphics
packages. Every step closer to a perfect copy, threatened to become more
impersonal. Fortunately there were also enormous advantages which made this
price bearable: these involved systematic control of representation which came
through mastery of scale, size and distance.
5.Scale
In pre-literate societies, where there were no fixed rules of vision and
representation, there were no concepts of scale, size and distance. A voodoo witch
could use a tiny doll to affect a large man whether he were near or far away. The
size of the doll, the size of the victim, the distance between the two, were
meaningless factors in a magical context. Greek theories of vision and
representation included some ideas of lines, angles and proportion. This brought a
concept of scale to individual objects rather than contexts, as becomes clear if we
return to our earlier example of the planisphere (fig. 64a). When the tropic of
cancer was projected onto the equator its scale was reduced. Whether the drawing
involved was small as it is here or as large as the actual size of the earth made no
difference. Hence although scale within a drawing was important, the scale of the
drawing itself was irrelevant. This applied to all representations (sculptures,
paintings and drawings) where proportions were constant (fig. 64.b-c). Hence tiny
statuettes and monumental statues had the same effect, and there was no incentive
to change scale in order to bring objects into focus and study them more closely.
Only changes in angle and proportion were significant (fig. 64. d-e).
256
Fig. 64 Greek projection methods concentrated on scale within an object rather
than scale between objects. Whether a diagram was small or large did not matter.
Only changes in angle were important.
The advent of perspective in the Renaissance integrated Greek geometrical ideas
of line, angle and proportion with measured size and distance. A small picture
might represent small objects which were nearby or large objects at a distance.
Size now became a relation between apparent and measured size which varied with
distance. It was not distance between isolated objects, but distance between planes
that counted. If distances were too great and objects too small, this could be
solved by changing their scale. Perspective thus brought incentives for the
development of telescopes and later of microscopes. All this shifted attention from
scale within an object to scale between objects in a given plane and scale between
objects and contexts: persons and buildings to townscapes and landscapes, and
these in turn to surveyors' charts, topographical views and maps. An inverse
size/distance law governed these relations and all one needed to do was to decide
which scale was appropriate for which purpose. This had enormous consequences
for representation: scenes, townscapes, landscapes, views and maps could all be
coordinated systematically. A sense of mastery and domination of nature emerged,
a sense that everything could be measured, but a key to objective control had been
found. Objectivity was simply a question of changing scale in order to get things
into focus.
6. Fractals and Scale
Renaissance perspective was based on the assumption that every object has a fixed
measured size, that size and shape within a given plane are constant and that size
varies only with distance. The advent of microscopes called these assumptions into
question. Within a certain range of magnification objects simply appeared larger,
i.e. scale affected only size. Magnification beyond this range affected both the size
and shape of objects. This was known in the seventeenth century and it became
obvious in the eighteenth century when instrument makers such as Brander and
Martin began using telescopes and microscopes in connection with perspective.
Electron microscopes introduced more vivid examples. Yet, curiously enough, the
philosophical implications of the discrepancy remained unnoticed and it took the
development of fractals to recognize that this principle involved something far
more basic than special conditions in microscopes and telescopes.
James Gleick used a map of England as an example. If one uses a ruler one
kilometer in length then the coast has a certain number of corners and a given
length. If one uses a ruler one meter in length than the same coast has a thousand
more corners. If one uses a ruler one centimeter in length the same coast may have
100,000 more corners then the same coast measured in terms of kilometers. The
coast measured in centimeters will also have a far greater circumference than the
coast measured in kilometers. Perspective assumed that scale affects only size.
Fractals confirm that scale affects shape as well as size.
257
7.Passive Recording and Active Intervention
The consequences of this corollary run deep. As long as scale affected only size, it
could be claimed that perspective, which recorded the world in different scales,
was a passive recording technique which did not interfere with the essential
characteristics of that which it examined. Perspective was therefore a model for
the scientific method of passive, objective observation and recording without
active subjective intervention. If, however, scale affected the basic shape of what
was studied, then perspective, which played with scale, was tampering with the
evidence that it claimed to be recording and was subjective in a way that Panofsky
and his followers had not suspected.
8.Objective and Subjective Reconsidered
The problem is partly conceptual. The subject-object distinction as formulated by
Cassirer, was mainly in terms of a Cartesian duality, as if subjective and objective
were in opposition to one another like mind and matter or quality and quantity; the
subjective actively imposing itself onto the world, the objective passively
recording the world. This model was too simplistic. Perspective might aim to
record the outside world passively but to do so required reducing nature's
incredible complexity to simple forms and patterns which could easily be traced on
the picture plane. Hence it was no coincidence that regular polygons and regular
architectural forms such as arches and cupolas played so prominent a role in early
perspectival treatises. In the case of fields and landscapes the problem was
resolved by reducing their complex irregular surfaces to a small number of station
points which could then be joined to produce simple polygonal forms. Passive
recording of a landscape required an active imposition on its surface of
geometrical shapes amenable to being recorded.
Heisenberg's indeterminacy principle introduced the idea that one could not study
problems in quantum physics without disturbing the evidence. Perhaps we need to
see the whole of early modern science in these terms: that universal measurement
in the Renaissance needed more than a conviction that the language of nature was
written in the alphabet of geometry. It required an active imposition of Euclidean
geometry on nature, and this particular kind of active, subjective interference with
nature was paradoxically inseparable from the passive objective recording to
which it is frequently described as being opposed. And like the size of the mesh in
a fish net which determines the size of fish which can be caught, the geometrical
grid of Euclidean geometry determined the scale of reality which could be
recorded. Accordingly geometrical figures with straight lines and circles replaced
the complex curves of botany and biology in early scientific textbooks. Nor did
this change dramatically in the nineteenth century with the non-Euclidean
geometries of Lobachewsky, Bolyai and Riemann which projected these simple
geometrical forms onto spherical and hyperbolic surfaces. Mandelbrot's fractal
geometry was the first to offer new possibilities in recording nature's complexity.
258
Hence the distinction between inner subjective and outer objective forms remains
valid, as do the quest for quantitative measurement traditionally associated with
objectivity and perspectival projection principles which apply equally whether one
records a simple square or a fractal form. But more is involved than a passive
recording of an object in one scale onto a picture plane in a second scale (fig. 65).
Fig. 65 The recording principles of perspective apply whether the object recorded
be a Euclidean square or a fractal form. Yet the scale of the original object affects
the shape as well as the size of the object to be recorded.
An active choice is required to decide the initial scale of the first object for this
determines the shape as well as the size of the object to be recorded. In other
words, besides actual measurement of an external physical object, objectivity
involves a subjective decision about the scale of measurement which provides
parameters and tolerances of what is to be measured.
9.Scales and Samples
Simple as these distinctions may seem, they have basic consequences for concepts
of knowledge and are very much bound up with western culture. In cultures where
there was no distinction between subjective (inner, mental) and objective (outer,
physical) images, knowledge was internal, psychological and lay in a person's
conception of an image with no need to study further examples and no incentive to
communicate this conception. In this extreme case knowledge could stop with a
sample of one. Already in Greece, the west embarked on a different course. Plato
combined this approach with a belief in ideal images which theoretically required
only introspection but in practice assumed the external stimulus of dialogue. His
student Aristotle argued that knowledge was something to be collected rather than
meditated, appropriated from outside rather than sought inside, an approach
259
inherited by Islam and in turn by the Christian West, where it was reinforced by a
belief in Creatural realism, particularly through the Franciscans and Dominicans.
The development of perspective brought into focus a distinction between outer
images which could be seen, recorded and measured and inner images which could
not.
Perspective introduced systematic rules for recording external objects. Instruments
such as the perspectival window or compass and ruler, and later the proportional
compass and pantograph were intended to simplify this process. They also
revealed that the process was much more complex in practice than in theory and
that the catalogue was potentially much larger than suspected.
While visionaries such as Francis Bacon made pleas for a catalogue of all possible
examples, two decisive factors stood in the way. First, the neo-Platonic heritage
fostered deep-seated assumptions about the regularity of knowledge which limited
attention to ideal examples. Secondly, as we have noted, the recording process
itself used the idealizing filter of Euclidean geometry. This meant that knowledge
was limited to an empirical example of regular cases. Nonetheless, the
development of ever more precise instruments assumed that the recording and
collecting process continued to be cumulative. For instance, the camera revealed
many new complexities in the process of recording and greatly expanded the size
of the potential catalogue. The computer is doing the same. A recent study at the
Bell Laboratories compared vocabularly used in the New York Times over a six
month period with that of standard dictionaries and found that over 30% of the
words in the newspaper were not in standard dictionaries. International projects of
Greek vases, coins, statues or bibliographies such as the present one all point in the
same direction: earlier claims were all made on the basis of surprisingly small
samples which were frequently kept deliberately small.
An interesting pattern thus emerges. Societies where no distinction was made
between inner and outer tended to be closed, and focussed attention on their own
culture, rather than looking futher. Societies with some awareness of inner and
outer began to appropriate knowledge from other cultures. As the distinction
became more clearly defined, this process of appropriation became more visible.
The emergence of perspective in early fifteenth century Florence thus went hand in
hand with an unprecedented interest in other cultures through the collection of
Hebraic, Arabic, Chaldaian, Babylonian and other sources, leading gradually to the
disciplines of anthropology, archaeology, ethnography and comparative religion
which have developed in the west as nowhere else, although ideologies such as
fascism and other-isms have tried to limit this looking outwards and control ideas
even more systematically than in earlier closed societies.
Perspective, as described by Panofsky and most subsequent authors, was a
phenomenon linked specifically with the Renaissance. Its impact, as they described
it, was mainly in the domain of painting, the creation of a particualr approach to
space. We have shown that it had fundamental consequences for both science, art
260
and literature; that it changed the way western man constructed his environment,
and we are suggesting that it transformed the ways in which he acquired
knowledge, that the distinctions between inner and outer which it set in motion, led
to an increasing externalization and objectivization of the world, which focussed
attention away from verbal universals to visual particulars and thereby challenged
him to use ever larger samples in making claims concerning knowledge.
Meanwhile, the concepts of scale which perspective introduced had long term
implications for both the recording and organization of knowledge. For these
reasons perspective needs to be seen as more than a cultural expression specific to
the Renaissance, and recognized as one of the pivotal concepts of European
culture, the implications of which are still being explored. For what began as a
looking into, a seeing through, has led from a literal fixing of the horizon to a
metaphorical looking beyond one's horizons and a study of other cultures. What
began as a symbol for a fixed approach to space has become an emblem of spatial
play, of imagination and freedom.
261
10. NOTES
Introduction
1. William M. Ivins Jr. Art and geometry, Cambridge Mass.: Harvard University
Press, 1946; Martin Foss, The idea of perfection in the western world, Lincoln:
University of Nebraska Press, 1946.
2. Julius von Schlosser, Die Kunstlitteratur, Vienna: Schroll, 1924; translated by
Otto Kurz as La letteratura artistica, Scandicci (Florence): La nuova Italia
editrice, 1964 (reprint 1986).
3. Samuel Y. Edgerton, Jr., The Renaissance Rediscovery of Linear Perspective,
New York: Basic Books, 1975.
Chapter 1
1. Objective as used here refers to a systematic relationship between object and
representation without necessary intervention of the human eye. A school of
modern artists characterized by Hansen (e.g. 1987) disagrees with this definition
and would include as objective all mathematical systems which attempt to record
impressions of or at the eye.
2. Vitruvius, The Ten Books on Architecture, tr. Morris Hicky Morgan, New York:
Dover, 1960, p. 198. For the original Latin see, Vitruvii De architectura libri
decem, ed. Dr. C. Fensterbusch, Darmstadt: Wissenschaftliche Buchgesellschaft,
1976, p. 308.
3. See, for instance, John White, The Birth and Rebirth of Pictorial Space,
London: Faber and Faber, 1957, chapter XVI, "Spatial design in Antiquity." The
other major exponent of the view that the Greeks had knowledge of linear
perspective is A.M.G. Little, Roman Perspective Painting and the Ancient Stage,
Shiremanston: Moretus Press, 1971. Against this view is G.M.A. Richter,
Perspective in Greek and Roman Art, London: Phaidon, 1970.
4. Vitruvius, tr. Morgan, as in note 2, p. 211; c.f. Vitruvius, ed. Fensterbusch, pp.
332-335.
5. See, for instance, H .G. Beyen, Die Pompejanische Wandekoration vom und bis
zum 4 Stil, The Hague: Martinus Nijhoff, 1938-1960, 2 vols.
6. See, Alfonso de Franciscis, La villa romana di Oplontis, Recklinghausen:
Verlag Aurel Bongers, 1975.
262
7. This point has been made by Miriam Shild Bunim, Space in Mediaeval Painting
and the Forerunners of Perspective, New York: Columbia University Press, 1940,
p. 31.
8. John Pennethorne, The Geometry and Optics of Ancient Architecture, London:
Williams and Norgate, 1878.
9. Plato, "The Sophist," 236 a-c in The Collected Dialogues of Plato ed. Edith
Hamilton and Huntington Cairns, Princeton: Princeton University Press 1961; p.
978-979 (Bollingen Series LXXI).
10.
For this and other examples see Jurgis Baltrusaitis, Anamorphoses, ou
magie artificielle des effets merveilleux, Paris: Olivier Perrin, 1969, pp. 10-14.
There is an English translation by W.J. Strachan, Anamorphic Art, Cambridge:
Chadwyck-Healey Ltd., 1977.
11. For an introduction to this complex story see J. Baltrusaitis, as in note 10
above, pp. 71-78. For more details see Hans Willem Van Helsdingen, Historier en
peindre: Poussins opvattingen over kunst in het licht van de discussies in de franse
kunstlitteratur in de twede helft van de zeventiende eeuw, Proefschrift, Utrecht,
1971.
12. L. F. Shegin, Die Sprache des Bildes, Form und Konvention in der alten Kunst,
Dresden: VEB Verlag der Kunst, 1982.
13. This point was made in Leon Battista Alberti, On Painting, ed. John Spencer,
New Haven: Yale University Press, 1956, p. 121. Cf. Alberti, De pictura ed. Cecil
Grayson, Rome: Laterza, p. 55:
id velum quod ipse inter familiares meos sum solitus appelare
intercisionem, cuius ego usum nunc primum adinveni.
14. For a transcription of this passage see the author's Leonardo da Vinci and the
Visual Dimensions of Science and Art (Munich: Deutscher Kunstverlag, 1986),
p.443.
15. See Michel Gallet, Les origines de la perspective linéaire. Evolution de
l'optique picturale pendant la renaissance. Thèse presentée pour le diplôme
supérieur de l'Ecole du Louvre, 1955.
16. Joseph Harnest, "Dürer und die Perspektive" in: Albrecht Dürer, ed. Peter
Strieder, Königstein: Langewiesche, Karl Robert, Nachfolger Hans Koster, 1981,
p. 358.
263
17. Our figure 17 is a translation from the classic article by M. D'Avezac "Coup
d'oeil historique sur la projection des cartes de géographie," Bulletin de la société
de géographie, Paris, avril, mai, juin 1863, p. 152.
For a brief introduction to historical methods see Johannes Keuning, "The
history of geographical map projections until 1600," Imago mundi, London, vol.
12, 1955, pp. 1-24. For a standard modern textbook on the subject see J.A. Steers,
An Introduction to the Study of Map Projections, London: University of London
Press Ltd., 1927, etc. On the complex problems of Ptolemy's cartographic methods
see: Mollweide, "Mappirungkunst des Claudius Ptolemaeus, ein Beitrag zur
Geschichte des Landkarten," Monatliche Correspondenz zur Beforderung der Erd
und Himmelskunde von Baron von Zach, Gotha, Bd. 11, Apr. 1805, S. 319-340,
504-415; "Die Gradnetze des Ptolemaus im ersten Buche seiner Geographie.
šbersetzung der Kapitel 21 bis 24 nebst Anmerkurgen und Figuren," Beilage zum
Jahresbericht des Königlichen Gymnasiums zu Chemnitz fur das Schuljahr, Ostern
1908, bis Ostern 1909....Chemnitz: Druck von J.C.F. Pickenhahn & Sohn, pp. 1-28
(Programm-Nr. 726). The idea that Ptolemy developed a third method of
projection was put forward by Konstantin Cebrian, Geschichte der Kartographie.
I. Altertum, Gotha; Justus Perthes, 1922, p. 98 and Abb. 6 and developed by Otto
Neugebauer, "Ptolemy's Geography. Book VII, Chapter 6 and 7", Isis, Cambridge,
Mass., vol. 50, 1959, pp. 22-29; Kirsti Andersen, "The Central projection in one of
Ptolemy's map projections," Centaurus, vol. 30, 1987, pp. 106-113. Also
important in this context are Lauri O. Th. Tudeer, "On the origin of the maps
attached to Ptolemy's Geography," Journal of Hellenic Studies, London, vol. 37,
1917, pp. 62-76; Dr. Paul Schnabel, "Die Enstehungsgeschichte des
kartographischen Erdbildes des Klaudios Ptolemaios," Sitzungsberichte der
preussischen Akademie der Wissenschaften, Philosophisch-historische Klasse,
Berlin, Stuck VIII, 6 März 1930, 214-250; Hans von Mzik, "Neue Gesichtspunkte
zur Würdigung der Bedeutung der Geographie des Klaudios Ptolemaos fur die
Orientalistik...," Litterae orientales, Leipzig, vol. 54, Apr. 1933, 1-16; Ptolemaeus,
Theorie und Grundlagen der Darstellenden Erdkunde, tr. Hans v. Mzik, Friedrich
Hopfner, Vienna: Gerold und Co., 1938. (Klotho, Bd. 5. Des Klaudios Ptolemaios
Einführung in die darstellende Erdkunde); Leo Bagrow, "The origin of Ptolemy's
Geographia," Geografaska annaler. Utgivna av Svenska sallskapet for antropologi
och geografi, Stockholm, vol. 27, 1945, pp. 318-387.
It is perhaps not irrelevant to note that Danti (1583) in his annotation to
Problema VIII. Proposizione XXXVI refers not to Ptolemy's Geography but rather
to his Almagest, Bk. I, Chap. 9 regarding inscription of regular polygons in circles
and similar geometrical problems. Stevin (1605) in his 1st definition mentions that:
"Optics as genus has several species such as catoptrics, dioptrics, planispheres,
sun-dials, perspective proper and several others." In other words there are links
between optics, perspective and astronomy rather than with geography.
264
18. The relevant passages have been translated and analysed in the author's work
on Leonardo, as in note 14 above, pp. 143-169
19. See, for instance, Timothy K. Kitao, "Prejudice in perspective: a study of
Vignola's perspective treatise," Art Bulletin, New York, vol. 44, Sept. 1962, pp.
173-194 and Robert Klein, "Pomponius Gauricus on perspective," Art Bulletin,
New York, vol. 43, Sept. 1961, pp. 211-230.
20. Cf. Wilfred Theisen, The Mediaeval Tradition of Euclid's Optics, University of
Wisconsin, Ph.D. Thesis, 1972.
21. Al-Farabi, Catalogo de las ciencias, ed. A. G. Palencia, Madrid: Consejo
superior de investigaciones cientificas, Patronato Menendez y Pelayo, Instituto
Miguel Asia, 1953.
22. See the author's thesis Renaissance Optics and Perspective. A Study in the
Problems of Size and Distance, D. Phil. Thesis, Warburg Institute, University of
London, 1975, pp. 15-73.
23. Spencer edition, as in note 13 above, p. 69.
24. See Rocco Sinisgalli, Borromini a quattro dimensioni, Rome: Universita degli
studi di Roma - Facolta di architettura, 1981.
25. Cf. the title to Vredeman de Vries, Perspective, id est, celeberrima ars
inspicientis aut transpicientis oculorum aciei in pariete...Leiden: Hondius 1604.
26. For a standard analysis of Saenredam's methods see Rob Ruurs, Saenredam.
The Art of Perspective, Amsterdam: Benjamins/Forsten Publisher, 1987. (Oculi,
Studies in the arts of the Low Countries, volume 1.)
27. See: Il libro di Victruvio architecto tradocto di latino in lingua et sermone
proprio et volgare da Fabio Calvio Ravenate. In casa di Raphaello da Giovanni di
Sacte da Urbino et a sua instantia, Munich, Bayerische Staatsbibliothek MS. 1034,
Ital. 37 inter cimel. 380.
For the context of this and other Vitruvian editions see Pier Nicola Pagliari,
"Vitruvio da testo a canone" in Salvatore Settis, ed. Memoria dell antico nell'arte
italiana, Turin: Giulio Einaudi, 1986, pp. 7-85, which is followed by an article by
Arnold Nesselrath, "I libri di disegni di antichita. Tentative di una tipologia," pp.
89-147 and a basic contribution by Settis himself: "Continuita, distanza,
conoscenza. Tre usi dell'antico," pp. 375-486.
28. Views of Rome then and now. 41 etchings by Giovanni Battista Piranesi and
corresponding photographs and text by Herschel Levit, New York: Dover
Publications, 1976.
265
29. Edgerton, as in note 3 of the introduction, pp. 74-75.
30. Sir E. H. Gombrich, Means and Ends. Reflections on the History of Fresco
Painting, London: Thames and Hudson, 1976, p. 32.
31. See Antonio Manetti, The Life of Brunelleschi, trans. Catherine Enggars, ed.
Howard Saalman, University Park: Pennsylvania State University Press, 1970, pp.
118, 151.
Some of these connections have been considered in the author's Military
Surveying and Topography: the Practical Dimension of Renaissance Linear
Perspective. Lisbon: Junta de investigacoes cientificas da ultramar 1979. (Centro
de estudos de cartografia antiga. CXXIX.)
32. See: Jean Lejeune, Les van Eyck. Peintres de Liège et de sa cathédrale, Liege:
Georges Thone, 1956; Armand Jean Heins, Une rue de Gend peinte par Hubert
van Eyck. Essai d'identification de la vue de ville représentée sur le revers de
deux volets de polyptique de l'Agneau mystique, Ghent: N. Heins, 1907.
33. Cord Meckseper, Kleine Kunstgeschichte der deutschen Stadt in Mittelalter,
Darmstadt: Wissenschaftliche Buchgesellschaft, 1982. Cf. Pierre Lavedan,
Représentation des villes dans l'art du moyen age, Paris: Vanoest, 1954 and
Claudio Buttafava, Visioni de citta nelle opere d'arte del medioevo e del
rinascimento, Milan: Libreria Salto, 1963. (Politecnico di Milano, Istituto di
urbanistica della facolta di architettura.)
34. Cf. IR. R. Meischke, Amsterdam Burgerweeshuis, Hague: Staatsuitgeeverig,
1975 (De nederlandse monumenten van geschiedenis en Kunst. De Provincie
Noordholland. De gemeente Amsterdam Deel 1)
35. Giovanni Paolo Lomazzo, Idea del tempio della pittura, Milan: P.G. Pontio,
1590, p. 17:
Mantegna c'ha fatto alcuni disegni di prospettiva, dove ha delineato le
figure poste secondo il suo occhio, delle quali io ne ho veduto alcune di
sua mano con suoi avertimenti in scritto.
36. Ibid...pp. 17, 52, 149. Cf. Giovanni Paolo Lomazzo, Trattato dell'arte de la
pittura, Milan: Appresso Paolo Gottardo, 1585, pp. 336, 100-101.
37. Benvenuto Cellini, Trattati dell'oreficeria e della scultura, ed. C. Milanesi,
Florence: Le Monnier, 1857, p. 226:
un libro scritto in penna... In fra le altre mirabili cose, ch'erano in su esso,
trovai un discorso della prospettiva, il piu bello che mai fusse trovato da
altro uomo al mondo, perche le regole della prospettiva mostrano
solamente lo scortare della longitudine e non quella della latitudine a
266
altitudine. Il detto Leonardo aveva trovato le regole re le dava ad
intendere con tanta bella facilta et ordine, chi ogni uomo che la vedeva era
capacissimo.
38. Lomazzo Re: Bramante see; Lomazzo, 1585, as in note 36, pp. 370, 100, 320
and 1590, as in note 35, pp. 150, 16. Re: Bramantino see: Lomazzo, 1585, 271272, 274-275, Lomazzo, 1590, 150, 16, Re: Foppa see: Lomazzo, 1585, 275, 100,
320 and Lomazzo 1590, 108, 150.
39. Luca Pacioli, Libellus in tres partiales tractatus in Divina proportione, Venice,
1509, fol. 22r:
Lectore non te maravigliare se de simili corpi composti de diverse e varie base
non te se mette sempre in margine loro figure conciosia ch'le sieno facte per
mano de bono perspectivo que non si possano sempre havere a sua posta come
sua humanita feci el nostra Lionardo da vinci.
Chapter 2
1. Giorgio Vasari, Lives of the Painters, Sculptors and Architects, trans. William
Gaunt, London: Dent, 1927 (Everyman's Library 784-787), 4 vol.
2. Jacob Burckhardt, Die Cultur der Renaissance in Italien, Basel: Schweighauser,
1860. Trans. Dr. Ludwig Geiger and Professor Walther Gotz, The Civilization of
the Renaissance, New York: Harper and Row, 1929, 2 vol.
3. André Chastel, Renaissance méridionale, Paris: Librairie Gallimard, 1965.
4. André Chastel, Le grand atelier d'Italie, Paris: Librairie Gallimard, 1965.
5. Enrico Castelnuovo e Carlo Ginzburg, "Centro e periferia," Storia dell'arte
italiana, Turin: Giulio Einaudi, 1979, pp. 285-352. Cf. Ferdinando Bologna, La
coscienza storica dell'arte d'Italia, Turin: UTET, 1982.
6. Alessandro Parronchi, Studi su la dolce prospettiva, Milan: Aldo Martello,
1964, pp. 583 ff.
7. For an analysis of this treatise see the author's work on Leonardo, as in I.1, note
14, pp. 57-60, 68-86.
8. Christiane L. Joost-Gaugier, "The tuscanization of Jacopo Bellini: Part 1: the
relation of Jacopo to problems of the 1420's," Acta historiae artium, Budapest, vol.
23, fasc. 1, 1977, pp. 95-112 and "The tuscanization of Jacopo Bellini: Part II: the
relation of Jacopo to problems of the 1430's," Acta historiae artium, Budapest, vol.
23, fasc. 2, 1977, pp. 292-312.
267
9. André Corboz, Canaletto: una Venezia immaginaria, Milan: Alfieri Electa,
1985, 2 vol. is a penetrating and fundamental study.
10. G. Vasari, Lives, as in note 1 above, vol. II, pp. 44.
11. Ibid., p. II, 141.
12. This sermon is sufficiently remarkable to deserve citation in full. Below I give
a translation followed by the original:
May the spirit of divine grace illuminate our senses and our heart. Amen.
Reverend lords, venerable fathers, excellent doctors, magnificent men, most keen
students of this faculty and other most outstanding citizens. Of all arduous and
difficult things, the most difficult is proportion. For it is this alone which
penetrates deeply and most high and individual aspects of the trinity and is studied
most carefully by the sacred theologues. For this is what is often called "relatio" in
their volumes, or "respectus" or even "habitudo." Or in an intellectual discourse it
is called by another name, "comparatio." Its acquaintance is something of which
divine philosophers are most desirous when preparing metaphysical works for
publication. It is ardently followed by natural philosophers such as Socrates,
Plato, Aristotle and all the rest when they are treating the nature of things of the
universe. Nor is it different with the universe of things above: for surely their debt
is to be sought in proportion or "habitudo" just as with inferior things. And if they
apply themselves to sacred scriptures, how can they explain the procession of the
holy spirit from the father to the son caused by their reciprocal love and are able to
express language with the pen, unless they first perceive amongst themselves the
relation of the father to the son. This the greatest maker always has in front of his
eyes in the disposition of things of the heavens and earth while he disposes the
movement and path of the stars and all the planets in most orderly fashion. And
this when he established the air above and appended the fundament of the earth
and liberated the sources of water and gave to the sea its boundary, placing a law
on the waters that they would not overflow their bounds, by which the waters
were all together. And what delight would there be for the human race if from so
great a diversity of things no proportion arose? As is often said it is variety which
delights. Moreover how could one be grouped by the love of the invisible unless
one perceived some relation of created to creator? And although no proportion is
predicated from the finite to the infinite, it is not denied by the learned that a
proportion between them was attained by the sacred. Moreover, the natural
philosophers, as mentioned above, sought for the proportions of natural things
assiduously, as is found in their texts and above all Aristotle, whose works are at
hand more than others. For in his physics the proportion of movements of sound
are most subtly examined. And from the ten commandments from which comes
the number ten, all physicists are content to deduce one of relation or add spatially
something of this sublime investigation of proportion. I shall omit some of the
other almost innumerable places where there is most frequent discussion of
proportions and proportionalities. Among these it is especially to doctors (as I
268
conclude from De naturalibus) who are most illustrious (and in whose hands is the
health of all) that they are noted and must be out of necessity. For hot and cold,
dry and wet will not have their proper ratios in their medicine, unless (doctors)
have found one of these scales which we have mentioned which, after having
proportioned from many qualities, they make one which exhibits characteristics
appropriate for the sick body. How would the astronomers who abandoned
proportion act other than mindless blind men? Those who feel, speak, as the
Egyptians say, such as Ptolemy, Albategni, Alfraganus, Geber, Albumaser and the
others who by utmost diligence have reached the forefront of proportion. Similarly
the chorographers and cosmographers. And Marinus, whom Ptolemy often attacks,
Strabo and the others who have most accurately handed down the positions of the
entire orb on our maps could they have put so much into a single book if they had
not observed proportion? I ask them to speak of all the architects and inventors of
different machines past and present: Pythius, who first designed the temple of
Venus in a noble style, Dinocrates, Archimedes, Vitruvius, Frontinus, Vegetius
and many others who excelled in the construction of buildings. Do the profuse
ruins by which they are remembered bear witness by what means it was they built
such things? It is surely that they had proportion as a guide as all their work
shows. Why should the most famous painters Apelles, Myron, Polyclytus and
others whom the historians name worthy of praise for their perspective in the sight
of posterity, if in their figures, their lines and distances did not use proper heights
and lengths proportionately. The same applies to stone carvers or sculptors of
stone, Phidias, Praxiteles and Appollonius, Nestor and others in such occupations
as the aforementioned if they did not use the same proportion most diligently in
their marble and statues, just as the missing bits thereof can be easily be put back
into place if these [proportions] be found. Likewise, the musicians seek nothing
else in their melodies except a proper mode of voice and sounds, that is,
sesquialtera, sesquitertia, diapente, diapason and with other proportions of this
kind (as Boethius attests) which are in proportion, such that they resonate more
sweetly and smoothly in the ears of the audience and bring to them the greatest
delight which could scarcely be achieved without proportion and proportionality.
Imitating this manner the poets compose their songs (with practically the same
measures) the ductyl, iambus, trochee, anapest, tritrachus and procleumaticus, and
using the other feet in proportion in their place. And like these, the rhetoricians
also assign to their orations the necessary parts and congruent numbers. Grammar,
the origin and fundament of all the liberal arts, is also found to observe this when it
deals in the teaching of beginners in properly speaking and writing, to end with
grave, acute and circumflex accents. Which is also the way of the most just
Justinian laws. And [how could] his canons form proper judgments if these did
not support both types of justice namely the commutative and distributive? Of
which the one, namely, the distributive, belonging to geometry, has been shown to
direct so much proportion (as Aristotle in the Ethics and Plato in the Laws and the
Republic testify), added to which the just man himself, the judge of the living and
the dead will one day give retribution to the human race bringing into proportion to
one another the merits and dismerits of all as can clearly be gleaned from the
sacred scriptures. The foremost patrons of public affairs of this age also observe
269
the commutative part assiduously when selling things for money or settling or
dealing in some other way. And the industry of each of the other mechanical arts
has its due proportions which moderate it as experience testifies. But since we are
history such, what shall we say of our arithmeticians and geometers who are
always usually first among equals, such as Pythagoras and Nicomachus who are
cited as having been the inventors of the first numbers among the Greeks, although
Boethius and Apuleius were held to have been so among the Romans? Did not
these serve some proportions more diligently which (according to Euclid) they
called rational? Geometers truly are indifferent in their care for either one,
namely, rational or irrational. Finally this proportion is an infinite thesaurus for
men by the use of which they are made participants in the friendship of Christ
through the gift of discipline of the Commandment. I have disseminated this
purpose without deception and to those desirous of it without envy I communicate
it showing its virtue most openly. Hence Euclid entered upon the necessary
observance of these proportions and proportionalities in order that all that which he
said would have greater fruit. Of these same matters he deals most thoroughly in
the fifth book, writing thirty four definitions with their premises and then as is his
manner their conclusions (which makes up the whole of this book). And he
concludes against his adversaries most firmly and irrefutably.
For which reason if someone aspires to any speculation in any faculty of art
or science he will approach this fountain whence the rivers of the waters of life
flow always. And its ingenuity is to be extolled above the stars. But the case
demands that we now come to the text, which begins as follows: A part is
The original is in: Euclid, Euclidis megarensis opera, ed. Luca Pacioli, Venice:
Paganinus de Paganinis ,1509, fol. 30:
Sermo habitus per Reverendum patrem M Lucam Paciolum de burgo
Sancti Sepulchri Ordo. minorum In ecclesia Sancti Bartholomei. Venetiis.
1508. Die. xi. augusti in quintum Euclidis. Spiritus sancti gratia illuminet
sensus et corda nostra. Amen. Arduarum difficiliumque rerum omnium.
Reveredi domini uenerandi patres: excellentissimi Doctores: Magnifici
viri: Acutissimi cuiuscunque facultatis studentes vosque caeteri
prestantissimi ciues : difficillima est proportio. Haec est illa quae sola
intima altissimae idividuaeque trinitatis penetrat; et a sacris theologis
solertissime investigatur. Haec enim est quae saepius in eorum uolu
minibus relatio dicitur: aliquando respectus: nonnunque habitudo.
Interdum intellectualis discursus: et nomine alio comparatio nucupatur.
Huius notitiam divini philosophi fummopere cupierunt: dum Metaphysicen
opera in lucem prodere curarent. Hanc pro viribus naturales prosequti
funt: ut Socrates: Plato: Aristoteles: caeterique omnes. Cum de rerum
uniuvuersique natura agerent. Non enim aliud in rebus universis
superioribus: scilicet et inferioribus quae debita earum adinvicem
proportio seu habitudo queritur. Nunquam enim sacris litteris
incumbentes: processionem sancti spiritus a patre et filio ex eorum
270
reciproco amore causa tam in lingua calamoque explicare potuissent: nisi
prius relationem inter eos patris ad silium: et econtra percepissent. Hanc
preoculis summus opifex in caelestium terrestriumque rerum dispositione
semper habuit. Dum orbium motus cursusque syderum et planetarum
omnium ordinatissime disponeret. Haec quando aethera firmabat sursum:
et appendebat fundamenta terrae: et librabat fontes aquarum: et mari
terminum suum circundabat: legemque ponens aquis: ne transirent fines
suos: cum eo erat cuncta componens. Que nam esset humano generi
delectatio si ex tanta rerum diversitate proportio non oriretur? Cum saepe
dicatur: varietas est que delectat. Quo pacto insuper in invisibilium
raperetur amorem nisi habitudinem quandam creaturae ad creatorem
cerneret. Et quamvis finiti ad infinitum proportio nulla esse predicetur:
attingentie tamen inter ea proportio a sacris non negatur doctoribus.
Naturales autem et ipsi (ut paulo ante diximus) persedulo rerum
naturalium proportiones quaesivere: prout in eorum codicibus passim
habetur. Presertim Aristotelis cuius opera pre aliis assidue premanibus
habentur. Nam inde physico auditu proportionem motuum inter se
subtilissime perscrutatur. Et ex decem predicamentis quo numero denario
omnes philosophi contenti extitere: unum relationis seu ad aliquod huic
tam sublimi indagatrici proportioni seu spatialiter addicauit. Omitto loca
alia pene innumerabilia ubi de proportionibus et proportionalitatibus
saepissime disseritur. Que omnia ( ut de naturalibus concludam:) medicis
praesertim peritissimis (quibus omnium cura commissa est) nota sunt et
essere de necessitate debent. Non n calidi et frigidi: humidi et sicci in
medelis disponendis rectam rationem habebunt nisi gradum cuiuslibet
predictarum nouerint quem postea ex multis proportionando qualitatibus:
unam efficiunt egrotam ti corpori debite exhibemdam. Quo et Astronomi
proportione relicta agerent: nnone velut amentes ceci que discurrerent.
Narrent hii qui sentiunt: dicant egyptii ut Ptolomeus: Ali. Albategni,.
Alfagranus, Geber. Albumaseri et ceteri omnes qui proportione previa
peritissimi evassere.
Qualiter corograpoi cosmographique. Marinus
quem saepe Ptolom eus inpugnat Strabo et alii qui totius orbis situm nobis
tabulis quibusdam accuratissime tradiderent tot si tanta simul unico libello
complecti potuissent? nisi matrem divinum observassent proportionem.
Dicant queso architecti omnes et diversarum machinarum inventores prisci
et presentes: Pythius qui primus aedem minerve nobiliter architectatus est.
Dinocrates: Archimedes: Vitruvius: Frontinus: Vegetius: et alii
quamplures quae in aedificiorumque structuris summe excelluerunt:
quoque memoriam persuse ruinae adhuc nobis asserunt quo medio talia
ederint? Certe proportione duce se omnia prefissecrespondebunt.
Quomodo pictores celeberrimi. Appeles, Miron, Policletus et caeteros quos
historiae nominant aliquid laude dignum prospectivo aspectu suis posteris
reliquissent. Si in eorum figuris liniamenta distantiasque debitas
altitudines et latitudines proportionaliter non servassent.
Lapicidae
quoque seu lapidum sculptores Phidias: Praxiteles. Appollonius. Nestor et
reliqui industria tali prediti: non ne eandem diligentissime proportionem
271
marmoreis aeneisque statuis accomodarunt. prout indies frustis talium hinc
inde repertis facile datur intelligi. Pariter et Musici :nil aliud in eorum
melodiis: armoniisque querunt nisi modum debitum vocum et sonorum: hoc
esti: Sesquialtera sesquitertia. Diapente: Diapason: et aliis huiusmodi
proportionibus (teste Boetio) proportionatum. ut in auditorum auribus
dulcius ac suavius resonent. et summam illis delectationem ingerant: quae
sine proportione et proportionalitate minime Causari potest. Quem morem
imitando poetae Carmina sua (eisdem fere mediis) Datilo: Iambo:
Spondeo: Trocheo: Anapesto: Tribraco. Proceleumatico. Ceterisque
proportionis loco utendo pedibus. Componunt.
Necnon et rethores (ad
istorum instar) Orationum suarum partes debitis. ac congruis numeris
assignant.
Hoc idem origo et fundamentum omnium liberalium artium
grammatica observare videtur: dum normam recteloquendi recteque
scribendi discere incipientibus tradit. gravi: acuto: circumflexoque:
acentibus terminatam.
Qua et via aequissimae sanctiones. Justiniana
scilicet et canonica suas recte formarent sententias: si iustitiam utranque
commutativam scilicet et destributivam non supponerent. Quarum altera
videlicet distributiva penes geometricam tantum proportionem attendi
comprobatur (ut in ethicis Aristoteles: et plato inde legibus et republica
testantur) iuxta quam iustus iudex vivorum et mortuorum olim humano
generi retribuet merita ac demerita omnium adinvicem proportionando ut
ex sacris aperte elicitur litteris. Hanc assidue et commutativam observant
rerum publicarum fautores dignissimi huius seculi negociatores res
pecunia vendendo. emendoque seu quovis alio modo pertractando.
Aliarum quoque unaquaeque mecanicarum industria suas debitas habet
proportiones ipsam moderantes: experientia teste.
Sed dum talia
percurimus quid de arithmeticis geometrisque nostris dicemus: qui
precipui inter alios semper habitae sunt: ut Pitagoras et Nicomacus: qui
prirni numerorum apud graecos inventores fuisse perhibentur: quis apud
latinos Boetius et Apuleius habeantur. Non ne hi ceteris diligentius
proportionem servant: quam (teste Euclide) rationalem vocant. Geometre
vero utrique indifferenter rationali scilicet et irrationali curam adhibent.
Hec denique proportio infinitus thesaurus est hominibus quo qui usi sunt
participes facti sunt amicitie dei propter disciplinae dona Commendati.
Hanc ego proposse sine fictione didici et cupientibus sine invidia
communico virtutem eius apertissime ostendendo.
harum igitur
proportionum et proportionalita tum Euclides necessariam cemens
observantiam ut omnium que dixerit fructus uberior habeatur. De his ipsis
disertissime hoc in quinto egit. Diffinitiones earundem premittens ac
deinceps more suo conclusiones trigintaquator numero. (quibus iste totus
complectitur liber) exarando. Et contra adversarium eas firmissime atque
inrefragabiliter concludit. Qua propter siquis ad speculationem aliquam
quacunque in facultate scientia: arteque: aspirat ad hunc properet fontem:
a quo aquae vive semper flumina fluunt. Et super astra eius extolletur
ingenium. Sed ut iam ad litteram veniamus res expostulat. Que sic incipit
videlicet. pars est.
272
13. Vasari, Lives, as in note 1 above, p.252.
14. Ibid., p.264.
15. Ibid., p.272.
16. Ibid., vol.II, pp.14-16
17. Ibid., vol. I, p.302
18. Paul Lawrence Rose, The Italian Renaissance of Mathematics, Geneva:
Librairie Droz, 1975.
19. Margaret Daly Davis, Piero della Francesca's Mathematical Treatises,
Ravenna: Longo editore, 1977.
20. Cf. Chastel, as in note 3, pp. 251-263.
21. See: Henry de Geymüller. Les projets primitifs pour la basilique de Saint
Pierre, Paris: J. Baudry, 1875, 2 vol.
22. Wolfgang Lotz, "Das Raumbild in der italienischen Architekturzeichung der
Renaissance," Mitteilungen des Kunsthistorischen Instituts in Florenz, Florence,
Bd. 7, 1953-1956, pp. 193-226. Cf. also his: Studies in Italian Renaissance
architecture, Cambridge Mass., MIT Press, 1977.
23. G. Vasari, Lives, as in note 1 above, Vol. I, p. 326.
24. Giovanni Paolo Lomazzo, 1590, as in I.1, note 35, pp. 16-17, 52, 149-150.
25. See the author's study of Leonardo, as in I.1 note 14 for documentation and
analysis of these claims.
26. See Sergio Marinelli, "The Author of the Codex Huygens," Journal of the
Warburg and Courtauld Institutes, London, vol. 44, 1981, pp. 214-220, pl. 30-35.
27. Erwin Panofsky, "Die Perspektive als symbolische Form," Vorträge der
Bibliothek Warburg 1924-1925. Leipzig, 1927, Taf.XIII, Abb.22.
28. Liliane Brion Guerry, Jean Pélerin Viator. Sa place dans l'histoire de la
perspective, Paris: Société d'édition les belles lettres, 1962. (Les classiques de
l'humanisme, Vol. VIII).
29. René Descartes et Beeckman, "Correspondence" (Breda, 26 mars 1619),
(Copie Ms. Middlebourg, Provinciaal Bibliotheek Zeeland, Journal de Beeckman,
273
fol. 288v) in: Oeuvres de Descartes, ed. Charles Adam et Paul Tannery, Paris:
Leopold Cerf, vol. 8, 1908, pp. 156-157:
Et certe, ut tibi nude aperiam quid moliar, non Lullij Artem brevem, sed
scientiam penitus novam tradere cupio, qua generaliter solvi possint
quaestiones omnes quae in quolibet genere quantitatis, tam continuae
quam discretae, possunt proponi.
30. Ibid., p. 157:
alia solvi non posse, nisi cum aliis lineis curvis, sed quae ex unico motu
oriuntur, ideoque per novos circinos duci possunt, quos non minus certos
existimo et geometricos, quam communis quo ducuntur circuli.
31. Rene Descartes, "Trait‚ de l'homme" in: Oeuvres de Descartes, ed. Charles
Adam et Paul Tannery, Paris: Leopold Cerf, 1909, vol. XI, p. 130:
Ainsi que vous pouvez avoir vue, dans les grottes et les fontaines qui sont
aux jardins de nos Roys que la seule force dont l'eau se meut en sortant de
sa source est suffisante pour y mouvoir diverses machines et mesme pour
les y faire iouer de quelques instrumens, ou prononcer quelques paroles,
selon da diverse disposition des tuyaux qui la conduisent.
32. Jurgis Bultrusaitis, as in I.1, note 10, p. 41.
33. Jean Francois Nicéron, La perspective curieuse, Paris, 1652 (as cited in
Baltrusaitis, 1956, p. 41):
Philon le Juif aux livre De specialibus legibus dit expressement en ces
termes...que la vraye magie, ou la perfection des sciences consiste en la
perspective, qui nous fait cognoistre et discerner plus parfaictement les
plus beaux ouvrages de la nature et de l'art et qui a este estimée de tous
temps non seulement du commun des peuples, mais encore des plus
puissans monarques de la terre.
34. See, for instance, Otto Mayr and Klaus Maurice, The Clockwork Universe:
German Clocks and Automata, 1550-1650, New York: N. Watson, 1980.
Originally: Die Welt als Uhr, Munich: Deutscher Kunstverlag, 1980; Cf. Klaus
Maurice, Die deutsche Räderuhr: Zur Kunst und Technik des mechanischen
Zeitmessers im deutschen Sprachraum, Munich: Beck,1976, 2 vol.
35. James Mitchell Collier, Linear Perspective in Flemish Painting and the Art of
Petrus Christus and Dirk Bouts, Ph.D., University of Michigan, 1975.
274
36. For a recent discussion of this problem see Marisa Dalai Emiliani, "Per amore
dell'arte della segreta prospettiva..." in: Carlo Pedretti ed., Leonardo il Codice
Hammer e la mappa di Imola, Florence: Giunti, 1985, pp. 185-186.
37.
Hieronymus Rodler, ed., Perspectiva. Eyn schön nützlich Buchlein...so sich
der Kunst des Messens (Perspectiva zu latein genannt)...Simmeren: Hofdruckerei
1531.
38. See: Pierre de la Ramée, (Ramus), Praelectiones in Ciceronis orationis octo
consulares una cum ipsius vita per Joannem Thomam Freigium, Basel: P.
Pernam, 1580, pp. 338-339.
39. Heinrich Kreisel, Die Kunst des deutschen Möbels, Munich: C.H. Beck, 1968.
40. See Maximilian Bobinger, Alt-Augsburger Kompassmacher, Augsburg: Hans
Rösler Verlag, 1966. (Abhandlungen zur Geschichte der Stadt Augsburg.
Schriftenreihe des Stadtarchivs Augsburg, 16).
41. Maximilian Bobinger, Christoph Schissler der Ältere und der Jüngere,
Augsburg, Basel: Verlag der Brigg, 1954.
Chapter 3
1. This was technically the first discussion of ground-plan and elevation in
connection with perspective, although it is frequently assumed that Brunelleschi
combined a ground plan and elevation in arriving at his construction. Indeed,
Vasari, Lives of the artists, as in I.2, note 1, claims this in vol. 1, p. 272:
He paid great attention to perspective, which was badly understood at the
time, many errors being perpetrated, and spent much time over it, but at
length he discovered unaided a method of getting it perfectly true; this was
to trace it with the ground plan and elevation by means of intersecting
lines, a useful addition to the art of design.
Elsewhere, however, Vasari suggests that Paolo Uccello was the innovator,
in his Lives, vol. 1, p. 232:
But Paolo, without ever wasting a moment was always attracted by the
most difficult things of art, and brought to perfection the method of
representing buildings, to the tops of their cornices and roofs, in
perspective from their plans and elevations. This was done by intersecting
lines, diminishing at the centre; the point of view, whether high or low,
being first decided. He laboured so hard over these difficulties that he
invented a method and rules for planting figures firmly on their feet and for
their gradual foreshortening and diminution in proportion as they recede, a
matter that was previously left to chance. He also discovered the method
275
of tracing the ribs and arches of vaulting, the foreshortening of floors by
diminishing the receding beams, and the way to make round columns
follow the turn made by the sharp corner of a house, doing this from a
ground plan.
2. For an analysis, see the author's work: Leonardo, Studies I, as in I.1, note 14,
pp.57-60, 68-86.
3. See: Gezenius ten Doesschate, De derde commentaar van Lorenzo Ghiberti in
verband met de middeleuwesche optiek, Proefschrift, Utrecht, 1940.
4. For instance, Alberta, On Painting, as in I.1, note 13, pp. 47 and 49:
Nor is this the place to discuss whether vision, as it is called resides at the
juncture of the inner nerve or whether images are formed on the surface of
the eye as on a living mirror...
Let us omit the debate of philosophers where the original source of colours
is investigated.
Both of these passages are in the Latin text and are omitted altogether from
the Italian version.
5. This quote is from the first English edition: Sebastian Serly, The second book of
architecture, London: Printed for Robert Peake, 1611, fol. Ai v.
6. Pietro Accolti, Lo inganno de gl'occhi, Florence: Appresso Pietro Cecconcelli
1625, p. 116:
E cosi grande l'autorita di Vitellione, unico, e principal capo della scuola
de perspetttivi, che chiunque ardisca pronunciare egli haver falsamente, o
dimostrato, o insegnato, puo di facile esser reputato, temerario, o ardito o
molto...
7. Ibid., p. 116: "Falsa dimostrazione, e meno vera dottrina di Vitellione circa
l'obliquo passaggio de i lumi, Cap. XVII."
8. Ibid., p. 13: "Che la prospettiva non sia altro in effetto che una rappresentativa
sezione della piramide visiva."
9. Giacomo Barozza, il Vignola, Le due regole della prospettiva pratica, ed.
Egnazio Danti, Rome, 1583, preface:
Maestro Pietro della Francesca dal Borgo S. Sepolcro, del quale
abbiamo oggi tre libri scritti a mano, eccellentissimamente disegnati.
10. Ibid., p. 49:
276
Perche oltre alla descrittione delle figure rettilinee, apporta gran
commodita al prospettivo il saperle trasmatare d'una nell'altra, ho voluto
in queste tre seguenti propositioni mostrare il modo secondo la via
commune non solamente di trasmutare il circolo e qual si voglia figura
rettilinea in un altra, ma anco di accrescerle e diminuirle in qual si voglia
certa proportione, accio in questo libro il prospettivo habbia tutto quello,
che a cosi nobil pratica fa mestiere.
11. Guidobaldo del Monte, Perspectivae libri sex, Pesaro: Apud Hieronymum
Concordiam, p. 1:
Architecturam, atque picturam reliquas omnes anteire artes, quae citra
manuum usum sola ingeniorum applicatione, atque solertim, quod
intendunt, moliri, ac perficere nequeunt (quae propterea mechanicae
appellantur) nemini certe egregia earum opera consideranti, ambigendum
censeo.
12.
Simon Stevin, Derde stuck der wisconstighe ghedachtnissen van de
deursichtighe, Leiden: Ian Bouwensz, 1605:
maer willen een voorghestelde verschaeulicke saeck volcomelick
afteyckenen, met kennis der uirsaken en sign wisconstich bewijs.
13. The quote has been adapted from the first English edition of Serlio, as in note
5, fol. Aiv.
14. Pietro Cataneo, I quattro primi libri, Venice: Aldus, 1554, fol 1r:
Quel che piu facci di bisogni all architetto e di quanto importanza gli sia
l'essere buono prospettivo.
15. Ibid:
Ma se l'architetto non sera prospettivo, non potra mai cosi bene ne
honorarsi, ne mostrare per disegno il suo concetto, per eccellente
disegnatore chei si fusse: e da se stesso sconscera di questa importanza gli
sia il non essere nella prospettiva ben prattico.
16. The phrase il suo alzato per ordine di prospettivo appears in the following
chapter headings I.VIII, IX, X, XIII, XVII, XVIII, XIX; III.introduction, II, VII,
IX. Cf. Ibid, 44v:
La figure qui appresso che segue rappresenta la meta del tempio nella
parte interiore di ordine Corinto, tirato dalla sua pianta passata per
ordine di prospettiva.
277
17. Vincenzo Scamozzi, L'Idea della architettura, Venice: Expensis auctoris,
1617, 47:
Poi la prospettiva, serve per rappresentare per via di linee artificiali tutte
le cose, come dice anco Vitruvio, stando in certo determinato luogo:
corrispondono a raggi nostri del vedere naturale, in modo tale che
apportano a gli occhi nostri de specie e l'imagine vere, de gli edifici, che
sono disegnati in iscorcio nelle scene e altrove.
18. Ibid.:
e certo e mirabil cosa il vedere, che il piano delle tele, o delle tavole, con
colori, siano talmente ben disposte, e lineate dall'arte, che a quelli, che le
mirano paiano che siano di rilievo, e piu alto, e piu basso.
19. Ibid.:
e di questa facolta sino nella nostra prima gioventu ne abbiamo scritto sei
libri, ne quali e molto numero di disegni, e cosi delle cose superficiali e in
piano, come de corpi e parti di cinque ordini, i quadri speriamo in Dio di
metterli in luce, dopo questa nostra lunga e faticosa opera d'architettura.
20. Cf. Rodler (1531). An example at the turn of the 17th century is Jan Vredeman
de Vries, Perspective, id est, celeberrima ars inspicientis...perutilis ac necessaria,
omnibus pictoribus, sculptoribus, statuariis, fabri ferrariis, architectis,
inventoribus caementariis, scrinariis, fabrilignariis, et omnibus artium
amatoribus, qui huic arti operam dare volent, majori cum voluptate, et minori cum
labore, Leiden: Hondius, 1604.
21. Jean Dubreuil, La perspective pratique, necéssaire a tous peintres, graveurs,
architectes, brodeurs, sculpteurs, orferres, tapisseurs et autres qui se meslent de
desseigner, Paris: Chez Jean Du Puis, 1643-1649. 3 vol.
22. Giovanni Battista Benedetti, Diversarum speculationeum liber, Turin: Apud
haeredem Nicolai Bevilaquae, 1585, p. 119: "hunc solum esse verum modum."
23. For a more detailed discussion of these developments see the appendix to the
author's work on Leonardo, as in I.1, note 14.
24. Plato, Timaeus, trans. H.D.P. Lee, Harmondsworth: Penguin, 1965, pp. 72-78.
25. See: Regiomontanus, "Commensurator," ed. Wilhelm Blaschke und Gunther
Schoppe, in: Abhandlungen der Akademie der Wissenschaften und der Literatur in
Mainz, Mathematisch-naturwissenschaftliche Klasse, Wiesbaden, Nr. 7, Jahrgang,
1956.
278
26. Wenzel Jamnitzer, Perspective corporum regularium...durch einen newen
behenden und gerechten Weg der vor nie in gebrauch ist gesehen, Nürnberg, 1567.
27. Ibid.: wie auss denselbigen funff Corpern one Endt gar viel andere Corper
mancherley Art und gestalt gemacht unnd gefunden werden mügen.
28. Julius Hoffman, Die Kupferstiche des Meisters PP mit der Schlinge, Vienna:
Gesellschaft fur vervielfältigende Kunst, 1911.
29. See Linda Dalrymple Henderson, The Fourth Dmension and non-Euclidean
Geometry, Princeton: Princeton University Press, 1983.
30. This problem has been studied in an unpublished essay by Geoffrey Smedley,
"Notes concerning Piero della Francesca's Prospectiva pingendi," unpublished
Typescript, Vancouver: University of British Columbia, c. 1986.
31. Giovanni Paolo Lomazzo, as in I.1 note 36, 1585, pp. 270, 175, cf. 100, 320;
1590 as in I.1, note 35, 108, 150, cf. 16.
32. See the author's study of Leonardo, as in I.1, note 14, pp. 202-239
33. See: Sergio Marinelli, as in I.2, note 26.
34. E.g. Serlio, as in note 5, Bk. III, A1v-A2r:
with part of the sciographies of the most famous antiquityes of Rome...and
that I may goe forward orderly in these antiquities. The first figure shall be
the ichnography. The second, the orthography, the third, the sciography.
This led Barbaro, 1568, p. 129-130 to note:
che la prospettiva era molto necessaria all'architetto, e cosi hanno
interpretato quella parola sciographia per la prospettiva, la quale e come
una adombratione.
Molti anche hanno letto scenographia, in luogo di sciographia, & hanne
inteso lo istesso, cioe la descrittione delle scene, laquale ricerca
miribilmente l'uso della perspettiva...
These debates continued in the seventeenth century. See, for instance,
Vitruvius, De architectura, Amsterdam: L. Elzevirium, 1649, page 6, note b or
Claude Perrault's edition of Vitruvius, Les dix livres d'architecture, Paris, 1684, p.
10, note 7 beginning:
Barbaro a mis sciographie au lieu de scenographie que Hermolaus
Barbaro en ses gloses sur Pline a restitue avec beaucoup de raison,
puisque la definition que Vitruve apporte du mot dont il s'agit, et qui est
279
proprement celle de la perspective convient tout a fait au mot de la
scenographie...
Professor Werner Oechslin (Zürich) is working on this problem.
35. Daniele Barbaro, La pratica della perspettiva, Venice, 1568, p. 129-158:
parte quarta, nella quale si tratta della scenographia, cioe descrittione
delle scene.
36. Giacomo Barozzi, il Vignola, Le due regole, ed. Egnazio Danti, Rome: Zanetti,
1563, pp.
37. Antonio Manetti, The Life of Brunelleschi, ed. Howard Saalman, University
Park: Pennsylvania State University Press, 1970, p. 54.
38. Ibid., p. 54:
Since they undertook excavations to find the junctures of the membering
and to uncover objects and buildings in many places where there was some
indication, they had to hire porters and other laborers at no small expense.
No one else attempted such work or understood why they did it.
On the question of ruins see: Paolo Arrigoni e Achille Bertarelli, Piante e
vedute di Roma e del Lazio, Milan: Castello Sforzesco, 1939.
39. Daniele Barbaro, as in note 35, p. 159:
Parte quinta, nella quale si espone una bella e secreta parte di
perspettiva.
40. Egnazio Danti, as in note 36, p.
41. See Carlo Pedretti, "Un ritratto anamorfico di Francesco I, di probabile
invenzione Vinciana," in: Ibid, Documenti e memorie rigunrdanti Leonardo da
Vinci a Bologna e in Emilia, Bologna: Editoriale Fiammenghi, 1953, pp.121-123.
42. Julius Deininger, Eine neue Theorie der malerischen Perspektive und deren
praktischen Resultate, Vienna: Gerlach und Weidling, 1914, p.14:
Daraus aber folgt, dass es einzig und allein auf einer solchen
Kugeloberfläche möglich ist, alle diese Längenmasse, das heisst alle
perspektivischen Dimensionen in ihren richtigen Zusammenhänge und
ihrer richtigen Grösse graphisch darzustellen.
280
43. Adelbert Ames, Jr. and C.A. Proctor, "Dioptrics of the Eye," Journal of the
Optical Association of America, Rochester, vol. 5, 1921, p. 22. The article covers
pp. 22-84.
44. Ivan Jobin, Ligne droite on ligne courbe? Cone ou sphère optique, Montreal:
Editions Albert Levesque, 1932, p. 13:
La seconde partie s'attache à démontrer que la ligne courbe, déterminé par
les principes de la sphère optique, constitue, aujourd'hui une théorie de
vision supérieure à celle de la ligne droite établie selons les principes du
cône optique.
45. For an introduction to this history see Massimo Scolari, "L'idea de modello,"
Eidos, Asolo, vol. 2, 1989, 16-39.
46. Cf. Peter Jeffrey Booker, A History of Engineering Drawing, London: Chatto
and Windus, 1963.
47. Ptolemy, L'optique de Claude Ptolémée, ed. A. Lejeune, Louvain: Publications
universitaires de Louvain, 1956, p. 74 (II. 124):
Et ideo pictores domorum constituunt colores rerum quas remotas volunt
ostendere, aeros latentes.
Lejeune notes (104): “C'est le principe de la perspective aérienne. Meme
sujet dans un intérressant fragment papyrologique publie par K. Wessely, dans
Wiener Studien, Vienna, XIII, 1891, pp. 319-323.”
48. Pompilius Azalus, De omnibus nebus naturalibus quae continentur in mundo,
Venice: Apud Octavianum Scotum, 1544, fol. 74v:
Ab hae naturali experientia, ars pictoria optimus canones accepit, ut in
libello and Jacopum Bellinum venetum pictorem insignem certi descripsi,
quibusque modis colores obscuros et claros opponere sciret, tali cum
ratione quod non solum unius imaginis partes relevatae videruntur in
plano depictae, verum extra manum vel pedum porrigere crederentur
inspectae, et eorum quae in eadem superficie hominum animalium vel
montium equantur quaedam per miliaria distare apparent atque ejusmodi.
Is quidem pingendi docet propinqua claris, remota obscuris, mediasque
permiutis sub coloribus tingi debere.
49. Cf. Janis Clearfield-Bell, Color and Theory in Seicento Art, Zaccolini's
Prospettiva del Colore and the Heritage of Leonardo, Ph.D., Brown University,
1983.
281
50. Louis Clement de Brunel de Varennes, Métroscopographie, Paris: Troyes,
1830, p. 19:
Nous divisons la perspective en deux principales sections. La premiere est
la perspective linéaire; la seconde est la perpective aérienne, dans laquelle
sont comprises la théorie des ombres, celle des reflets, et la réflexion des
objets dans l'eau et sur les surfaces polies.
51. Armand-Denis Vergnaud, Manuel de perspective, Paris: Roret, 1835, pp. 7475:
Définition - La perspective à pour but de représenter sur une seule et meme
surface, l'ensemble et les détails des objets que la nature répartit à
distances inégales sur des surfaces variées à l'infini: il est, pour atteindre
ce but, deux parties bien distinctes dans la perspective. L'une doit
déterminer les contours apparens des corps et leurs positions respectives
sur les differentes surfaces ou ils se trouvent, l'autre doit saisir la couleur
meme de ces objets, avec toutes les modifications que lui font subir et les
accidens de la lumière et les couches plus ou moins épaisses d'air
atmosphérique qui les séparent les uns des autres. La première est une
science positive, ou l'on est guid‚ rigoureusement par les principes les plus
simples de la géométrie: c'est la perspective linéaire, sans laquelle on ne
peut être dessinateur. La seconde, qui semblerait au premier abord pouvoir
s'obtenir d'une manière non moins rigoureuse, à l'aide de la géométrie et
de la physique, constitue la perspective aérienne, sans laquelle on ne peut
être peintre: mais il ne faut pas espérer en ateindre la magie des couleurs
et la sublimité, si l'on n'est pas doué de cette sensibilité exquise et de cette
chaleur d'imagination, étincellés du feu sacre sans lequel il ne peut exister
de véritable artiste. En un mot on peut, à l'aide de la perspective linéaire,
produire de belles statues dont les formes seront pures et agréables, mais
pour lesquelles la perspective aérienne ne cessera jamais d'être le souffle
créateur de Prométhée.
52. Barnabé Brisson, Théorie des ombres et de la perspective, Paris: Bachelier,
1838, p. 24:
On voit qu'ici, comme dans la théorie des ombres, on doit admettre deux
parties distinctes: l'une est purement géométrique, et son objet est de
déterminer d'une manière précise sur le tableau la position de chaque
point représenté; l'autre à pour objet la recherche de la teinte d'ombre et
de lumière qu'on doit donner à chaque partie du tableau, et c'est par des
considérations physiques qu'on peut en général la traiter. Cette dernière
partie, qu'on designe sous le nom de Perspective aérienne, rentre
entièrement dans le cercle des recherches qui nous essaierons d'exposer
plus tard, pour completer la théorie des ombres.
282
53.
Jules De La Gournerie, Traité de perspective linéaire, Paris: Dalmont et
Dunod, 1859, p.1:
La Perspective est l'art de représenter les objets sur un tableau en
conservant leur apparence. Elle est linéaire ou aérienne, suivant qu'elle
s'occupe des formes ou de la coloration. Il ne sera pas question dans cet
ouvrage de la perspective aérienne.
54. Ernst Wilhelm Brücke, Principes scientifiques des beaux arts, Paris: Germer,
Baillière et Cie., 1878, particularly, pp. 62-65.
55. Dictionnaire de pédagogie et d'instruction primaire, ed. F. Buisson, Paris:
Hachette, 1882, vol. 2, p. 1555:
Perspective Pratique - La perspective est l'art de reproduire sur une
surface plane l'aspect des objets tels qu'ils se présentent à nous dans
l'espace.
La perspective linéaire étudie la réproduction des contours des objets; la
perspective aérienne s'occupe plus spécialement des modifications
qu'apporte aux ombres et aux teintes la couche d'air interposée entre les
objets et l'oeil du spectateur.
56. Louis Delaistre, Cours complet de dessin linéaire, Paris: Gauthier Villars,
1894, p.1:
La perspective, considérée dans son ensemble, est l'art de représenter les
objets sur une surface plane suivant leurs effets d'optique; c'est-à-dire
selon les lois de la vision et celles de la lumière, ce qui fait qu'on la divise
en deux classes: l'une que l'on nomme linéaire, l'autre que l'on nomme
aérienne. La perspective linéaire se fait par les lignes seules. La
perspective aérienne se fait par la dégradation des couleurs résultant de
l'éloignement de la lumière comme de l'éloignement successifs des objets,
ainsi que de la qualité plus ou moins intense des vapeurs terrestres qui
s'interposent entre l'oeil du spectateur et ces memes objets.
57. Leon Battista Alberti, On painting, as in I.1, note 13, p. 82:
But I should like the [highest level of attainment] in industry and art to rest,
as the learned maintain, on knowing how to use black and white. It is well
worth all your study and diligence to know how to use these two well
because light and shade make things appear in relief.
The original reads:
Tutta la somma industria e arte sta in sapere usare il biancho e il nero,
pero che il lume e ombra fanno parere le cose rilevate.
283
58. Piero della Francesca, De prospectiva pingendi, ed. G. Nicco Fasola, Florence:
G.C. Sansoni, 1942, p. 63:
Colorare intendiamo dare i colori commo nelle cose se dimostrano, chiari
et scuri secondo che i lumi li devariano.
59. See the authors study of Leonardo, as in I.1, note 14., pp.278-305.
60. Alberti, as in I.1, note 13, pp. 71.
61. For an introduction to these problems see: Thomas Da Costa Kaufmann, "The
perspective of shadows: the history of the theory of shadow projection," Journal of
the Warburg and Courtauld Institutes, London, Vol. 32, 1975, pp. 258-287.
62. Domenico Tessari, Applicazioni della geometria descrittiva. Vol. 1. La teoria
delle ombre e del chiaro scuro, ad uso delle universita...degli ingegneri, architetti
e disegnatori, Turin: Camilla e Bertolero, 1880.
63. E.g. J. J. Gibson, The Ecological Approach to Visual Perception, Boston:
Houghton Mifflin Co., 1979.
Chapter 4
1. As Panofsky noted in "Die Perspektive als symbolische Form," as in I.2 note 27,
p. 291, the term goes back to Boethius, Analytica posteriorum Aristotelis,
Interpretatio, I.7, I.10, (Opera, Basel 1570, pp. 527, 538).
2. See, for instance, Aristotle, Analytica posteriora, trans. G.R.G. Mure in: The
Works of Aristotle, ed. W.D. Ross, London: Oxford University Press, 1928, (Bk.
I.13), 78b 35-79a 5, 10-20, Cf. Ibid., vol. II, Physica, trans. R. P. Hardie and R. K.
Gaye, 1930, 194a 9-12.
3. On the question of mediaeval classification of the sciences see James A.
Weisheipl, O.P., "The nature, scope and classification of the sciences," Studia
mediewistyczne, Warsaw, Vol. 18, 1977, pp. 85-101 and his "Classification of the
sciences in mediaeval thought," Mediaeval Studies, Toronto, vol. 27, 1965, pp. 5490.
4. On the history of the seven liberal arts see: Joseph Mariétan, Problème de la
classification des sciences d'Aristote à Saint Thomas, Thèse, Paris, 1901.
5. John Pecham and the Science of Optics. Perspectiva communis, ed. David C.
Lindberg, Madison: University of Wisconsin Press, 1970, p. 60:
284
inter physice considerationis studia lux iocundius afficit meditantes. Inter
magnalia mathematicorum certitudo demonstrationis extollit preclarius
investigantes. Perspectiva igitur humanis traditionibus recte prefertur, in
cuius area linea radiosa demonstrationum nexibus complicatur, in qua tam
physice quam mathematice gloria reperitur utriusque floribus adornata.
6. Gregorius Reisch, Margarita philosophica, Basel: Michael Furterius, 1517, fol.
aiiv:
1 Grammaticae, 2 Dialecticae, 3 Rhetoricae, 4 Arithmeticae, 5 Musicae,
6 Geometrie elementa, 7 Astronomie, 8 Naturalis philosophie principia,
9 Originem primordialem et productionem omnium verum naturalium.
Alchimie, 10 Anime vegitative et sensitive, 11 Anime rationalis, 12
Philosphia moralis.
7. Joachim Fortius Ringelbergius, Opera, Lyons: Apud Gryphium, 1531:
Grammaticen, Dialecticen, Rhetoricca, Mathematicen (Sphaera,
Institutiones astronomiae, Cosmographia, Liber de tempore, Tabula de
tempore, Optice, Chaos Mathematicum), Divinatio, Communis cuiusdam
naturae sunt (Chaos, Experimenta, Liber de homine).
8. John Dee, Mathematicall Praeface annexed to: Euclides, The Elements, trans.
H. Billingsley, London: I. Daye, 1570. Cf. John Dee, The Mathematicall Preface
to the Elements of Geometrie of Euclid of Megara, ed. A. Debus, New York:
Science History Publications, 1975.
9. Ioannis Valentini Andreae, Collectaneorum mathematicorum decades XI.
Centum et decem tabulis aeneis exhibitae, Tübingen: Typis Iohan Alexandri Cellii,
1614:
Geometrica, Arithmetica, Statica, Astronomica, Gnomonica, Authomatica,
Optica, Architectonica, Munitoria, Mensurata, Lineata.
10. Robert Fludd, Utriusque cosmi maioris scilicet et minoris metaphysica,
physica atque technica, Oppenheim: aere Johan-Theodori de Bry, 1617, fol. 3:
Arithmeticam, Musicam, Geometriam, Perspectivam, Artem Pictoriam,
Artem Militarem, Motus Scientiam, Temporis Scientiam, Cosmographiam,
Astrologiam, Geomantiam.
11. Josephus Blancanus, Sphaera mundi, Bologna: typis S. Bonomij, 1620,
pp.388-390:
1 Geometria, 2 Arithmetica, 3 Optica, seu Perspectiva, 4 Mechanica, 5
Musica, 6 Astronomia.
285
12.
Ibid., p.390:
1 Geometria practica, 2 Arithmetica practica, 3 Perspectiva practica,
4 Mechanica practica, 5 Musica practica, 6 Astronomia practica.
13. Johann Ciermanns, Annus positionum mathematicarum quas defendit ac
demonstravit Perill. Dom. D. Wolffgangus Philippus Iacobus Unverzagt, Baro de
Ebenfurt, Louvain: In Collegio Societatis Iesu, 1641, Ordo disputationum:
Mense October
Novembri
Decembri
Ianuvario
Februario
Martio
Aprili
Maio
Iunio
Iulio
Augusto
Septembri
Geometricae
Arithmeticae
Opticae
Staticae
Hydrostaticae
Nauticae
Architectonicae
Polemicae
De machinis bellicis
Geographicae
Astronomicae
Chronologicae
Optics, he further subdivided into:
Perspectivae, Orthographica, Scenographica, Practica, Compendiosa,
Sciographica, Curiosa, Problemata.
14. Daniel Schwenter, Deliciae physico mathematicae, Nürnberg: Jeremiae
Dumlers, 1651:
I.
II.
III.
IV.
V.
VI.
VII.
VIII.
IX.
X.
XI.
XII.
XIII.
XIV.
XV.
Arithmetica
Geometria
Sterometria
Musica
Optica Perspectiv
Catoptrica
Astronomia,Astrologia
Gnomonica,Thaumatopoetica
Statica
Motum
Pyrobolia
Pneumatica
Hydraulica
Calligraphia
Architecturam
Rechenkumst
Feldmessen
Messung Cörperlicher Ding
Singkunst
Sehkunst
Spigelkunst
Sternseher,Sternenkunst
Zubereitung der Sonnen und Schlaguhren
Wag und Gewichtkunst
Kunstliche Bewegung
Feuer
Lufft
Wasser
Schreibkunst
Baukunst u. Handwercker
286
XVI.
Chymia
und andere Kunsten
15. R.P. Claudii Francisei Millet Dechales, Cursus seu mundus mathematicus,
Lyons: Apud Anissonios, 1690, 4 vol, Tractatus:
I
Euclidis libri XIV
II
Theodosii sphaerica
III
De Sectionibus conicis
IV
Arithmetica
V
Trigonometria
VI
Algebra, Hypotheseon Cartesianarum refutatio
VII
Geometria practica
VIII Mechanices
IX
Statica
X
Geographia
XI
De magnete
XII
Architectonica civilis
XIII Ars tignaria
XIV De lapidum sectione
XV
Architectura militaris
XVI Hydrostatica
XVII De fontibus et fluviis
XVIII De machinis hydraulicis
XIX De navigatione
XX
Optica
XXI Perspectiva
XXII Catoptrica
XXIII Dioptrica
XXIV Musica
XXV Pyrotechnia
XXVI Astrolabium
XXVII Gnomonica
XXVIII Astronomia
XXIX Astrologia
XXX App. ad Astronomiam seu Tract. de Meteoris
XXXI Kalendarium
16. Catalogi librorum impressorum bibliotecae regiae, Göttingen, tomus XI.V,
Mathematicae:
1.
2.
3.
4.
5.
Geometria speculativa et practica, Arithmetica, Algebra
Optica, Catoptrica, Dioptrica
Cosmographia, De sphaera, globis, etc.
Astronomia
Gnomonica
287
6. Astrologia Judiciaria
7. Physiognomia. Chyromantia et aliae artes Divinatrices
8. Architectura civilis
9. Architectura militaris
10. Ars militaris
11. Ars nautica
12. Ars Hydraulica et Hydrostatica. Machinae
13. Ars pictoria et sculptoria
14. Ars scriptoria
15. Musica
16. Artes mechanicae et illiberales
17. Pierre Hérigone, Cursus mathematicus...nova, Paris: Piget, 1644:
T.1 Euclides Elementorum lib. 15 appendicem geometriae
planorum Data. Apollonii Pergei de loco resoluto lib. 5. Doctrinam
angularium sectionum.
T.2 Continens arithmeticam practicam computum ecclesiasticum et
algebram cum ratione componendi ac demonstrandi per regressum sive
repetitionem vestigiorum analyseos
T.3 Continens constructionum tabularium sinum et logarithmorum cum
earum usu in anatoxism et triangulorum rectilineorum dimensione
geometricam practicam, artem muniendi, militam et mechanicas.
T.4 Continens sphaerae mundi doctrinam, geographiam.
T.5 Continens opticam, catoptricam, dioptricam, perspectivam,
sphaericorum trigonometriam, theoricas planetarum...gnomonicam et
musicam.
T.6 Continens geometricas aequationum cubicarum purarum, atque
affectarum effectiones
18. Jacques Ozanam, Cours de mathematique, Paris: Jombert, 1697:
T.1
T.2
T.3
T.4
T.5
Introduction aux mathématiques et les elemens d'Euclide
L'aritmétique, la trigonométrie et les tables de sinus
La géométrie
La méchanique et la perspective
La géographie et la gnomonique
19. Christian von Wolff, Elementa matheseos universae, Halle: Rengerianum,
1730-1738:
288
T.1 Que commentationem de methodo mathematica, arithmeticam,
geometriam, trigonometriam planam et analysin, tam finitorum quam
infinitorum
T.2
Mechanicum cum statica, hydrostaticam, aerometriam atque
hydraulicam
T.3
Opticam, perspectivam, catoptricam, dioptricam, sphaerica et
trigonometria sphaericam atque astronomiam tam sphaericam quam
theoricam
T.4
Geographiam cum hydrographia, chronologiam, gnomonicam,
pyrotechniam, architecturam militarum atque civilem.
20. Johann Nikolaus Frobes, Encyclopaediae mathematicae memorialis,
Helmstedt: Schnorr, 1743-1746:
Pt. 1 Succincta matheseos purae, hoc est arithmeticae, geometriae ac
trigonometriae delineatio
Pt. 2 Succincta mechanicae, hydrostaticae, aerometriae atque
hydraulicae...
Pt. 3 Succincta pyrotechniae, atque architecturae militaris pariter ac
civilis...
Pt. 4 Succincta opticae, catoptricae, dioptricae et perspectivae...
Pt. 5 Succincta astronomiae...
Pt. 6 Succincta geographiae, chronologiae et gnomonicae...
21. Heinrich Wilhelm Clemm, Mathematisches Lehrbuch, Stuttgart: bey Johann
Benedict Mezler, 1764:
Der arithmetischen Wissenschaften
erstes Hauptstuck, von der Rechnung der Zahlen
zweites Hauptstuck, von der Buchstabenrechnung
drittes Hauptstuck, von der praktischen Rechenkunst
Der geometrischen Wissenschaften
erstes Hauptstuck, von der gemeinen oder Elementar-Geometrie
zweytes Hauptstuck, von der Trigonometrie
zweytes Hauptstuck 1. Kap von der ebenen Trigonometrie
zweytes Hauptstuck 2. Kap von der sphärischen Trigonometrie
drittes Hauptstuck, von der praktischen Geometrie
viertes Hauptstuck, von der höheren Geometrie
Der statischen Wissenschaften
erstes Hauptstuck, von der Statik, sonst Mechanik
zweytes Hauptstuck, von der Hydrostatik
drittes Hauptstuck, von der Aerometrie
289
vierdtes Hauptstuck,von der Hydraulik
Der optischen Wissenschaften
erstes Hauptstuck, von der Optik besonders
zweytes Hauptstuck, von der Catoptrik
drittes Hauptstuck, von der Dioptrik
viertes Hauptstuck, von der Perspectiv
22. Johann Nikolaus Martius, Unterricht in der natürlichen Magie, völlig
umgearbeitet von Johann Christian Wiegleb, Berlin and Stettin: bei Friedrich
Nicolai, 1786, etc.:
I Elektrische Kunststucke
II Magnetische "
III Optische
"
IV Chemische "
V Mechanische "
VI Rechen
"
VII Oekonomische "
VIII Karten
"
23.
Abraham Gotthelf Kästner, Anfangsgründe der angewandten Mathematik,
Gottingen: Vandenhoek und Ruprecht, 1792:
Abth. 1 Mechanische und optische Wissenschaften
Abth. 2 Astronomie, Geographie, Chronologie und Gnomonik
24.
Johan Friedrich Lorenz, Grundriss der reinen und angewandten
Mathematik, Helmstedt: Fleckeisen, 1798-1800:
Th. 1 Grundriss der Arithmetik und Geometrie
Th. 2 Grundriss der mechanischen optischen und astronomischen
Wissenschaften
Th. 3 Grundriss der allgemeinen Grossenrechnung
25. We have made no attempt here to be exhaustive. There was another tradition in
the eighteenth century which skipped optics altogether in lists of the mathematical
sciences. For our purposes the following five examples will suffice:
Allain Manesson Mallet, La géométrie pratique, Paris: Anisson, 1702:
T.1
T.2
T.3
T.4
Les élémens de la géométrie
La trigonométrie
La planimétrie
La steréométrie
290
Benjamin Hederich, Anleitung zu den furnehmsten mathematischen
Wissenschaften, bennantlich der arithmetica, geometria, architectura,
astronomia und gnomonica, Wittenberg: Zimmermann, 1710.
Jakob Hermann, Abrégé des mathématiques, St. Petersburg: Académie
impériale des sciences, 1728, 2 vol.:
T.1 L'arithmétique, la géométrie et la trigonométrie
T.2 L'astronomie et la géographie
T.3 La fortification
Abbe Deidier, La mesure des surfaces et des solides par l'arithmétique des
infinis et les centres de gravité, Paris: Jombert, 1740-1741:
S.1 Le calcul différentiel et le calcul expliqués et appliqués à la géométrie
S.2 La méchanique générale contenant la statique, l'airométrie,
l'hydrostatique et l'hydraulique
25. Georg Gottlieb Schmidt, Anfangsgründe der Mathematik, Frankfurt:
Varrentrapp, 1814-1816:
Abth. 1 Statik, Hydrostatik, Aerostatik und Mechanik fester Körper
Abth. 2 Hydraulik und Maschinenlehre
26.
John Dee, Mathematical Praeface, as in note 8 above:
27. Leonard Christoph Sturm, Tractatus de natura et constitutione matheseos,
Frankfurt: Schrey, 1706, p. 308.
Generalis
Theoretica
Lucis & umbra
Ithyoptica quantitatis
declarans
figurae
phaenomena situs,& numeri
motus
Specialis Catoptrica
agens de
Dioptrica
agens de
Optica
est vel
reflexione radiorii
coloribus reflexis
speculis planis
speculis sphaericis
refractione
refractione colerata
lentium forma
lentium compositione
Technica
291
Perspectiva
Effectiva
Verticalis unita sv. pictoria separata
sv.scenica
Horizontalis
Planisphaerica
Anamorphotica Ithyoptica
Catoptrica
Dioptrica
28. Paul Guldin, De Centro gravitatis, Vienna: G. Gelbhaar, 1635-1641, p. 20:
Proprie Optica, ut Perspectiua
Prospectiua
OPTICA Catoptrica, de Speculis
Orthographica
Stereographica
Scenographica
Planis
Convexis
Concauis
Ustorijs
Dioptrica
Diocatoptrica
29. Theodosius Haesel, Geistliche Perspectiva, Dresden: W. Seyffert, 1652:
Brevis synopsis disciplinarum mathematicarum:
Generalis
OPTICA
Specialis
Proponitur
sub triplici
radio
Recto seu
Directo in
Ichnographia
Orthographia
Scenographia
Sciographia
Reflexo in
Catoptrica
sive Speculis
Planis
Concavis
Convexis
Refracto seu
Vitrum
infracto in
Aquam
mesoptica vel per Aerem
30. Johann Christoph Adelung, Kurzer Begriff menschlicher Fertigkeiten, Leipzig:
Christian Gottlieb Hertel, 1781, pp. 258-258:
Die Perspektive theilet sich übrigens in die Linearperspecktive, welche
durch Hülfe der Geometrie die richtige Verkürzung der geraden Linien,
z.B, an den Theilen eines Gebäudes lehret; in die Luftperspective, welche
292
ganz in das Fach des Malers einschlägt, und Licht und Schatten nach den
Veränderungen bestimmen lehret, welche die Farbe der Luft in einer
gewissen Entfernung an den Körpern und ihren Farben hervorbringet; und
in die Spiegelperspective, welche unordentlich und verzerrt scheinende
Figuren zeichnen lehret, welche die sphärischen, komischen und anderen
Spiegel wieder in ihrer ordentliches Gestalt darstellen.
I am grateful to Professors Loris and Maria Rita Sturlese for this quote.
31. These are cited in note 13 above.
32. Wiegleb, as in note 22 above, vol. III. Optische Kunststücke:
Das Auge und dessen Nachahmung
Die curiose Perspektive
Planspiegel
Hohl und erhabene Spiegel
Prisma und prismatischen Farben
Erhabene und hohle Glaser
Perspektiv
Instrumente und Maschinen zum Zeichnen.
33. Julius von Schlosser, Die Kunstliteratur, as in Introduction, note 2, 1924,
(IV.1), p. 227; cf. 1977, ed. Kurz, pp. 259-260.
34. Erwin Panofsky, "Die Perspektive als symbolische Form," as in I.2, note 27, p.
274.
35. Leonardo da Vinci, Treatise on Painting [Codex Urbinas 1270], trans. A.
Philip McMahon, Princeton: Princeton University Press, 1956, vol. II, fol. 231r:
Delle ombrosita et chiarezze de monti...Prospettiva commune.
36. On this copy of John Peckham's Perspectiva communis, now in Milan,
Bibliotheca Ambrosiama, Cod. Inc. 1105 see: Zenale e Leonardo. Tradizione e
rinovamento della pittura lombarda, ed. Mauro Natale, Alessandra Mottola
Molfino e Marisa Dalai Emiliani, Milan: Electa, 1983, p. 165.
37. Louis Leger Vallée, Théorie de L'Oeil, Paris: Baillière, 1844, pp.ix-x:
Tel était l'état de la science lorsque, en 1821, nous publiames le Traité de
la science du dessin. Dans cet ouvrage, nous considerons la peinture, le
dessin, dans ses différents genres, et g‚n‚ralement l'art d'imiter les objets
de manière à produire plus ou moins d'illusion, comme une application des
règles au moyen desquelles on peut tromper l'oeil. La théorie de la vision
sert donc de base à notre traité ou elle est exposée avec quelque détail, et
293
souvent envisag‚e sous des aspects nouveaux. Dans cet ouvrage, dont la
perspective et les ombres sont des parties importantes, la géométrie nous
guide constamment, et elle nous a conduit à une explication de
l'achromatisme de l'oeil fondée sur la non-homogenéité du corps vitre.
38. John Ruskin, The Elements of Perspective, London: Smith, Elder and Co.,
1859, pp. 1-3.
39. Ibid., pp. 99 ff.
40. Armond Théophile Cassagne, Pratique de la perspective, Paris: Claude
Fouraut et fils, 1879, pp. 18, 50.
41. Jules De La Gournerie, Traité de perspective linéaire, Paris, Dalmont et
Dunod, 1859, pp. xix-xx:
La Perspective est un art graphique spécial; elle présente des difficultés
pratiques qui lui sont propres et qui, dans le courant de plusieurs siècles,
ont occupé un grand nombre de savants et d'artistes. Les auteurs qui l'ont
traitée comme une simple application de la Géométrie descriptive n'ont pas
pu lui donner les développements necéssaires. Il y a d'ailleurs lieu de
croire que plusieurs d'entre eux avaient dédaigné‚ d'étudier les anciens
ouvrages. Les élèves de Monge croyaient, en effect, presque tous, que les
arts graphiques ne presentaient avant leur maître qu'incertitude et
confusion. On trouve dans les écrits de plusieurs des plus célèbres d'entre
eux des assertions tout a fait érronées à cet égard.
42. See, for instance, Hermann von Helmholtz, Handbuch der physiologischen
Optik, Hamburg, Leipzig: Teubner, 1856.
43. Panofsky, as in I.2, note 27, pp. 265, 301. Cf. the author's: "Panofsky's
perspective: a half century later" in: Marisa Dalai Emiliani, ed., La prospettiva
rinascimentale, Florence: Centro Di, 1980, p. 567.
44. A history of professions mentioned in title pages would make a very interesting
topic of study.
45. For a list of model books see: R. W. Scheller, A History of Mediaeval Model
Books, Haarlem: De Erven F. Bohn N.V., 1963.
46. The standard edition remains: Villard de Honnecourt, Kritische
Gesamtausgabe des Bauhüttenbuches Ms. Fr. 19093 der Pariser National
Bibliothek, ed. R. Hahnlohser, Vienna: A. Schroll, 1935. 2nd ed. Graz:
Akademische Druck und Verlagsanstalt, 1972.
294
47. For an introduction to this vast literature see: Leonardo Olschki, Geschichte
der neusprachlichen wissenschaftlichen Literatur, Heidelberg: Winter, 1919-1922,
2 vol. and Bertrand Gilles, Les ingénieurs de la Renaissance, Paris: Hermann,
1964.
48. For a good introduction see Lawrence Wright, Perspective in Perspective,
London: Routledge and Kegan Paul, 1983. The deeper problems involved in these
distinctions have greatly interested my mentor Sir Ernst Gombrich: e.g., Art and
Illusion, Princeton: Princeton University Press, 1960.
49. For an introduction see Edmond R. Kiely, Surveying Instruments. Their
History-Classroom Use. New York: Bureau of Public Teachers College, 1947
(National Council of Teachers of mathematics 19th Yearbook).
50. Franz Reuleaux, Theoretische Kinematik Grundzüge einer Theorie des
Machinenwesens. Braunschweig: Vieweg, 1875. English trans. Alex B.W.
Kennedy, Kinematics of Machinery. Outlines of a Theory of Machines, London:
Macmillan, 1876.
51. Very little has been done on the history of this subject. Useful is Booker, as in
I.3 note 46 above and a dissertation by Joachim Kuns, Betrachtungen zur
Geschichte der technischen Zeichnungen, Dissertation, Rheinisch-Westfälischen
Technischen Hochschule, Aachen, 1980.
52. Pierre Larousse, Grand dictionnaire universel du XIX siecle, Paris:
Administration du grand dictionnaire universel, 1870, vol. 6, p. 592:
Dessin lineaire. Le genre se divise en plusieurs branches suivant le but que
l'on se propose et la nature des objects a representer. Il comprend le tracé des
épures de géometrie élémentaire, descriptive et analytique; la perspective
ordinaire et isom‚trique; les dessins d'architecture et de machines la
topographie.
53. Leonardo da Vinci, as in note 35, fol. 167-171: "De panni."
54. Jost Amman, Kunstbüchlein, Frankfurt: Romanus Beatus in Verlegung Johann
Feyrabends, 1599. A complete collection of the illustrations of Amman is
painstakingly being done by Dr. Ilse Franke.
55. E.g., Hieronymus Cock, Compartimentorum quod vocant multiplex genus
lepidissimis historiolis poetarumque fabellis ornatum, Antwerp: Cock, 1560. Cf.
Iacques Floris, Veelderhande cierlijke compertementen..., Antwerp: Hans
Liefrinck, 1564.
295
56. Heinrich Vogtherr, Kunstbüchlein, Strasburg: Christian Müller, 1572. Reprint:
Zwickau: Verlag von F. Ullmann, 1913, (Zwickauer Facsimiledrucke, Nr. 19).
57. H. Soden-Smith. A List of Books and Pamphlets in the National Art Library,
South Kensington Museum on Drawing, Geometry and Perspective, London: Eyre
and Spottiswoode, 1888, p. 41.
58. Ibid., pp. 50-51 and 48-50.
59. Ibid., pp. 43-48. Cf. Gerlind Werner, Nützliche Anweisung zur Zeichenkunst.
Illustrierter Lehr und Vorlagenbücher aus den Beständen der Bibliothek des
Germanischen Nationalmuseums. (Ausstellung der Bibliothek der Germanischen
Nationalmuseums 21.Juni-7. September,Nürnberg, 1980), Nürnberg: Kuch-Druck,
1980.
60. E.g., Robert Dudley.
61. Soden Smith, as in note 57 above, p. 51.
62. G.-P. Lomazzo, as in I.1 note 36.
63. Cf. Roger De Piles, Principles of Painting, London: J. Osborn, 1743, p. 294
where he lists expression, colouring, design and composition.
64. Felix Bracquemond, Du dessein et de la couleur, Paris: G. Charpentier et Cie.,
Editeurs, 1895, p. 283:
Table: Le dessin, la couleur; Chaleur, froideur; Dessinateur, coloriste;
Reflet, Clair-obscur; Valeur; Trait, model‚ Ligne, masse, silhouette;
Perspective, Effet, Execution Ornement, La nature.., Le modelé, l'art et la
physique.
65. See the catalogue by Werner, cited in note 59.
66. Samuel van Hoogstraeten, Inleyding tot de hooghe schoole der schilderkonst,
Rotterdam: Francois van Hoogstraeten, 1678:
1. Euterpe
2. Polymnia
3. Clio
4. Erato
5. Thalia
6. Terpsichore
7. Melpomene
8. Calliope
9. Urania
De Redewikster
De Rederijkster
De Historyschrijffster
De Minnedichtster
De Kluchtspeelster
De Poetersse
De Treurdichtster
De Heldedichster
De Hemelheffster
296
67. For an introduction to this complex debate see Georg Kauffmann, PoussinStudien, Berlin: De Gruyter, 1960.
68. John Locke, Some Thoughts Concerning Education, London: Printed for A.
and J. Churchill, 1693.
69. Jean Jacques Rousseau, Emile; ou, de l'éducation, The Hague [i.e., Paris]: Jean
Neaulme, 1762, 4 vol.
70. For an introduction to these problems see: Theodor Wunderlich, Illustrierter
Grundriss der geschichtlichen Entwicklung des Unterrichts im Freien Zeichnen,
Stuttgart: W. Effenberger, 1892 and D. Lako, Overzicht van de geschiedenis van
het teeken onderwijs in Nederland, Tiel: D. Mijs, 1899. Cf. Ben Schasfoort,
Bibliographie van Nederlandstalige literatuur...met betrekking tot tekenonderwijs,
Enschede: Stichting von der Leerplanontwikkeling, 1986.
71. See also Oskar Pupikofer, Geschichte des Freihandzeichen-Unterrichts in der
Schweiz, St. Gall: Druck der M. Kälin'schen Buchdruckerei, 1890.
72. Cf. A. Fr. Herbold, Die Methode des Zeichenunterrichts der Brüder Ferdinand
und Alexander Dupuis, Darmstadt: Druck und Verlag von Carl Wilhelm Leske,
1848.
73. Encyclopédie ou dictionnaire raisonné des arts et des métiers, ed. M. Didérot
et M. D'Alembert, Paris: Chez Briasson, David...,1751, vol. 1, pp.889-891:
Les draperies, les fleurs, les fruits, tout enfin doit être dessiné, autant qu'on le
peut sur le naturel.
74. See Wunderlich, as in note 70, p. 35:
1.
2.
3.
4.
Übungen zur Bildung der Hand fur das Zeichnen.
Zeichnungsübungen im Schaffen und Erfinden schöner Formen.
Übungen, die zur Bildung und Befestigung der Imagination führen.
Übungen im realen oder mathematischen Abzeichnen der Gegenstände der
Natur.
5. Übungen in der perspektivischen Entwicklung.
75. Cf. Lako, as in note 70, p. 63.
76. Ibid., pp. 68-69.
77. Cf. Wunderlich, as in note 70, p. 92:
297
a) Zeichnen menschlicher Kopfe (la figure), zuerst nach Gipsmodellen,
dann nach lebenden Modellen;
b)
Zeichnen ganzer menschlicher Figuren (l'académie), nach
Gipsmodellen;
c) Zeichnen von Zieraten (l'ornement), nach Gipsmodellen;
d) Blumenzeichnen (le dessin des fleurs), zuerst nach einer angemessenen
Reihe künstlicher, dann nach natürlichen Blumen.
78.
See Lako, as in note 70, p. 97:
I.
Het teekenen van rechte lijnen, hoeken en krommelijnen.
II. Het teckenen van eenvoudige voorwerpen in omtrek.
III. Het teekenen van eenvoudige voorwerpen met verlichting.
IV. Het bloemen-en ornamentteekenen.
V. Het landscapteekenen.
VI. Het figuurteekenen.
VII. Het dierenteekenen.
VIII. Van de perspectief.
IX. De schaduwleer.
79. Larousse, Dictionnaire universel du XIX siecle, as in note 52, p. 59:
Dessiner, a-t-il dit, n'est pas reproduire un objet tel qu'il est; ceci est la
besogne du sculpteur, mais tel qu'il parait, et ceci est celle du dessinateur
et du peintre; ce dernier achève au moyen de la d‚gradation des teintes ce
que l'autre a commencé au moyen de la juste disposition des lignes, c'est la
perspective, en un mot, qu'il faut mettre non pas dans l'esprit, mais dans
l'oeil de l'élève. Vous ne m'apprenez, dirai-je au maître, avec vos
proportions exactes et votre perspective par A plus B, que des vérités, et
dans l'art tout est mensonge: ce qui est long doit paraître court, ce qui est
courbe paraîtra droit, et réciproquement. Qu'est-ce, en definitive, que la
peinture dans sa définition la plus littérale? L'imitation de la saillie sur
une surface plane. Avant de faire de la poésie avec la peinture, il faut
avoir appris à faire venir les objets en avant. Il a fallu des siècles pour en
arriver là. On a commencé par un trait sec et aride, on a fini par les
merveilles de Rubens et du Titien, dans lesquelles les parties saillantes
comme les simples contours, prononc‚s chacun dans la measure
convenable, sont arrivés à cacher l'art tout à fait, à force d'art: voilà le nec
plus ultra, voilà le prodige, et ce prodige est le fruit de l'illusion. Quel que
soit l'object qu'il se propose de réproduire, le dessinateur est donc tenu
avant tout de connaitre, de respecter les lois de la perspective. Il y a la
perspective linéaire et la perspective aérienne: la première, dont la
géométrie descriptive fournit les regles, suffit au dessin ou il n'est fait
usage que de traits, de contours; la seconde, qui a pour objet les
modifications apparentes que font subir aux formes les jeux de la lumière
et de l'ombre, trouve son application dans les images colori‚es, soit
298
monochromes (comme sont les dessins à la sepia, à l'encre de Chine), soit
multicolores. On peut dire que, dans un tableau, le dessin donne la
perspective lin‚aire, et la couleur en perspective a‚rienne. Le dessin et la
couleur sont donc indispensables, l'un et l'autre, à la peinture. Aussi ne
comprenons-nous guère les interminables disputes qui se sont elev‚es sur
la question de savoir auquel de ces deux moyens de l'art il convient
d'accorder la pre-éminence. Vouloir résoudre cette question, a dit Wattelet,
c'est la meme chose que vouloir décider si c'est l'âme ou le corps de
l'homme qui constitue la partie la plus éssentielle à son existence.
80. Dictionnaire de pédagogie, as in I.3, note 55, p. 576:
La théorie développée de la perspective fait connaître les procédés imaginé
par les géomètres pour obtenir des apparences exactes dans toutes sortes
de cas ou il est necéssaire, en effet, pour un peintre de profession, et
surtout pour un architecte, d'en savoir executer de telles.
81.
Ibid., p. 579:
Le terme de l'étude est le dessin d'après nature. Mais c'est ou commence
l'enseignement approfondi. Dans un enseignement élémentaire on ne
dépassera pas le dessin d'après la bosse.
82.
Ibid, p.580:
Course élémentaire
Tracé des lignes droites et leur division en parties égales. Evaluation des
rapports des lignes entre elles. Reproduction et évaluation des angles.
Premiers principes du dessin d'ornement. Circonférences, polygones
reguliers, rosaces étoilées.
Cours moyen
DESSIN A MAIN LEVEE. Courbes géométriques usuelles: ellipses,
spirales,etc. Courbes empruntées au règne vegétal: tiges, feuilles, fleurs.
Copie de plâtres représentant des ornements plans d'un faible relief.
Premières notions de dessin géométral et éléments de la perspective.
Représentation géométrale au trait et représentation perspective, au trait,
puis avec les ombres, de solides géométriques et d'objets usuels simples.
DESSIN GEOMETRIQUE. Emploi (au table) des instruments servant au
tracé des lignes droits et des circonférences: règle compas, équerre et
rapporteur.
Se borner, dans cette partie du cours, à faire comprendre aux élèves
l'usage de ces instruments dont ils acquerront le maniement dans le cours
supérieur.
299
Cours supérieur
DESSIN A MAIN LEVEE. Dessin, d'après l'estampe et d'après le relief,
d'ornements purement g‚om‚triques: moulures, oves, rais de coeur, perles,
denticules, etc.
Dessin , d'apres l'estampe et d'après le relief, d'ornements empruntant
leurs elements au règne végétal: feuilles, fleurs et fruits, palmettes,
rinceaux etc.
Notions élémentaires sur les ordres d'architecture données au tableau par
le maître (3 lecons).
Dessin de la tete humaine: ses parties, ses proportions.
DESSIN GEOMETRIQUE. Execution sur le papier, avec l'aide des
instruments, des traces géométriques qui ont été faits au tableau dans le
cours moyen.
Principes du lavis à teintes plates.
Dessin reproduisant des motifs de décoration de surfaces planes ou d'un
faible relief: carrelages, parquetages, vitraux, panneaux, plafonds. Lavis a
l'encre de Chine et à la couleur de quelques uns de ces dessins.
Releveé avec cotes, et représentation géométrale au traité de solides
géométriques et d'objets simples, tels: assemblages de charpente et de
menuiserie, dispositions extérieures d'appareils de pierre de taille, grosses
pieces de serrurerie, meubles les plus ordinaires, etc. Emploi du lavis pour
exprimer la nature des materiaux. Lavis des plans et des cartes.
Ibid., p.575:
L'étude du dessin ne devait pas conduire seulement une partie de ceux qui
s'y adonnerait à acquérir de représenter les formes des choses visibles, soit
par une pure imitation, soit en imaginant et inventant, et en s'élevant ainsi
jusqu'à l'art, mais que ceux qui n'arriveraient pas à acquérir ce talent ou
qui ne l'acquerraient que dans une faible mesure, cette étude, si on la
fondait sur l'imitation d'excéllents modèles, leur apprendrait à apprecier ce
qui est, en fait de choses visibles, exacts ou inéxact, correct ou incorrect,
surtout beau ou laid, gracieux ou disgraciuex, s‚ant ou mal séant; qu'elle
enseignerait ainsi à mieux voir et a mieux juger, qu'elle formerait enfin,
l'oeil et le goût, dont l'utilit‚ est presque universelle.
84. Louis Cloquet, Nouveau traité élémentaire de perspective, Paris: Bachelier,
1823, pp. vi-viii:
Il m'est arrivée plusieurs fois de demander à des artistes qui m'avaient
témoigné leur désir de savoir la Perspective, s'ils avaient quelque teinture
des premiers élémens de la Géométrie. Ils m'ont répondu negativement,
disant d'ailleurs qu'ils n'en avaient pas besoin, qu'ils ne voulaient savoir
que la Perspective seule, ou plutot que la Perspective des peintres. Et
cependant il n'y a qu'une seule et unique Perspective, et autant vaudrait-il,
à mon avis, en manifestant un pareil désir, demander écrire sans vouloir
300
apprendre a lire. Ma manière de raisonner les a eu bientot convaincus,
mais ne les a pas tous persuadés. J'ai toujours observé‚ que ceux qui s'en
sont rapportés à moi, que ceux qui ont bien voulu se résigner à étudier les
principes préliminaires, ont appris très facilement et véritablement la
Perspective, science qu'aucun peintre ne doit ignorer. C'est là ce qui m'a
engagé à réduire les élémens de la Perspective à ses principes éssentiels, et
a les mettre à la portée des lecteurs qui n'ont aucune notion des
Mathématiques, ce qui est assez rare heureusement. J'ai donc divis‚ cet
Ouvrage en cinq parties. La première traite de la Géométrie élémentaire,
dont j'ai cru devoir retrancher toutes les choses étrangères à notre objet,
telles que celles qui concernent la mesure des surfaces, des solides, etc. La
deuxième contient les principes purement élémentaires de la Géométrie
descriptive, qui n'est elle-meme qu'une suite ou une application des
principes de la première partie. La troisième traite seulement de la partie
de l'Optique qui a un rapport direct à notre objet, c'est à'dire de l'Optique
considérée plutot sous la rapport de la Peinture que sous celui de la
Physique. La quatrième contient les règles de la Projection des Ombres,
très necéssaires, non-seulement aux Peintres, mais encore aux Architectes,
aux Dessinateurs, etc. Enfin, la cinquième traite de la Perspective, qui est
le dernier et principal objet que nous nous sommes propos‚ de traiter.
Il n'existe, à ma connaissance, aucun ouvrage rédigé sur ce plan.
85. A.W. Cunningham, Notes on the History, Methods and Technological
Importance of Descriptive Geometry, Edinburgh: 1868. For a brief discussion of
this see P.J. Booker, as in I.3, note 46, pp. 130-132. For a standard treatment of the
french context see M. Le Comte de Laborde, De l'union des arts et de l'industrie,
Paris: Imprimerie impériale, 1866, 2 vol.
86. Felix Klein, Vergleichende Betrachtungen über neuere geometrische
Forschungen, Erlangen: A. Deichert; Cf. David Hilbert, Anschauliche Geometrie,
Dover: New York, 1952.
87. K. Lother Wolf and Robert Wolff, Symmetrie Versuch einer Anweisung zu
gestalthaften Sehen und sinnvollem Gestalten systematisch dargestellt, Münster:
Böhlau Verlag, 1956, 2 vol.
88. H. M. S. Coxeter and S. L. Greitzer, Geometry Revisted, Washington:
Mathematical Association of America, 1967, particularly pp. 100-101.
89. H. M. S. Coxeter, Introduction to Geometry, New York: John Wiley, 2nd
edition, 1969, p. 175.
90. Margaret Hagen, Varieties of Realism, Cambridge: Cambridge University
Press, 1986, p.105.
301
91. Philip Steadman, Lionel March, The Geometry of Environment, London:
Methuen, 1974, p. 25.
92. Ernest R. Weidhaas, Architectural Drafting and Construction, Boston: Allyn
and Bacon Inc., 1981, particularly p. 39.
Chapter 5
1. For an introduction to these problems see Pierre Duhem, “Sozein ta
phainomena. Essai sur la notion de théorie physique de Platon a Galilee”, Annales
de philosophie chrétienne, Paris, vol.79/156 (ser.4,VI), 113-138,277-302,352377,482-514,576-592; translated as: To save the Phenomena: An Essay on the Idea
of Physical Theory from Plato to Galileo, Trans. E. Doland and C. Maschler,
Chicago: University of Chicago Press, 1969.
2. For a standard work on the astrolabe see: Henri Michel, Traité de l'astrolabe,
Paris: Gauthier Villars, 1947.
3. Alfarabi, as in I.1, note 21.
4. Gundissalinus, "De divisione philosphiae," ed. L. Baur, Beiträge zur Geschichte
der Philosophie der Mittelalters, Münster, Bd.IV, Heft 2-3, 1903, pp. 112-114.
5. Witelo, Opticae Thesaurus...Vitellonis Thuringopoloni Libri X, Basel: Per
Episcopios, 1572 (Cf. New York: Johnson Reprint Corporation, 1972, The Sources
of Science, No. 74), p. 217: (Liber Quintus.57):
Possibile est speculum unum planum in camera propria taliter sisti, ut in
ipso videantur ea, quae geruntur in domo alia vel in vicis et plateis.
Ptolemaeus 7th 2 catoptr.
Sit in camera videntis locus aliquis, in quo existente visu placet videre per
speculum planum omne illud, quod alibi agitur: qui locus camerae in quo
sistitur centrum visus, sit signatus puncto a: et sit locus, in quo est voluntas
aliquid videndi, quod in illo loco agitur, signatus puncto b: sitque rima sive
fenestra in camera videntis opposita loco b, que sit g: et ducatur linea bg:
& producatur in continuum & directum intra cameram ad aliquam
punctum, qui sit d: quod totum postest fieri per astrolabium sive
quadrantem vel aliud instrumentum certificationis visuum.
7. Reinerus Gemma Frisius, De radio astronomico et geometro structura,
Antwerp: Apud G. Bontium, 1545, 21r:
Omitto autem hic ex proposito, quomodo pictor aliquis insignis imo
consistens loco, aut arcem integram, aut aedem sacram, aut civitatem
quoque (si velit) ad rationem opticae delineare possit huius nostri radii
adminucilo: eo quad haec tum anten narratis, tum ex iis quae dicentur,
302
quivis ingeniosus facile colligem possit. Non possum tamen silentio
praeterire summam et facilitatem & commoditatem huius nostri radii,
quam architectus aliquis aut pictor adsequi potest, dum stans pede in uno
(ut dici solet) totam aedifici faciem sibi opposition in tabulam graphice
secundum partium symmetriam depingere possit.
Cf. A. Pogo, "Gemma Frisius, his method of determining differences of
longitude by transporting timepieces (1530) and his treatise on triangulation
(1533)," Isis, Cambridge Mass., vol. 22, no. 2, February 1933, pp. 467-485.
8.
Jacques Bassentin, Amplification de l'usage de l'astrolabe, ed. J. Focard,
Paris: Cavellat, 1551, p. 91:
Et pource qu'il n'est pas du tout possible, que le sens et la raison puissent
bien connoitre le vraye quantite de l'anglet aigu et variable, par ainsi il
seroit tres difficile de naturellement comprendre la certaine quantite d'une
chose, par la science de la perspective seulement. A cest cause les anciens
geometriciens et mesureurs, ont inventés certains instruments artificiels: et
par le moyen d'iceux ont donné facilement a connoitre des quantitez des
choses, avec la certitude d'icelle. Mais pour ce qu'il y ha plusieurs et divers
instrumens servans & faits pour cest art comme sont un cadran, un triangle
geometrique, baculus Jacob, umbraculum visorium, verge geometrique,
horloge manuel, quilindre, et autres, desquelz l'usage seroit long a
declairer: je passe outre...
10. Manetti, as in I.1 note 31, pp. 44-45.
11. Antonio Averlino detto il Filarete, Trattato di architettura, ed. Anna Maria
Finoli e Liliana Grassi, Milan: Edizioni il Polifilo, 1972, p. 653:
guardo uno pavimento che ci sia distesi legni quadri o vuoi guardare uno
solare di sotto su: tutte le travature sono equidistanti l'una dall'altra, e
sguardando ti parra che sieno e più e meno: secondo chelle ti saranno
appresso, ti paranno piu equali, e quantu piu ti si dilungano, tanto piu ti
paranno accostate insieme l'una a dosso all'altra, in modo che ti paranno
tutt'una. E meglio le vuoi considerare, torrai uno specchio e guarda dentro
in esso: vedrai chiaro essere cosi; e se ti fussino al dirimpetto dell'occhio,
non ti parebbono se non tutti iguali. E cosi credo che Pippo di ser
Brunelleschi fiorentino trovasse il modo di fare questo piano, che
veramente fu una sottile e bella cosa che per ragione trovasse che nello
specchio ti si dimostra bench‚ coll'occhio ancora, se ben considerrai, tu
vedrai quelle mutazioni e diminuzioni.
12. Over one hundred articles have been written on this topic in the past century.
For two recent assessments see: Renzo Beltrame "Gli esperimenti prospettici del
Brunelleschi,"Accademia nazionale dei Lincei. Rendiconti della classe di scienze
303
morali, storiche e filologiche, Rome, series B, vol. 28, fasc.3, March, 1973,
pp.417-468 and Martin Kemp,"Science, non science and nonsense: the
interpretation of Brunelleschi's perspective", Art History, London, vol.1, 1978,
pp.134-161.
13. Simon Stevin, Derde stuck der wisconstighe ghedaechtnissen van de
deusichtighe, Leiden: Ian Bonwensz, 1605 in: The Principal Works of Simon
Stevin, ed. D. J. Struik, Amsterdam: N.V. Swetz & Zeitlinger, 1958, vol. II.13, pp.
959-961.
14. Leon Battista Alberti, as in I.i, note 13, pp.56-57.
15. Cf. the author's: Military Surveying and Topography, as in I.1 note 31.
16. For a discussion of these see the author's work on Leonardo, as in I.1, note 14,
pp. 108-109
17. David Hilbert, Anschauliche Geometrie, Dover: New York, 1944; translated
as: Geometry and the Imagination, New York: Chelsea Publ. Co., 1952.
18. See, for instance: G. Pauschmann, "Zur Geschichte der linsenlosen
Abbildung," Archiv für Geschichte der der Mathematik, Naturwissenschaften und
der Technik, Leipzig, Bd. 9, 1922, 86-103.
19."Guillaume de St. Cloud, Astronome," Histoire littéraire de la France, Paris,
tom. XXV, 1869, p. 73.
20. Re: Levi ben Gerson Cf. Maximilian Curtze, "Die Dunkelkammer, Eine
Untersuchung über die Vorgeschichte derselben," Himmel und Erde, Berlin, Jg.
XIII, 1901,pp. 226- 232. See also that author's: "Die Abhandlung des Levi ben
Gerson über Trigonometrie und den Jacobstab", Bibliotheca Mathematica,
Stockholm, N. F., Bd. 12, no. 4, 1898, pp. 97-112.
21. See the author's "Leonardo and the camera obscura" in: Studi Vinciani in
memoria di Nando de Toni. Brescia: Ateneo di scienze lettere ed arti. Centro
ricerche Leonardiane, 1986, pp. 81-92.
22. Vitruvius, De architectura, ed. Cesare Cesariano, Como: 1521, fol. xxiii:
Excellentemente tange una pulcherima ratione de optica quale fu experta
et verificata dal Monastico Architecto Don Papnutio de Sancto Benedicto:
si concavo al torno farai un circolo in qualche assicula di quantitate di
uncie quatro vel sei, il concavo uncie due vel circa: et questa habia nel
centro del concavo uno parvo et brevissimo spectaculo seu foramine quod
scopus etiam dicitur: et infixo concordantemente in una valve seu anta di
qualche fenestre clause per tal modo in lo loco dove sei non possa introire
304
altra luce: et habi uno pocho di biancho papero vel altra cosa che recipia
suso quello che si representera du epso in sino in tuta la terra et coelo
sono contenuto.
23. See John Hammond, The Camera Obscura. A Chronicle, Bristol: Adam Hilger
Ltd., 1981 for a general treatment. For a concise article with citations from sources
see J. Waterhouse, "Notes on the early history of the camera obscura,"
Photographic Journal, London, vol. 25, 1901, pp. 270-290.
24. Anonymous, Unterweisung im Landschaftmalen und Prospektzeichnen nebst
den Hauptregeln der menschlichen Theile, Nurnberg: Verlag der Raspeschen
Buchhandlung, 1796, p. 9:
Es glauben wohl einige, dass man durch die Camera obscura eine Gegend
am richtigsten aufnehmen kan und es ist wohl wahr, ich bekomme die
Gegend richtig, aber es ist viel schöner und besser, wann ich nach der
Natur selbst und ohne Camera obscura zeichne.
Die Camera obscura ist hauptsächlich ein gutes Mittel fur Liebhaber, und
solche, die nicht nach der Natur zeichnen Können, oder es lernen wollen.
25. Luca Pacioli, Summa di arithmetica, geometria, proportioni e proportionalità,
Venice: Paganinus de Paganinis, 1494, Preface:
La perspectiva se ben si guarda senca dubio nulla sarebbe se queste non li
se accomodasse. Cioe apieno dimostra el monarcha ali tempi nostri de la
pictura maestro Pietro di franceschi nostro conterraneo... Cioe qui in
vinegia Gentil e Giovan bellini carnal fratelli. E in perspectivo desegno
Hyeronimo Malatini. E in Fiorenza Alexandro Boticelli, Philippino e
Domenico grilandaio. E in peroscia Pietro ditto el perusino. E in Cortona
Luca del nostro Maestro Piero degno discipul. E in Mantua Andrea
Mantegna. E in Furli Melocco con suo caro alievo, Marco Palmezzano.
Quali sempre con libella e circino lor opera proportionando a perfection
mirabile conducano. In modo che non humane ma divine negliochi nostri
sapresentano....
28. E.g., Leonardo da Vinci, A 106v (BN 2038 26v, 1492). Cf. the author's
Leonardo Studies I, as in I.1, note 14, p.109.
29. Vitruvius, Architettura con il suo commento, ed. M. Gianbatista Caporali,
Perugia: Iano Biganzzini, 1536, fol. 6r:
Hora sia il sesto stato trovato da chi el sia che piu necessario e stato alli
mesuramenti di geometria, & prospettiva che a qualunque altro istrumento
sia: perche con essu si mesurano tutte be liniali dimostrationi e le
angularie cose alle quale si expetta le terminationi delle linie e divisioni...e
tanto piu quanto e maggiore la multiplicatione per la inequalita de punti
305
come e notissimo alli experti liniatori, di che specialmente sono di
prospettiva.
30. On the problem of universal measurement see the author's "Measurement,
quantification and science": L'époque de la renaissance IV (1560-1600), ed. Tibor
Klaniczay, Budapest: Akademiai Kiado, 199?.
31. On Fabrizio Mordente see: Paul Lawrence Rose, "The Origins of the
proportional compass from Mordente to Galileo," Physis, Florence, anno X, fasc.
1, 1968, pp. 53-69.
32. Fabrizio Mordente, Il compasso del Signor Fabritio Mordente con altri
istromenti mathematici ritrovati da Gasparo suo fratello, Antwerp: apresso
Cristofano Plantino, 1584 (Cf. manuscript copy, Munich, Bayerische
Staatsbibliothek, Cod. it. 11).
33. For a survey of these problems and a brief history of the proportional compass
or sector see: Ivo Schneider, Der Proportionalzirkel. Ein universelles
Analogrecheninstrument der Vergangenheit, Munich: R. Oldenbourg Verlag 1970,
(Deutsches Museum. Abhandlungen und Berichte, 38 Jg., 1970, Heft 2).
34. On the question of gauging see Menso Folkerts, "Die Entwicklung und
Bedeutung der Visierkunst als Beispiel der praktischen Mathematik der fr hen
Neuzeit, "Humanismus und Technik, Berlin, Band 18, Heft 1, 31 Mai 1974, pp. 141. Cf. Grete Leibowitz, Die Visierkunst in Mittelalter, Phil. Diss, Heidelberg,
1933.
35. On Schissler see the excellent book by Maximilian Bobinger, as in chapter 2,
note 40.
36. This will be the subject of another study by the author. Here by way of
introduction some preliminary facts may be noted. A compass by Coignet, in the
collection of Commmandant Rasquin (Antwerp) contains the following lines:
A augenda vel diminuenda planorum
divisiones aequales
augenda vel diminuenda solidorum
B figurarum polygonalium aequalium
substense graduum
latera polygonalium regularium in dato circulo
C quinque corporum regularium
sinuum divisiones
metallorum marmores et petra
D segmentorum circuli
tangentium
segmentorum globi
306
The Newberry Library manuscript attributed to Lencker contains the lines:
Fundamentalis linea
Partes datae ratione lineae rectae dividendae
Partes datae ratione lineae circularis dividendae
Proportiones homologorum planorum augendo
Proportiones homologorum corporum augendo
Peripheria diameter
Reductio planorum
Reductio corporum
A sixteenth century German manuscript in Munich, Bayerische
Staatsbibliothek, Germ. N.4154, contains 8 different lines. A Manuscript by
Zugmesser, with whose colleague Galileo quarreled, now in Stuttgart,
Landesbibliothek, HB XI 19, contains 15 lines.
37. Hans Lencker [attributed], Perspectiva, Chicago, John M. Wing Foundation,
Newberry Library, Ms.B.128.
38. See, for instance, Ludolf von Mackensen, Die erste Sternwarte Europas mit
ihren Instrumenten und Uhren - 400 Jahre Jost Bürgi in Kassell, Munich:
Callwey, 1982.
39. Lencker, as in note 37 above.
40. See Stillman Drake, "Tartaglia's Squadra e Galileo's compasso," Annali
dell'istituto e museo di storia della scienza di Firenze, Florence, anno II, fasc. 1,
1977, pp. 35-54. Also his "Galileo gleanings IX. An unrecorded manuscript copy
of Galileo's Use of the Compass," Isis, Cambridge, Mass., vol. 51, 1960, pp. 5663. Cf. The introduction to his translation of Galileo Galilei, Operations of the
geometric and military compass, Washington: Smithsonian Institute, 1978.
41. Re: Michel Coignet see: G. Enestrom, "Uber den Partometer von Michel
Coignet," Bibliotheca Matematica, Stockholm, 3 Folge, Band 7, Heft 4, p.397.
42. Ladislao Reti, "Elements of machines," in: L. Reti, ed., The Unknown
Leonardo, London: Hutchinson and Co., 1974, pp. 272-273. For an early
seventeenth century expression of these connections see Blancanus, as in chapter
4, note 11, when speaking of the six speculative mathematical [sciences], p.389:
Quarta, mechanica, quae de machinis agit, sive, ut ait Aristoteles versatur
circa artificata, sicuti naturalia de sex machinis praecipuis, libra, vecte,
trochlea, axe in peritrochio, cuneo, cochlea egregia demonstrat: et quia in
eis considerat quantitate virium moventium, ponderum motuum, temporum,
quibus moventur, & machinas ipsas tanquam lineas quasdam circa centra
revolutas, ideo geometrae subalternatur, idest, geometrice demonstrat.
307
Eius pars subtilissima est, quae centra gravitatis in planis, ac solidis
perscrutatur.
43. On the question of the four powers see: Kenneth D. Keele, Leonardo da Vinci's
Elements of the Science of Man, New York: Academic Press, 1983, particularly,
pp. 93-130.
44. Leonardo da Vinci, W19070v (K/P 113r):
Il libro della scientia delle macchine va inanzi al libro de govamenti.
45. Leonardo da Vinci, K 49 [48 et 15]r:
La proportione non solamente nelle numeri e misure fia ritrovata ma etiam
nelli suoni, pesi, tempi essiti ecqualunche potentia sicia.
46. Leonardo da Vinci, Ca 203va:
Ma direno solamente i moti essere di 2 nature, delle quali l'uno e materiale
e l'altro spirituale, perche non e compreso dal senso del vedere, overo
direno d'uno essere visibile e l'altro invisibile.
47. See, for instance, CA 66rb (186r, c.1505):
Il notare sopra dell'acqua insegna alli omini come fanno li uccelli sopra
dell'aria.
48. For a full analysis of percussion in relation to Leonardo's physics see the
author's Leonardo da Vinci Studies II: 1.2
49. For an analysis of these passages see the author's Leonardo da Vinci Studies
III.
50. Hence, on CA 252rb (681r, c.1490-1492), he speaks, for instance of: "questa
terrestre e mundiale macchina".
51. E. J. Dijksterhuis, The Mechanization of the World Picture, trans. C.
Dikshoorn, London: Oxford University Press, 1961.
52. On the general mathematical context see: Paul Lawrence Rose, The Italian
renaissance of mathematics, Geneva: Librairie Droz, 1976 (Travaux d'humanisme
et renaissance, CXLV).
53. See: Giuseppe Boffito, Il primo compasso proporzionale costruito da Fabrizio
Mordente e la operatione cilindri di Paolo dell'Abbaco, Florence: Seeber, 1931.
308
Cf. Maria Luisa Bonelli, "Di una bellissima edizione di Fabrizio Mordente...",
Physis, Florence, vol. 1, 1959, 127-148, particularly p.144.
54. On Egnazio Danti see Thomas Settle, "Egnazio Danti's great astronomical
quadrant," Annali dell'istituto e museo di storia della scienza di Firenze, Florence,
anno IV, fasc. 2, 1979, pp. 3-13. Cf. Thomas Settle, "Ostilio Ricci. A Bridge
between Alberti and Galileo," XII congrès internationale d'histoire des sciences,
Paris, tome 3 B, 1971, pp. 117-122; also his "The Tartaglia Ricci problem; towards
a study of the technical professional in the 16th century." Atti del convegno
internazionale di studio. Giovanni Battista Benedetti e il suo tempo. Istituto veneto
di scienze lettere ed arte, Venice, 1987, pp. 217-226.
55. Giorgio Vasari, Jr., Raccolta fatto dal Cav. Giorgio Vasari di varii instrumentii
per misurare con la vista, 1600, Florence, Biblioteca Riccardiana, Ms. 2138. Cf.
Loredana Olivato, "Profilo di Giorgio Vasari il giovane," Rivista dell'istituto
nazionale d'archeologia e storia dell'arte, Rome, n. s. anno 16-17, 1969-1970, pp.
181-229.
56. On Ursus see Nick Jardine, The Birth of History and Philosophy of Science.
Kepler's A Defence of Tycho against Ursus...,Cambridge: Cambridge Univesity
Press, 1984.
57. Cf. Ernst Zinner, Deutsche und niederlandische astronomische Instrumente des
11-18 Jhdt, Munich: Beck Verlag, 1956.
58. Andreas Albrecht, Abriss und Beschreiburg eines sonderbaren nützlich
notwendigen Mechanischen Instruments, Nurnberg: Ieremiam Dumlerr, p.34:
Wie mit diesem Instrument ein Gebau, ein Landschaft oder andere
corperliche vor Augen stehende Ding perspectivich genommen und
aufgerissen werden sollen; p. 36: Zum Beschluss könnt ihr mit diesem
Instrument auch alle geometrische und perspectivisch Figuren in was
Gröss ihr wolt nur dass ihr die verjüngte Maass nach eurem Gefallen
verandert, verkleinern und vergrössern.
59. Leonardo da Vinci, Codice Atlantico, 190ra.
60. See, for instance, Codice Atlantico, 112ra, 251rb, BM 104ra. All the passages
involved have been considered in volume three of the author's Leonardo Studies.
61. For a conservative assessment of these passages see Albert van Helden, "The
invention of the telescope," Transactions of the American Philosophical Society,
Philadelphia, vol. 67, part 4, 1977, pp. 1-67.
309
62. E.g. Ernst Cassirer, Substance and Function, trans. William Curtis Swabey and
Marie Collins Swabey, Chicago: Open Court Publishres, 1923; New York, Dover
Publications, 1953.
63. Donald P. Greenberg, "Computer graphics in architecture," Scientific
American, New York, Vol. 230, May 1974, pp. 98-106. A basic text is William
M. Newman, Robert F. Sproull, Principles of Interactive Computer Graphics,
Tokyo: McGraw Hill, Koga Kusha Ltd., 1973.
64. R.A. Reynolds, Computing for Architects, London:
particularly p.64
Butterworths, 1987,
65. Alan Pipes, ed., Computer Aided Architectural Design Features, London:
Butterworths, 1986, particularly fig. 5.2.
66. Sherley Werner Morgan, Architectural Drawing, Perspective, Light and
Shadow, Rendering, New York, 1950, p.
Chapter 6
1. Vasari, as in I.2, note 1, vol.II, p.90.
2. Ibid., vol.I., p.233.
3. Ibid., vol.I, p.328; vol.II, pp.90-230; vol.III, pp.41, 55, 133; vol.IV, pp.60, 195.
4. Benedetto Dei, Cronaca Fiorentina dal 9 dicembre 1430 al 1480, Florence,
Archivio di stato, manoscritti no. 119, fol. 32v:
Florentia bella a 66 botteghe di speziali e a 84 botteghe di legnaiuoli di
tarssie e intagliatori.
Cf. his Memorie, Florence, Biblioteca Riccardiana, Cod. 1853, fol. 90r.
5. Vasari, as in I.2, note 1, vol.I, p.251.
6. Ibid., vol.I, p.308.
7. Ibid., vol.I, p.237.
8. Erich Auerbach, Mimesis, The Representation of Reality in Western Literature,
trans. Willard R. Trask, Princeton: Princeton University Press, 1945.
9. See, for instance, Hans Schüritz, Die Perspektive in der Kunst Albrecht Dürers,
Frankfurt: Heinrich Keller, 1919. Cf. Karl Rapke, Die Perspektive und Architektur
auf des Dürerschen Handzeichnungen, Strasbourg: J.H. Ed. Heitz, 1902.
310
10. Vasari, as in I.2, note 1, vol.I, pp.232-233.
11. Sir E. H. Gombrich, Means and Ends, as in chapter 1, note 30.
12. Cf. Franz Boas, Primitive Art, New York: Dover Publications, 1955. On the
problem of primitive mentality see: Ernst E. Baesch, Das Magische und das
Sch”ne. Zur Symbolik von Objekten und Handlungen, Stuttgart: FroomannHolzboog, 1983.
13. Sir E. H. Gombrich, The Sense of Order, London: Phaidon, 1979.
14. Cf. C. Van der Sleyen, Das alte Ägypten, Frankfurt: Verlag Ullstein, 1975, pl.
46, (Propyläen Kunstgeschichte, Bd. 15).
15. Sir E. H. Gombrich, Art and Illusion, Princeton: Princeton University Press,
1960, p.129.
16. Ibid., p. 131.
17. Cf. Heinrich Schäfer, Principles of Egyptian Art, tr. John Baines, Oxford:
Clarendon Press, 1974.
18. Pliny, Natural History, trans. H. Rackham, Cambridge, Mass: Harvard
University Press, vol. IX, 1968, pp. 306-311 (XXXV.65-66).
19. Ibid., vol. IX, 1968, pp. 176-177 (XXIV,XIX.65):
vulgoque dicebat ab illis factos quales essent homines, a se quales
viderentur esse.
20. One of the fundamental contributions of Sir Ernst Gombrich has been to
demonstrate that psychological projections continue to imbue art. See: Art and
Illusion. Princeton: Princeton University Press, 1960.
21. An image in the mind which is visual cannot be recorded or measured. It needs
a verbal description. Hence, although visual in the mind, it nonetheless needs a
verbal filter before it can be communicated.
22. Vasari, as in I.2, note 1, vol.I, p.209.
23. Auerbach, as in II.1, note 8.
24. Cf. Sir E. H. Gombrich, "Illusion and art," in: Illusion in Nature and Art, ed.
R.L. Gregory and E.H. Gombrich, London; Duckworth, 1973, pp. 193-243,
particularly pp. 230-231.
311
25. Michael Kubovy, The Psychology of Perspective and Renaissance Art,
Cambridge: Cambridge University Press, 1986, pp.52-64.
26. For an analysis see Marisa Dalai Emiliani, "Il ciclo del Foppa nella cappella
Portinari."
27. Alessandro Parronchi, Studi su la dolce prospettiva, as in I.2, note 6, pp.340348.
28. Alessandro Parronchi, Masaccio, Florence: Sadea Sansoni, 1966. His
reconstruction is reproduced in: L'opera completa di Masaccio, ed. Paolo Volponi,
Luciano Berti, Milano: Rizzoli, 1968, p.96.
29. Cf. Jean Seznec, The Survival of the Pagan Gods, trans. Barbara F. Sessions,
New York: Harper and Row, 1953.
30. For an analysis of the contents of these paintings, cf. S. J. Freedberg, Painting
in the High Renaissance in Rome and Florence, Cambridge, Mass.: Harvard
University Press, 1961, 2 vol.
31. Leonardo da Vinci, A 96r (BN 2038 16r, TPL 119, 1492):
Ti rispondo che tu debbi porre il primo piano col punto al'altezza de l'ochio de
riguardatori d'essa storia et in sul detto piano figura la prima storia grande e
poi diminuendo di mano in mano le figure e casamenti in su diverse colli e
pianure farai tutto il fornimento d'essa storia.
For another discussion of this passage see: Sir E. H. Gombrich, Means and
Ends, as in I.1, note 30, p. 10.
32. Gotthold Ephraim Lessing, Läokoon, oder über die Grenzen der Malerei und
Poesie, Stuttgart: Reclam, 1964, (271/71 a/b), p. 114:
Ich schliesse so. Wenn es wahr ist, dass die Malerei zu ihren
Nachahmungen ganz andere Mittel, oder Zeichen gebrauchet, als die
Poesie; jene nämlich Figuren und Farben in dem Raume, diese aber
artikulierte Töne in der Zeit; wenn unstreitig die Zeichen ein bequemes
Verhältnis zu dem Bezeichneten haben mussen: so können nebeneinander
geordnete Zeichen auch nur Gegenstände, die nebeneinander, oder deren
Teile nebeneinander existieren, aufeinanderfolgende Zeichen aber auch
nur Gegenstände ausdrucken, die aufeinander, oder deren Teile
aufeinander folgen.
312
33.
Ibid., p. 114:
Gegenstände, die nebeneinander oder deren Teile nebeneinander
existieren, heissen Körper. Folglich sind Körper mit ihren sichtbaren
Eigenschaften die eigentlichen Gegenstände der Malerei.
Gegenstände, die aufeinander, oder deren Teile aufeinander folgen,
heissen überhaupt Handlungen. Folglich sind Handlungen der eigentliche
Gegenstand der Poesie.
34.
Ibid., p. 127.
Denn wer sieht nicht, dass dem Dichter hier mehr an der
Auseinandersetzung der Teile, als an dem Ganzen gelegen gewesen? Er
will uns die Kennzeichen eines schönen Füllens, einer tüchtigen Kuh
zuzählen, um uns in den Stand zu setzen, nachdem wir deren mehr oder
wenigere antreffen, von der Gute der einen oder des andern urteilen zu
können; ob sich aber alle diese Kennzeichen in ein lebhaftes Bild leicht
zusammenfassen lassen, oder nicht, das könnte ihm sehr gleichgültig sein.
Ausser diesem Gebräuche sind die ausführlichen Gemälde körperlicher
Gegenstände, ohne den oben erwöhnten Homerischen Kunstgriff, das
Koexistierende derselben in ein wirkliches Sukzessives zu verwandeln,
jederzeit von den feinsten Richtern für ein frostiges Spielwerk erkannt
worden,zu welchem wenig oder gar kein Genie gehöret. Wenn der
poetische Stümper, sagt Horaz, nicht weiter kann, so fangt er an, einen
Hain, einen Altar, einen durch anmutige Fluren sich schlangelnden Bach,
einen rauschenden Strom, einen Regenbogen zu malen.
35. Ibid., p.129:
Es bleibt dabei: die Zeitfolge ist das Gebiete des Dichters, so wie der Raum
das Gebiete des Malers.
Zwei notwendig entfernte Zeitpunkte in ein und ebendasselbe Gemälde
bringen, so wie Fr. Mazzuoli den Raub der sabinischen Jungfrauen, und
derselben Aussohnung ihrer Ehemänner mit ihren Anverwandten; oder wie
Tizian die ganze Geschichte des verlornen Sohnes, sein liederliches Leben
und sein Elend und seine Reue: heisst ein Eingriff des Malers in das
Gebiete des Dichters, den der gute Geschmack nie billigen wird.
36. Leonardo da Vinci, Codex Urbinas 1270, fol. 123r (TPL 374): Delle otto [sic]
operazioni del huomo.
Fermezza, movimento, cuorso, ritto, apoggiato, a sedere, chinato,
ginocchioni, giaccente, sospeso, portare, esser portato, spingere, tirare,
batere, esser batuto, agravare e allegierire.
313
37. Andre Chastel, I centri del rinascimento Arte italiano 1460-1500, Milan:
Rizzoli, 1965, p.123.
38. Henry Heydenryk, The Art and History of Frames, London: Nicholas Vane,
1964, p.13.
39. Ibid., p.18.
40. For a good introduction to this theme see: Eve Borsook, Mural Painters of
Tuscany, London: Phaidon, 1960.
Chapter 7
1. Michael Kubovy, as in II.2, note 25, pp.127-149, has offered a psychological
explanation why the idea of a controlled viewpoint passed from favour.
2. Cf. Susan Koslow, "De wonderlijke perspectyfkas: an aspect of seventeenth
century dutch painting," Oud Holland, Amsterdam, vol. 82, no. 1-3, 1967, pp.3556.
3. For an analysis of these passages see the author's Leonardo da Vinci Studies I,
as in I.1, note 14, pp.165-169
4. Cf. J. Baltrusaitis, as in I.1, note 10, pp.54-60.
5. For an analysis of these effects see M. H. Pirenne, Optics, Painting and
Photography, Cambridge: Cambridge University Press, 1970, pp. 79-94.
6. Ibid., pp.155-157.
7. Cf. G. K. Loukomski, Jacques Vignole, sa vie, son oeuvre, Paris: A. Vincent et
Cie., 1927.
8. J. C. Shepherd and G. A. Jellicoe, Italian Gardens of the Renaissance, London:
Academy editions, p.25. Cf. Georges Gromort, Jardins d'Italie, Paris: A. Vincent,
1922. For these references, and for introducing me to the problem of perspective in
gardens I am much indebted to Professor C. Thacker (Reading).
9. Cf. Erwin Panofsky, "Die Skala Regia im Vatikan und die Kunstanschauungen
Berninis," Jahrbuch der Preussischen Kunstsammlungen, Berlin, Bd. 40, 1919,
pp.241-278.
10. Rocco Sinisgalli, Borromini a quattro dimensioni, as in Chapter 1, note 24.
314
11. For an introduction see: F. Crips, Mediaeval Gardens Flowery Medes and
Other Arrangements of Herbs, Flowers and Shrubs Grown in the Middle Ages...,
London: John Lane, 1924, 2 vol., Cf. New York: Hacker Books, 1966.
12. Ibid., vol. 2, fig. CLXXIII for an illustration.
13. Cf. A.R. Blumenthal, "Brunelleschi e il teatro del rinascimento," Bolletino del
centro internazionale di studi di architettura, Vicenza, vol. XVI, 1974, pp. 93-104,
fig. 37-50.
14. Cf. Mario Fabbri, Elvira Garbero Zorzi, Anna Maria Petrioli Tofani, Il luogo
teatrale a Firenze. Brunelleschi, Vasari, Buontalenti, Parigi, Florence: Electa,
1975. See also: Werner Oechslin, "The theatre of invention. Stage design and
architecture," Lotus International, Milan, vol. 17, 1977, pp. 66-77.
15. Cf. Ludovico Zorzi, Il teatro e la città, Turin: Einaudi, 1977, particularly,
pp.113 ff., and pl.76-80.
16. Salomon de Caus, Les raisons des forces mouvantes avec diverses machines
tant utiles que plaisentes ausquelles sont adjoints plusieurs desseings de grotes et
fontaines, Frankfurt: J. Norton, 1615. Cf. the work written by his son or nephew
cited below in II.4, note 43.
17. Cf. Loukomski, as in note 7, pl. XLIX-L.
18. Cf. note 12 above.
19. Cf. Patricia Rose, Wolf Huber Studies, New York: Garland Books, 1977,
particularly pl.190-192.
20. Cf. Ernest de Ganay, Les jardins de France et leur décor, Paris: Librairie
Larousse, 1949. See also: Alfred Marie, Jardins francais crées à la Renaissance,
Paris: Editions Vincent Fréal, 1955.
21. Olivier de Serres, Le théâtre d'agriculture et mesnage des champs, Paris:
Firmin Didot et Cie, p. 214:
notamment ceux que le Roi fait dresser en ses royales maisons de
Fontainebleau, de Saint-Germain-en-Laye, des Tuileries, de Monceaux, de
Blois, etc.... Ce ne peut vraiment etre sans émerveillement que l'on
contemple les herbes parlant en lettres, devises, chiffres, armoiries,
cadrans, les gestes des hommes et des betes, la disposition des édifices,
navires, bateaux et autres choses imit‚es en herbes et arbustes avec une
merveilleuse industrie et patience.
22. J.M. Morel, Théorie des jardins, Paris: Chez Pissot, 1776, pp.4-7:
315
Des que l'Architecte se fut emparé de la conduite des jardins, en dut
s'attendre que, confondant les principes des deux Arts (I) & trop
accoutumé aux formes régulieres, dont l'usage convient & s'adapte si bien
a ses productions, il chercheroit a lier par une mutuelle correspondance le
batiment, dont il fit l'objet principal, au Jardin qui ne lui parut que
l'accessoire. Entrainé par l'habitude de symmetriser les formes, de calculer
les espaces, il voulut assujettir la Nature a ses méthodiques combinaisons
& crut l'embellir; mais il la defigura. Il composa un Jardin comme une
maison; il le compartit en salles, en cabinets, en corridors; il en forma les
divisions avec des murs de charmilles percés de portes, de fenetres,
d'arcades, & leurs trumeaux furent chargés de tous les ornemens destinés
aux édifices.
Par une suite de cette fausse analogie, les Architectes donnerent a
ces pieces, ainsi qu'a celles de leurs batimens, des formes rondes, carrées,
octogones; ils les decorerent, comme un appartement, avec des vases, des
niches, des guaines; ils y logerent des statues, habitans insensibles bien
dignes d'un si triste séjour; ils les meublerent, comme des chambres, avec
des tapisseries de verdures, du treillage, des perspectives peintes, des lits,
des sieges de terre couverts de gazons; ils édifierent ainsi jusqu'a des salles
de théatre, des dortoirs, & imaginerent enfin le minutieux labyrinthe.
Toujours Architectes, quand il falloit etre Jardiniers, (1) ils
taillerent un arbre, comme une pierre, en voute, en cube, en pyramide, ils
asservirent a leurs contours jusqu'a l'eau fi mobile, dont la marche
irreguliere & libre fait tout le charme.
23.
Olivier de Serres, as in note 21, p.218:
Il est notable qu'a regarder de loin les compartiments, pour l'assiette du
jardin, il convient d'en faire les rang‚es plus loin l'une de l'autre que pour
les rang‚es que l'on voit de pres: on les rapprochera d'autant plus que la
vue en sera prochaine, pour la bienséance, la chose regardée se
rapetissant a mesure de son éloignement, par la raison de la perspective.
Par cette meme raison, les rangees du compartiment s'entrecouvrent quand
on les regarde du plan du jardin, en se promenant par les allees, parce
que, le point d'ou l'on regarde étant bas, la vue est occupée par les
premieres rangées d'herbe qu'elle rencontre, qui ne permettent pas d'aller
jusqu'aux autres. Pour cette raison il est a souhaiter que les jardins soient
regardés de haut en bas, soit des batiments voisins, soit de terrasses
rehauss‚es a l'entour du parterre, ainsi que, par artifice, le Roi a fait faire
aux Tuileries en sa belle allée de muriers, et a Saint-Germain-en-Laye,
aussi ou la Nature a beaucoup fourni de sien par l'assiette du lieu, tout a
fait favorable.
24. Claude Mollet, Théâtre des plan[ts] et jardinages, Manuscript, Munich,
Bayerische Staatsbibliothek, Cod. Gallici 496, cited in: E. de Ganay, as in note 20,
p.59:
316
Les allées, que vous ferez planter des plus larges, sont les plus nobles;
toutefois, il faut les proportionner selon la longueur que vous leur pouvez
donner, comme celles qui auront cent cinquante toises de long, leur faut
donner cinz toises de large, parce que la Perspective estrecit; et aussi le
Plan[t] des Palissades s'espaissit de chacun cote; de sorte que si vous
plantez vos Allées de cinq toises de large, avec le temps elles ne se
trouveront que de quatre toises et demie, ainsi des autres Allées.
25. Andre Mollet, Le jardin de plaisir, postface de Michel Conan, Paris: Editions
du Moniteur, 1981, p.31:
il est a noter premierement que les parterres les plus éloignés de la vue
doivent etre mis en plus grand volume que ceux qui en sont plus proches,
afin de paraitre plus agréables a l'oeil et mieux proportionnés.
26. Cf. Kenneth Woodbridge, Princely Gardens, London: Thames and Hudson,
1981, p. 254.
27. Antoine Joseph Dezallier d'Argenville, La théorie et pratique du jardinage,
Paris: P. J. Mariette, 1747, 3 Kap., Taf. 3, Cf. Ingrid Dennerlein, Die Gartenkunst
der Régence und des Rokoko in Frankreich, Worms: Werner'sche
Verlagsgesellschaft, 1981, p. 73 ff.
28. For illustrations of this stage see: Karl Meyer, Königliche Gärten, Hanover:
Fackelträger-Verlag, 1966.
29. Cf. Vitruvius, Morgan ed., as in I.1, note 2, p.211 and Fensterbusch ed., p.332:
ambulationibus vero propter spatia longitudinis varietatibus topiorum
ornarent ab certis locorum proprietatibus imagines exprimentes; pinguntur
enim portus, promunturia, litora, flumina, fontes, euripi, fana, luci, montes,
pecora, pastores caeteraque, quae sunt eorum similibus rationibus ab
rerum natura procreata; nonnulli locis item signorum megalographiam
habentes: deorum simulacra seu fabularum dispositas explicationes, non
minus troianas pugnas seu Ulixis errationes per topia.
30. For a discussion of this, with a reconstruction of the garden at Cythera see
Clemens Alexander Wimmer, Geschichte der Gartentheorie, Darmstadt:
Wissenschaftliche Buchgesellschaft, 1989, pp.34-47.
31. Erasmus, "The godly feast" in: Ten Colloquies, trans. Craig R. Thompson,
Indianapolis: Bobbs Merrill, 1967, pp.136-137.
32. Fra D. Francesco Bisagno, Trattato della pittura, Venice: Giunti, 1642,
pp.198-200:
317
Che sorti di pitture vadano dipinti nei fonti, ne'giardini, nelle camere, e
altri luoghi di piacere; e negli strumenti musicali. Cap.XXXI.
Possono accomodarvisi con non minor vaghezza in luogo di favole
prospettive diverse, le quali faccino allungare i portici, e le pareti del
Giardino, & oltre le colonne negli intervalli, paesi cosi accompagnati, che
paiano seguire il naturale, fingendovi alcune historie delle dette, che
convengono a tali luoghi, come per essempio Apolline, che dietro l'onde di
Tessalia segue l'amato Alloro, o Cefalo, che per tempo andando, fa di se
inamorare d'Aurora.
33. A. Mollet, as in note 25, p.31:
Aux extrémités de ces allées, on posera de belles perspectives peintes sur
toile, afin de les pouvoir oter aux injures du temps quand on voudra.
34.
Cited in E. de Ganay, as in note 24, p.73:
L'enfoncement offre une perspective dont le ciel est peint avec des couleurs
si naturelles qu'on assure que des oiseaux s'y sont trompés et que, croyant
voler en plein air, ils s'y sont tués.
35. Gartendirektor Zeyher und G. Roemer, Beschreibung der Garten Anlagen zu
Schwetzingen, Mannheim: Im Verlage der Benderischen Buchhandlung, 1809,
pp.32-33:
Ein dunkler Gang liegt vor uns, und in weiter Entfernung erscheint eine
freundliche Landschaft, breitet sich vor uns aus, die so täuschend nach
einer Zeichnung des Hofmahlers Ferdinand Kobell von einem gemeinen
Tuncher in Mannheim, Namens Truckenmüller, auf eine ovale Wand
gemahlt ist, dass man bey dem ersten Blicke wirklich glaubt, es entfalte
sich eine natürliche weite Gegend. Diese schöne Wirkung wird eines Theils
dadurch hervorgebracht, dass ein ganz beschatteter, drey hundert und
siebenzig Schuh langer Gang dahin führt, theils dass die Landschaft auf ein
Oval gemahlt ist, und das man nahe vor der Mahlerey an einer kleinen
durch einen künstlichen Felsen gebrochenen Grotte steht, in derem Becken
das von der Decke und den Wanden rinnende Wasser sich sammelt.
I am grateful to Professor Deirdre Vincent (Toronto) for kindly translating
this passage.
36. Cf. A. Rommel, Die Enstehung des klassischen französischen Gartens in
Spiegel der Sprache, Berlin: Akademie Verlag, 1954, p.36:
318
perspective f.: peinture qui représente des jardins, des batiments en
éloignement, et qu'on met au bout d'une gallerie ou d'une allée de jardin
pour tromper agréablement la vue.
37. Olivier de Serres, as in note 21, p.217:
Et afin que ces distinctions se voient avec plus de contentement, des terres
de diverses couleurs y sont ajoutées, dont on couvre le fonds de l'entredeux des rang‚es des herbes, auxquelles, par ce moyen, est donn‚ un grand
lustre, tout le compartiment du parterre ressemblant à un tableau d'exquise
peinture sorti di la main d'un bon maitre.
38.
Cited in Wimmer, as in note 30, pp.78-79:
De Serres stellt auch die für den Rationalismus so typische Verbindung zu
den andren Künsten, her, wenn er das Entwerfes eines Parterres mit der
Tätigkeit eines Malers vergleicht und von den Gärtnern, denen er keine
ausreichende Erfindungskraft zutraut, verlangt, dass sie sich nach den
Entwürfen von Malern (hommes entendues en la pourtraicture) richten
(II.5.96).
39. William Shenstone, "Unconnected thoughts on gardening," in: Ibid., The
Works in Verse and Prose of William Shenstone, Edinburgh: Printed for Alexander
Donaldson, 1765, vol. 2, pp.104-105.
40. Friedrich Kasimir Medikus, Beiträge zur schönen Gartenkunst, Mannheim:
Hof und akademische Buchhandlung, 1783, pp.290-291:
So wie der Landschaftmaler durch Zusammenrückung oder durch
Verbindung einzelner Natursch”nheiten einen unerschöpflichen Stoff zu
den schönsten Gemälden hat, die er mit erfinderischen Geiste nuzt und
ordnet: so muss hier der Gartenkünstler ebenfalls erst diese Schönheiten
der Natur studieren, und sich denselben vertraut machen, ehe er es wagen
sollte, dergleichen natürliche Gemälde in seinen zu erbauenden Garten
aufzustellen, um so mehr, da man seine Arbeiten nicht so leicht hinweg zu
räumen vermag, wie man das schlechte Gemälde eines Landschaftmalers
aus der Galerie eines Besitzers abhängen kann.
41. D.C. Seitz, Whistler Stories, New York: Harper and Brothers, 1913, p. 9. Cited
in: The Oxford Dictionary of Quotations, London: Oxford University Press, 1941,
p.566.
42. See Jules Guiffrey, Andre Le Nostre, Paris: Henri Laurens Editeur, 1913 with
an English translation Lewes: Sussex Book Guild 1986, and the important study by
F. Hamilton Hazlehurst, Gardens of Illusion. The Genius of André le Nostre,
Nashville: Vanderbilt University Press, 1980.
319
43. See Gerhard Gerkens, Das fürstliche Lustschloss Salzdahlum und sein Erbauer
Herzog Anton Ulrich von Braunschweig-Wolfenbüttel, Braunschweig: Selbstverlag
des Braunschweigischen Geschichtsverreins (Quellen und Forschungen zur
Braunschweigischen Geschichte, Band 22).
44. For a good survey see Sacheverell Sitwell, Great Houses of Europe, London:
Weidenfeld and Nicholson, 1961.
45. J. Dennis, The Landscape Gardener. Comprising the History and Principles of
Tasteful Horticulture, London: James Ridgway, 1835, p.86.
46. Shenstone, as in note 39, p.105.
47. For an introduction to the history of English gardens see: Henry Avray
Tipping, English Gardens, London: Country Life, 1925; Laurence Fleming, The
English Garden, London: Michael Joseph, 1979. Cf. British and American
Gardens in the Eighteenth Century: Eighteen Illustrated Essays on Garden
History, ed. R.P. Maccubbin and Peter Martin, Williamsburg: Colonial
Williamsburg Foundation, 1984.
48. Sir William Chambers, A Dissertation on Oriental Gardening, London: Printed
by W. Griffin, 1772, pp. iv-v. For examples of supposed Chinese gardens see: Paul
Decker, Chinese Architecture, Civil and Ornamental, London: Printed for the
author, 1759, pp.249-252 and G. L. Le Rouge, Plan général des nouveaux jardins
à la mode, Paris, 1776-1786, particularly, vol.2, pp.11, 14-17,19.
49. Chambers,Ibid., p.20.
50. Ibid., pp.41-42.
51. [Thomas Whately], Observations on Modern Gardening Illustrated by
Descriptions, London: T. Payne, 1770, pp.139-140.
52. Anonymous, L'art de former les jardins modernes ou l'art des jardins anglois.
Traduit de l'Anglois. A quoi le traducteur a ajouté un discours préliminaire sur
l'origine de l'art..., Paris: Charles-Antoine Jombert, 1771, pp.ii-iij:
Sans prétendre que leurs jardins soient exempts de défauts, je crois que
tous ceux qui les ont vues, et qui sentent combien la noble simplicité est
supérieure à tous les rafinemens symmétriques de l'art, leur donnent
préférence sur les notres.
For another assessment of the effects of English gardens on the French
tradition see: N. Vergnaud, (brother of Armand Dénis, the influential author on
320
perspective), L'art de créer les jardins, Paris: Roret, 1835, particularly pp. 34, 5961, 67-69.
53. Ibid., particularly pp. xiii-xiv, xx-xxxi.
54. Ibid., p.344:
Les objets animés sont un genre de beauté si interessant & si particulier
aux jardins Anglois, qu'il seroit a souhaiter que l'auteur leur eut consacré
une section; il eu rendu par-la, ce me semble, son ouvrage plus complet.
Toutes les especes d'animaux ne sont pas propres a tout perspective, &
quoique tout le monde sache que les chevres animent une scene de rochers,
& que des moutons répandus dans le fond d'un vallon, forment un tableau
champetre des plus agréables; il est encore, dans cette partie de l'art, qui
regarde la manière de distribuer les animaux, des nuances fines, connues
des Anglois, & que l'auteur nous eut parfaitement expliquees a sa maniere
l'eut voulu.
55. Anonymous, Planting and Ornamental Gardening; a Practical Treatise,
London: Printed for J. Dodsley, 1785, p.559. Cf. pp.572-573.
56. Ibid., p.604.
57. Ercole Silva, Dell'arte dei giardini inglesi, Milan: Stamperia e fonderia al
genio topografico, 1801, pp.62-63:
Avra cura l'esperto giardiniere, che la distribuzione de suoi verdi ottenga
l'effetto della prospettiva del colore, detta da pittori prospettiva aerea. Se
avra un ampio locale, ove tutto abbandonare all effetto, e all'interposizione
dell'aria l'allontanamento degli oggetti, allora sara in minor bisogno di
attenersi al rigore di questa legge: ma se avra un picciolo spazio, e bramo
di far sfuggire rapidadamente il suo bosco, il suo viale, i suoi cespugli da
un tale determinato punto di veduta, dovra esser sollecito di collocare
nell'avanti gli alberi, e le piante, che abbiano il verde piu cupo, le foglie
piu grandi, e dettagliate, e i tronchi dalla scorza piu rugosa, e nericcia,
mettendo al confine del sue orizzonte i verdi piu pollidi, i tranche piu lisci,
le foglie biancastre, che tanto brillante effetto producono dominate dal
sole. Cosi otterrà il maraviglioso effetto d'ingrandire il luogo per la
degradazione de'colori, appunto colle medesime regole, che la prospettiva
ha stabilite per il pittore paesista.
Cf. pp. 21, 26-27, 108-113, 175-180.
58. Humphrey Repton, Observations on the Theory and Practice of Landscape
Gardening, London: T. Bensley, 1805, p.6.
321
59. Ibid, “Chapter II. Optics or vision - At what distance objects appear largest.
Axis of vision - Quantity at field of vision - Ground apparently altered by situation
of observer.”
60. Ibid., pp.214-222.
61. Dennis, as in note 45, p.15.
62. Ibid., p. 87.
63. Is it a coincidence that Sir Ernst Gombrich, who has spent over forty years in
England, should emphasize the occlusion aspect of perspective? See, for instance,
Sir E. H. Gombrich, "Mirror and map: theories of pictorial representation,"
Philosophical transactions of the Royal Society of London, B. Biological Sciences,
London, vol. 270, no. 903, 1975, pp.119-149.
64. For a study of this phenomenon see: Richard Haas, An Architecture of Illusion,
New York: Rizzoli, 1981.
Chapter 8
1. Aristotle, De poetica, trans. Ingram Bywnter, 1457b 5-10 in: The Works of
Aristotle, trans. W.D. Ross, Oxford: Clarendon Press, 1946, vol. XI:
Metaphor consists in giving the thing a name that belongs to something
else; the transference being either from genus to species, or from species to
species, or on grounds of analogy.
2. Ibid., 1457b 10ff:
That from species to genus in 'Truly ten thousand good deeds has Ulysses
wrought,' where 'ten thousand,' which is a particular large number, is put in
place of the generic ' a large number.'
Cf. 1461a 17ff.:
the word aãavtes, all, is metaphorically put for 'many', since 'all' is a
species of 'many'.
3. Ibid., 1461b 10ff.:
For the purposes of poetry a convincing impossibility is preferable to an
unconvincing possibility.
Cf. Aristotle, Rhetorica, 1405a 9ff.:
322
Metaphors like epithets, must be fitting, which means that they must fairly
correspond to the thing signified: failing this, their inappropriateness will
be conspicuous.
It is striking that Aristotle treats similes and metaphors as interchangeable. See
Rhetorica, 1407 10ff.:
All these ideas may be expressed either as similes or as metaphors; those
which succeed as metaphors will obviously do well as similes and similes,
with the explanation omitted will appear as metaphors.
4. For an introduction to this complex topic see Rensselaer E. Lee, Ut pictura
poesis. The Humanistic Theory of Painting, New York: W.W. Norton & Co., 1967.
5. E. Auerbach, as in II.1, note 8.
6. For another analysis of this problem see W.M. Ivins, Jr., Art and Geometry,
Cambridge, Mass.: Harvard University Press, 1946.
7. Aristotle, as in note 1, 1460b 7-10.
8. Vitruvius, ed. Morgan, as in I.1, note 2, p.212; ed. Fensterbusch, p.334:
Neque enim picturae probari debent, quae non sunt similes veritati, nec, si
factae sunt elegantes ab arte, ideo de his statim debet 'recte' iudicari, nisi
argumentationes certas rationes habuerint sine offensionibus explicatas.
9. Cf. Aristotle, De poetica, as i note 1, 1458a 20 ff.:
On the other hand the Diction becomes distinguished and non-prosaic by
the use of unfamiliar terms, i.e., strange words, metaphors, lengthened
forms and everything that deviates from the ordinary modes of speech."
Accordingly in the Rhetorica, 1404, 33ff., Aristotle mentions that "two classes
of terms, the proper or regular and the metaphorical - these and no others - are
used by everybody in conversation." For a perceptive study of the historical
dimensions of these problems, why metaphor was a frill in Aristotle and later
became significant see: Wilhelm Köller, Semiotik und Metapher. Untersuchungen
zur grammatischen Struktur and Kommunikativen Funktion von Metaphera.
Stuttgart: J.B. Metzler, 1975 (Studien zur allgemeinen und vergleichenden
Literaturwissenschaft, Band 10).
10. The Comedy of Dante Alighieri the Florentine. Cantica II. Purgatory, trans.
Dorothy L. Sayers, Harmondsworth: Penguin Books, 1955, p.144 (Canto X. 37-
323
45). I am grateful to Professor Eva Engel Holland for drawing my attention to this
passage.
11. Ibid., p. 145 (Canto X.62).
12. Ibid., (Canto X.73).
13. Ibid., (Canto X.75).
14. Cf. Dennis Green (1982).
15. For a brief introduction to these problems see The Comedy of Dante
Alighieri...Cantica III. Paradise, trans. Dorothy L. Sayers and Barbara Reynolds,
Harmondsworth: Penguin, 1962, pp. 44-49. Cf. Northrop Frye, Anatomy of
Criticism, Princeton: Princeton University Press, 1957.
16. Metaphor has, in the past decade, become one of the most explosive topics of
study particularly among psychologists and semioticians. See, for instance: G.
Lackoff and M. Johnson, Metaphors We Live By, Chicago: University of Chicago
Press, 1980 and Marcel Danesi, ed., Metaphor, Communication and Cognition,
Toronto: Humanities Publishing Services, 1987-1988 (Monograph series of the
Toronto Semiotik Circle, No. 2).
A classic analysis of the problem remains Karl Bühler's chapter on "Die
sprachliche Metapher" in his Sprachtheorie. Die Darstellungsfunktion der
Sprache, Stuttgart: Gustav Fischer Verlags, 1965, pp. 342-356. For an idea of the
range of disciplines now involved in these discussions see: Metaphor and Thought,
ed. Andrew Ortony, Cambridge: Cambridge University Press, 1979. Philosophers
have shown increasing interest in the problem as, for instance, Max Black, Models
and Metaphors. Studies in Language and Philosophy, Ithaca: Cornell University
Press, 1962.
17. Philosophers have recently become interested in these connections between
philosophy, perspective and positive concepts of illusion. See: Michael Sukale,
"Denken und Anschauen" in his: Sprachlogik, Frankfurt: Peter Lang, 1988, pp.
163-182, (Studia philosophica et historica, 8).
18. The above citations are from the Oxford English Dictionary under metaphor.
19. For a study of this phenomenon see Dieter Arendt, Eulenspiegel-ein
Narrenspiegel der Geselleschaft, Stuttgart: Klett-Cotta, 1970, particularly 76-83.
20. Cf. Oscar Thulin, Cranach Altäre der Reformation, Berlin: Evangelische
Verlagsanstalt, 1955, particularly pp.97-98, 116, 118.
21. This is the subject of a penetrating study by Paul Böckmann, "Der dramatische
Perspektivismus in der deutschen Shakespearedeutung des 18. Jahrhunderts," in:
324
Ibid., Formensprache. Studien zur Literärästhetik und Dichtungs-interpretation,
Hamburg: Hoffman und Campe Verlag, 1966, pp. 45-97.
22. Percy Lubbock, The Craft of Fiction, London: J. Cape 1921.
23. Ortega y Gasset, Perspectiva y verdad, Madrid: Revista de occidente, 1966.
24. Claudio Guillen, "On the concept and metaphor of perspective," in C. Guillen,
Literature as System. Essays Toward the Theory of Literary History, Princeton:
Princeton University Press, 1971, pp.283-371.
25. E. g. Robert Weimann, "Strukturen epischer Weltaneigung in der Renaissance.
Zu Fragen des Menschenbildes, Der Erzählperspektive und des Fiktion Begriffs,"
Synthesis, Bucharest, vol. III, 1976, pp.47-63. This theme has become of enormous
importance. For a more recent study see: Jaap Lintvelt, Essai de typologie
narrative. Le point de vue, Paris: Librairie Jose Corti, 1981. A fuller analysis of
these trends follows in volume three: Literature on Perspective.
26. Cf. Lars Gustafsson, Sprache und Lüge. Frankfurt: Fischer Taschenbuchverlag,
1982.
27. Cf. Paul Robert, Le Robert, Dictionnaire alphabétique de la langue francaise,
Paris: Le Robert, vol. 8, p.918. Cf. p.919 where spectaculaire is defined as qui
parle aux yeux et a l'imagination. Cf. vol. 9, p.276.
28. For a detailed analysis of these debates see Hubert Damisch, Les origines de la
perspective, Paris: Flammarion, 1987, pp.157 ff.
29. See, for instance, De wereld is een speeltoneel, ed. M.C.A. Van der Heijden,
Utrecht: Prisma, 1968 (Spectrum van de nederlandse letterkunde, 13).
30. On the question of trompe l'oeil see, for instance, Miriam Milman, Trompe
L'Oeil Painting, New York: Skira Rizzoli, 1983 and her Trompe L'Oeil Painted
Architecture, New York: Skira Rizzoli, 1986 for excellent photographs. For a more
philosophical treatment of these problems see: Sven Sandström, Levels of
Unreality, Uppsala: Almqvist and Wiksell, 1963. (Figura. Uppsala series in the
history of art, New series, 4). The positive dimensions of trompe l'oeil have been
the subject of a number of recent exhibitions such as: Alfred Frankenstein, The
Reality of Appearance. The Trompe L’Oeil Tradition in American Painting, New
York: New York Graphics Society Limited, 1970. (Exhibition organized by
University art museum, Berkeley); Alberto Veca, Inganno e realtà. Trompe l'oeil
in Europa XVI-XVII sec., Bergamo: Galleria Lorenzelli, 1980; Musée-Château
d'Annecy, Trompe l'oeil, Décembre 1982- février 1983. Cf. the special issue of Du
on "Trompe l'oeil-Augentäuschung", Zürich, n.472, June 1980.
325
31. There has, in fact, been quite an amount of controversy on this. Cf. The
Complete Paintings of Giotto, Introd. A. Martindale, Notes by Edi Baccheschi,
New York: Harry N. Abrams, 1966.
32. Guido Ludovico Luzzatto, L'arte di Giotto, Bologna: N. Zanichelli, 1927
[cover: 1928].
33. The relevant passages have been analyzed in the author's Leonardo Studies I,
as in chapter 1, note 14, pp.336-337
34. Cf. Heydenryk, as in chapter 2, note 38, p. 55.
35. The Complete Essays of Montaigne, Trans. Donald M. Frame, Stanford:
Stanford University Press, 1965, p.135.
36. Lina Bolzoni, L'universo dei poemi possibili. Studi su Francesco da Cherso,
Rome: Bulzoni, 1980.
37. This topic has recently been studied by James A. Welu, "The sources and
development of cartographic ornamentation in the Netherlands", in: Art and
Cartography, ed. David Woodward, Chicago: University of Chicago Press, 1987,
pp.147-173.
38. For a standard introduction to mannerism see John Shearman, Mannerism,
Harmondsworth: Penguin, 1967.
39. Jacques Androuet Du Cerceau, Quinque et viginti exempla arcuum partim a me
inventa, partim ex veterum sumpta monumentis tum Romae, tum alibi etiam num
extantibus ut inscriptio sua cuiusque arcus indicabit, Paris: Benoist Prevost, 1549.
40. Vincenzo Scamozzi, Discorsi sopra l'antichità di Roma, Venice: Francesco
Ziletti, 1583, p 27:
Potria essere che questa tavola fusse disegnata da qualche cosa antica e
ch'io non havessi memoria di haverla veduta, ma molto piu puo stare che
ella sia fatta per un bel capriccio perche chi non si stancherebbe a
disegnare a punto ogni cosa dell antico, solo colui che non sa fare niuna
bella inventione.
41. For a standard work on this painter see Hans Mielke, Hans Vredeman de Vries,
Verzeichnis der Stichwerke und Beschreibung seines Stils, Phil. Diss., Berlin,
1967.
42. Cf. Comune di Gorizia, Capricci venezianni del settecento, ed. Dario Succi,
Turin: Umberto Allemandi & C., 1988. (Castello di Gorizia - Giugnio-settembre
1988). Cf. William L. Barcham, The Imaginary View Scenes of Antonio Canaletto,
326
New York: Garland, 1977. See also the fundamental work of Corboz, as in
chapter 2, note 8. Professor Corboz' magnum opus on the history of the temple of
Solomon (in preparation) will add many new insights into this very complex story.
For further discussion of architecture and the imagination see: Giuliano
Briganti, Les peintres de vedute, Paris: Electa France, 1971; Architettura e utopia
nella Venezia nel cinquecento, Venezia, Palazzo Ducale, luglio-ottobre, 1980,
Milan: Electa; Lionello Puppi, Le Venezie possibili. Da Palladio a Corbusier,
Milan: Electa, 1985 and La città e l'immaginario, ed. Donattella Mazzoleni, Rome:
Officina Edizioni, 1985.
43. As mentioned earlier, Salomon de Caus later went to France and to England,
where he became tutor to Henry Prince of Wales in 1608. From 1611-1613 he
worked on the south front of Wilton. He left a son or a nephew, Isaac de Caus,
who worked on the gardens at Wilton and was the author of a: Nouvelle invention
de lever l'eau plus hault que la source avec quelques machines mouvantes par le
moyen de l'eaux et un discours de la conduite d'icelle, (1644). See, Dictionary of
National Biography and Biographie universelle under De Caus. Cf. Lauro
Magnani, ed. Tra magia, scienza e meraviglia, Le grotte artificiali dei giardini
genovesi nei secoli XVI e XVII, Genoa: Sagep Editrice, 1984. See also: Marcello
Fagiolo, Natura e artificio. L'ordine rustico, le fontane, gli automati nella cultura
del manierismo europeo, Rome: Officina Edizioni, 1979.
44. Cf. P‚relle, Les places, ports, fontaines, eglises et maisons de Paris, Paris:
Langlois, c.1680. There is a copy in the Bibliothèque Nationale in Paris.
45. J. H. Lambert, "Mémoire sur la partie photométrique de l'art du peintre,"
Mémoires de Berlin, Berlin, vol. 24, 1768, pp.80-108.
46. Hermann von Helmholtz, Optisches über Malerei, in: Populäre
wissenschaftliche Vorträge, Braunschweig: Vieweg und Sohn, 1871-1873.
47. Ernst Brücke, Bruchstücke aus der Theorie der bildenden Künste, Leipzig: F.
A. Brockhaus, 1877. Brücke was Professor of Physiology in Vienna and also
translated Helmholtz's work, as in note 46, into French as: Principes scientifiques
des beaux arts, Paris, 1878.
48. E. g. Gustav Theodor Fechner, Vorschule der Aesthetik, Leipzig: Breitkopf und
Härtel, 1876.
49. Cf. Augustine, The City of God, Harmondsworth: Penguin, 1972, pp. 168-169
(Bk. IV.27).
50. On the special role of the Bible in western culture see: Northrop Frye, The
Great Code. The Bible and Literature, Toronto: Academic Press, 1982.
327
51. On this difficult problem see an important study by Brian Stock, The
Implications of Literacy. Written Language and Models of Interpretation in the
Eleventh and Twelfth centuries, Princeton: Princeton University Press, 1983. On
the history of printing see: Elizabeth L. Eisenstein, The Printing Press as an Agent
of Change, Cambridge: Cambridge University Press, 1979.
52. Modern art has many examples of paintings on the walls of rooms in paintings,
which function as background statements. With respect to Dali's case in particular
see his: Le mythe tragique de l'Angelus de Millet. Interprétation paranoiaquecritique, Paris: Jean Jacques Pauvert, 1963.
53. Detailed study of this complex topic has yet to occur. For two pioneering
explorations of the problem see: Wolfgang Kemp, Foto-Essays zur Geschichte und
Theorie der Fotografie, Munich: Schirmer Mosel, 1978, particularly pp. 51-101,
and Kirk Varnedoe, "The artifice of candour, photography, impressionism and
photography reconsidered," Art in America, New York, vol. 66, January 1980,
pp.66-78.
54. Cf. Sir E. H. Gombrich, "Botticelli's mythologies" in his: Symbolic Images,
London: Phaidon, pp.31-78.
55. Salvatore Settis, La Tempesta interpretata. Giorgione, i commitenti, il
soggetto, Turin: G. Einaudi, 1978.
56. Erwin Panofsky, Studies in Iconology. Humanistic Themes in the Art of the
Renaissance, New York: Oxford University Press, 1939, pp.86-91. (Mary Flexner
Lectures, 1937).
57. For examples of these artists see: H. H. Arnason, A History of Modern Art,
London: Thames and Hudson, 1977 etc., pp. 422-423, 427-431: (re: precisionists);
613-645 (re: pop art); 699-702 (re: new and photo realism). The references to
Arnason are intended to provide readers with handy examples of three movements,
and introduce them to the subject. No attempt is made here to give a serious
bibliography.
58. J. Baltrusaitis, as in I.1, note 10.
59. Cf. Arnason, as in note 57, pp. 73-74.
60. Albert Gleizes, Du cubisme et des moyens de le comprendre, Paris: Editions
'La Cible', 1921, p.47:
Au début, la charpente créée sur les principes perspectifs, était robuste,
mais elle fut renversée par les affolés de réalisme et ce fut
l'impressionnisme, qui se lanca éperduement sur les inconsistances
atmosphériques.
328
61. Ibid., pp.26-27:
Si l'artiste, dont la spécialité est de peindre des natures mortes
académiquement, renoncait tout à coup à ses sujets favoris et se
passionnait pour des sujets composés de briques, de cylindres et de
planchettes, il les peindrait avec la perspective optique et l'éclairage
conventionnel....
Beaucoup de tableaux cubistes ne sont que le produit de cette substitution.
62. Ibid., pp.18-19:
Prétendre l'investir d'une troisième dimension, c'est vouloir la dénaturer
dans son essence meme:
Le résultat obtenu ne devient que l'imitation trompe-l'oeil de notre réalité‚
matérielle à trois dimensions, par la superchérie des perspectives linéaires
et celle des conventions d'éclairage.
For a more vehement theoretical rejection of perspective see: Oeuvres
complètes de Guillaume Apollinaire, ed. Michel Décaudin, Paris: André‚ Balland
et Jacques Lecat, 1963, particularly pp.20-21, 24-25,42,47, 274-275,286-287, 432433.
63. Ibid., pp.23:
la peinture n'est donc pas une imitation d'objets. La réalité du monde
extérieur lui sert de départ, mais elle la dépouille de cette réalité pour
toucher l'esprit.
64. Cf. Arnason, as in note 57, pp.221-240, 323-330, 591-598.
65. Ibid., pp.375-76.
66. Ibid., pp.370-371, 389-391.
67. One of the great collections of these books is to be found at the Herzog August
Bibliothek at Wolfenbüttel. Professor Harriett Watts is presently engaged in a
study thereof.
68. Cf. Abraham Horodisch, Picasso als Buchkünstler, Frankfurt: Gesellschaft der
Bibliophilen, 1957.
69. Cf. Arnason, as in note 57, pp.507-508, 521-523, 652-653, 678-679.
70. Ibid., pp.78-80.
329
71. Ibid., p.290.
72. Ibid., pp.292-306.
73. Ibid., pp.219, 307-316, 395-396.
74. Ibid., pp.348-409.
75. Ibid., pp.658 ff., 703-706.
76. Cf. William Kurelek, William Kurelek's Vision of Canada, Winnipeg: Hurtig,
1980.
77. Arnason, as in note 57, p.567.
78. Cf. Christopher Grey, "Cézanne's use of perspective," College Art Journal,
New York, vol.19, no. 1, Fall 1959, pp.54-64.
79. See John Rewald, "Van Gogh vs. nature: did van Gogh of the camera lie?", Art
News, New York, vol.41, 1942, pp.8-11. Cf. Patrick Heelan, Space-Perception and
the Philosophy of Science, Berkeley: University of California Press, 1983, pp.114128.
80. Cf. Hermann von Helmholtz, Helmholtz's Treatise on Physiological Optics,
trans. James P.C. Southall, New York: Dover Publications, 1962, vol.3, p.181; F.
Hillebrand, "Theorie der scheinbaren Grösse bei binokularen Sehen,”
Abhandlungen der Akademie, der Wissenschaften zu Wien, Mathematischnaturwissenschaftliche Klasse, Vienna, Bd. 72, 1902; A.E. Ames, and C.A.
Proctor, "Dioptrics of the Eye," Journal of the Optical Society of America,
Rochester, Vol.5, 1921, pp.22-84. R. K. Luneburg, Mathematical Analysis of
Binocular Vision, Hanover: Dartmouth Eye Institute, 1947.
81. Guido Hauck, Die subjektive Perspektive und die horizontalen Curvaturen des
dorischen Styls, Stuttgart: Conrad Wittwer, 1879.
82. Erwin Panofsky, "Die Perspektive als symbolische Form," as in I.2, note 27.
83. Cf. Robert Hansen, "This curving world: hyperbolic linear perspective,"
Journal of Aesthetics and Art Criticism, Baltimore, vol.32, no. 2, winter 1973,
pp.148-161. Cf. Hansen's introductory commentary to his translation of Albert
Flocon and André Barre, Curvilinear Space. From Visual Space to Constructed
Image, Berkeley: University of California Press, 1987.
84. M. H. Pirenne, "The scientific basis of Leonardo da Vinci's theory of
perspective," British Journal for the Philosophy of Science, London, vol.3, 1952,
pp.169-185.
330
85. Dick Termes, Spherical Thinking, Spearfish, 1982.
86. Philippe Comar et Nöel Blotti, Stenopé. La représentation de l'espace, Paris:
Cité des sciences et de l'industrie (1987).
87. In: Marcia Clark, ed., The World is Round. Contemporary Panoramas, New
York: The Hudson River Museum, 1987, p.31.
88. Ibid., p.43.
89. Ibid., pp.43, 51, 35.
90. Ibid., pp.59, 27, 45.
91. Ibid., p.8.
92. Ibid., p.35.
93. Fritz Novotny, Cézanne und das Ende der wissenschaftliche Perspektive,
Vienna: Schroll, 1938.
94. Cf. Suzi Gablik, Progress in Art, London: Thames and Hudson, 1976.
95. Cf. Sidney J. Blatt, in collaboration with Ethel Blatt, Continuity and Change in
Art: the Development of Modes of Representation, Hillsdale: Lawrence Erlbaum,
1984. While disagreeing strongly with my colleagues and friends, I find their
book very stimulating. They document why the conceptual approach has gained
such a fascination among psychologists. I, personally, believe that perception
remains both interesting and important. For an analysis of problems with their
approach see the author’s Literature of Perspective, Chapter 1.
96. Erwin Panofsky, "Die Perspektive als symbolische Form", as in I.2, note 27.
97. For a discussion of Panofsky's context see the author's: Panofsky's
perspective: a half century later" in: Marisa Dalai Emiliani, ed., La prospettiva
rinascimentale. Codificazioni e trasgressioni, Florence: Centro Di, 1980, pp.565584.
98. H. Cohen, Ästhetik des reinen Gefühls, Berlin: P. Cassirer ,1912. Cf. his:
Kants Begründung der Ästhetik, Berlin: F. Dümmler, 1889.
99. Sir E. H. Gombrich, Aby Warburg. An Intellectual Biography, London:
Warburg Institute, 1970.
331
100. Sir E. H. Gombrich, Norm and Form, Studies in the Art of the Renaissance I,
London: Phaidon, 1966; Sir E.H. Gombrich, Symbolic Images, Studies in the Art of
the Renaissance II, London: Phaidon, 1972; Sir E.H. Gombrich, The Heritage of
Apelles. Studies in the Art of Renaissance III, London: Phaidon, 1976.
101. Sir E. H. Gombrich, The Sense of Order. A Study in the Psychology of
Decorative art. London: Phaidon, 1979, p.ix.
102. Ibid.
103. Sir E. H. Gombrich, Art and illusion. A study in the psychology of pictorial
Representation, Princeton: Princeton University Press, 1960 (Bollingen series
XXXV.5); R.L. Gregory and E.H. Gombrich, ed., Illusion in Nature and Art,
London: Duckworth, 1973; Sir E.H. Gombrich, The Image and the Eye. Further
Studies in the Psychology of Pictorial Representation, Oxford: Phaidon, 1982.
104. Sir E. H. Gombrich, The Sense of Order, as in note 101, p.ix.
105. Cf. Sir E. H. Gombrich, Art and Illusion, as in note 103, p.152. Cf. quote
relating to our note 104.
106. Cf. Sir E. H. Gombrich, The Ideas of Progress and their Impact on Art, New
York: Cooper Union School of Art and Architecture, 1971.
107. Ernst Cassirer, Individuum und Cosmos in der Philosophie der Renaissance,
Leipzig: B.G. Teubner, 1927 (Studien der Bibliothek Warburg, X); Cf. Ernst
Cassirer, Individual and the Cosmos in Renaissance Philosophy, trans. Mario
Domandi, New York: Harper and Row, 1964, particularly pp.123-191.
108. There are larger questions here. Joseph Campbell in Oriental Mythology,
Harmondsworth: Penguin, 1962, begins with a fascinating contrast between
Eastern and Western culture, suggesting that the separation of man from God and
nature has been an aspect of western culture from the outset in a way that is not the
case in the east. In other words, the subject-object distinction, although it came
into focus during the Renaissance, had Biblical roots in the West.
332
11. ILLUSTRATIONS
1. Three kinds of pseudo-perspectival methods: visual angles in the Bedford Hours
and Schwenter's Practical Geometry (1618); vertical axis or fishbone perspective
in wall decorations at Boscoreale and Cryptoporticus and inverted perspective in
Giotto's St. Francis Cycle, Assisi and in a detail from a Chinese handscroll in the
British Library (17th c.).
2. Duccio's Maestà as an example how recurrent use of spatial scenes serves to
connect different episodes in a story. A detail from the Maestà and a similar
polygonal building in Piero della Francesca's treatise on perspective about 180
years later as an example of how practice precedes theory.
3. Three further cases of how painting practice precedes perspectival theory.
4. Parallels between construction of space in churches: St. Pierre in Aulnaye le
Santage and Notre Dame in Paris; reconstruction of space in the Baptistery of the
Palace of the Kings of Majorca in Perpignan and representation of space in
Ghiberti's Gates of Paradise and the Limbourg Brothers' Presentation of the Virgin
in the Très riches heures de Duc de Berry.
5. How a given spatial motif of a barral vault recurs in different contexts and
media: fresco in Masaccio's Trinity; marble in D. da Settignano's Tabernacle in
San Lorenzo (Florence), façade of the Civic Hospital in Venice; fictive space in
Bramante's Choir in Santa Maria presso San Satiro (Milan) and Borromini's
illusionistic colonnade in the Palazzo Spada (Rome).
6. Further examples of the same spatial motif in Bellini's Sketchbooks, a painting
of the Mystic Figure of Christ in the National Gallery (London), and in Donatello's
Study for a Flagellation in the Uffizi (Florence).
7. Combinations of this motif with other motifs such as the shell form in Piero
della Francesca's Brera Altar (Milan) or with a cross vault in Cima da
Conegliano's Saint Peter Martyr, also in the Brera (Milan) and theoretical
treatment of these motifs in treatises by Piero della Francesca and Serlio.
8. The motif of a portal as a spatial device in Northern art.
9. The same motif in Italian art and architecture.
10. The motif of a cutaway wall as a spatial device in Northern practice and
theory.
11. Italian examples of the same motif.
12. The interior of a room as a spatial device in Northern painting.
333
13. The same device in Pollaiuolo's Annunciation (Berlin). Comparison of the
window motif in Italian and Northern art.
14.Colonnades as a spatial device in architectural interiors in Italian and Northern
engravings: Scamozzi, Vredeman de Vries and Cornelius Loos.
15. Further examples of the same motif in architectural exteriors: Benedetto da
Maiano's facade of Santa Maria delle Grazie (Arezzo), Barozzi's view of a loggia
in the Uffizi (Florence) and from a treatise by Vredeman de Vries (1601).
16. Church interiors as a spatial motif in sixteenth century Northern practice
(Pacher, Altdorfer), and theory (Rodler, 1531).
17. Church interiors as a spatial motif in seventeenth century Northern theory
(Hondius) and practice (Steenwyck II).
18. Tombs as a spatial device in Northern (Vredeman de Vries, 1633), and Italian
(Galli Bibiena,1740) treatises.
19 Church interiors as a spatial motif in eighteenth (Heinecke, 1737) and
nineteenth century treatises (Guiot,1845), La Gournerie, 1884).
20. Seventeenth century painting by Neefs and a twentieth century photograph of
the cathedral at Antwerp. Preparatory drawing vs. finished painting in two views
of the Grote Kerk in Haarlem by Saenredam.
21. Saenredam's preparatory drawings and painting of the town hall in Amsterdam.
22. Perspective brought not only spatial representation but also a systematic
treatment from different viewpoints. Two views of the main market place and
Grote Kerk at Haarlem by Berckheyde.
23. Two further views of the same by Ouwater and Berckheyde.
24. Perspective also introduced systematic rendering in different scales. Views of
the orphanage at Amsterdam in different scales. Egnatio Danti's maps in the Room
of the Globes in the Palazzo Vecchio (Florence).
25. Five views of the Netherlands in different scales in the atlas of Gerard de Jode
(1578) and in Vermeer's Allegory of Painting in the Kunsthistorisches Museum
(Vienna).
26. Views of Zürich in different scales in an altar by H. Leu, the elder (1497-1502)
and Hohenberg's atlas of European cities (1582). Maps of different scales together
in the Gallery of Geographical Maps in the Vatican.
334
27. Views of the earth and heavens in different scales in the work of Ptolemy,
Dürer and Barbaro.
28. There were two basic methods of perspective in the Renaissance. One was
based on geometrical diminution, illustrated here with examples from Alberti,
Piero della Francesca, Serlio and Barbaro. This subsequently became associated
with the distance point construction.
29. Further examples of this method in treatises by Pélerin (1505), Androuet Du
Cerceau (1576) and Galli da Bibiena (1740).
30. A second method known as the legitimate construction became identified with
demonstrations involving perspectival windows, such as those illustrated by
Alleaume (1643).
31. More complex examples of intersections using the window principle in
Marolois (1633), Hamilton (1738) and Monge (1838).
32. Study of intersecting planes in perspective was closely linked with conic
sections in the treatises of Lencker (1571), and Frézier, who applied these
principles to practical problems of stone cutting.
33. In the nineteenth century perspectival study of conic sections was frequently
dealt with in the context of descriptive geometry as in these examples from
Cloquet (1823) and Tilscher (1865).
34. In the latter half of the nineteenth century perspectival study of conic sections
became ever more abstract as in Tilscher (1865) and emerged as an independent
theme in mathematical literature.
35. The regular solids were a significant theme in treatises on perspective as
illustrated by Dubreuil (1642-1649), Courtonne (1725) and Highmore (1763).
36. Study of the regular solids went hand in hand with interest in spatial
representation of the semi-regular solids by Leonardo (c.1496-1499), Jamnitzer
(c.1560-1565) and Sirigatti (1596).
37. This interest, combined with goldsmiths' activities as jewellers, led to ever
more extravagant forms in the treatises of Jamnitzer (1568) and Sirigatti (1596).
38. Religious forms such as the cross became a theme of perspectival play in the
treatises of Halt (1625), Kirby (1755) and a subject of modern symbolism in a
painting by Salvador Dali in the Metropolitan Museum (New York).
335
39. Letters became another theme of perspective in the treatises of De Bry (1615),
Lencker(1596), Haesel (1672) and Stoer (c.1567).
40. As early as the 1470's the PP Master in Ferrara was exploring perspectival
treatment of semi-regular shapes. Beams and columns became a favoured theme in
the popular treatise of Dubreuil (1642-1649).
41. Musical instruments, particularly lutes were a frequent perspectival theme in
inlaid wood (e.g. the Ducal palace at Urbino), in paintings such as Holbein's
Ambassadors and later in treatises by Jamnitzer (c.1560-1565) and Sirigatti (1596).
42. Chairs were another favoured theme in treatises on prespective and
anamorphosis by Vasari, Jr. (1594), Dubreuil (1642-1649), and Nicéron (1646)
and have remained important in our century through the Ames demonstrations and
recent art by Daniel Berset (1986).
43. Stairs have been another constant theme in treatises on perspective by Barozzi
(1583), Heinecke (1727), Charles Wilson Peale's painting (Boston) and Vredeman
de Vries (1633). Escher's work provides both further examples and subtle variants
as in the case of his paradoxical Waterfall (1961).
44. Architectural columns have been an important theme in treatises on perspective
as in these examples from Blum (1550), Nic‚ron (1646), Bosse (1648) and Bretez
(1751).
45. More complex examples of the same theme from Pozzo (1706), Kirby (1755)
and Huret (1670).
46. Shadows became a theme in treatises on perspective through Barbaro (1568
based on Dürer, 1525) and increasingly important in the work of Highmore (1763),
Dubreuil (1642-1649) and Cloquet (1823.
47. Nineteenth century wxamples of shadows as a theme of perspective in treatises
by Cloquet (1823) and Gennerich (1865).
48. Links between sundial projection, regular solids and perspective in treatises by
Welper (1708) and Bosse (1648).
49. Further connections between sundials and perspective in Huret (1670), Welper
(1708) and Maignan (1648).
50. Reflections and perspective in treatises by Dubreuil (1642-1649), Valenciennes
(1803) and Cole (1921).
51. Further examples of reflection in treatises on perspective by Jeaurat (1750),
Cloquet (1823), Robert (1905) and Brook Taylor (1749).
336
52. Reflections in convex mirrors in a fifteenth century Boccaccio manuscript
(Paris, BN), and in a painting by Petrus Christus in the Metropolitan Museum
(New York). Practical use of such convex mirrors may have been responsible for
the curvilinear effects in the miniature by Fouquet (Chantilly) and a painting by
Witz (Nürnberg, Germanisches Nationalmuseum).
53. Plane mirrors and perspective by a member of the school of Fontainebleau and
Velazquez as well as in treatises by Stevin (1605) and Highmore (1763).
54. Perspectival instruments in treatises by D rer (1532), Pfintzing (1599) and
Faulhaber (1610).
55. Further perspectival instruments in treatises by Barozzi, il Vignola (1583),
Marolois (1633) and Martius (1789).
56. Perspectival pantographs in Lencker (1571), Marolois (1633), Grollier de
Servière (1719) and Watson (19th c.).
57. Camera obscuras and perspective in treatises by Kircher (1646) and Bettini
(1645).
58. Links between perspectival instruments and surveying in treatises by Hulsius
(1605), Dubreuil (1642-1649), Werner (1763), Specklin (1579) and Bosse (1648).
59. Connections between Roman ruins and perspective as illustrated by Du Pérac
(1575), Piranesi (1740) and a modern photograph by Herschel Levit (1976).
60. Links between townscapes and perspective in two watercolours of the former
court at Innsbruck, attributed to Dürer and engravings from a treatise edited by
Rodler (1531).
61. Links between perspective, building practice and machines in the Sketchbooks
of Bellini, a painting by Piero di Cosimo (Sarasota, Ringling Museum of Art) and
in a treatise edited by Rodler (1531). Machines perspectivally rendered
subsequently became an independent genre through authors such as Ramelli
(1588).
62. Links between perspective, architecture and landscape in a treatise by Edwards
(1805).
63. Further examples of perspective, architecture and landscape from Edwards
(1805) and Kirby (1755).
64. Multiple views of a scene in Edwards (1805).
337
65. Perspective and townscapes in Wood (1809), Edwards (1805) and Tilscher
(1865).
66. Perspective and secular interiors from Pélerin (1505), Dubreuil (1642-1649),
Marolois (1633) and Albrecht (1623).
67. Further examples of perspectival interiors from Rodler (1531), Bischoff
(1741), Wood (1809), and Bärtschi (1976).
68. Perspective and geometrical treatment of the body in Dürer (1534), Barbaro
(1568), Schön(1538), Braccelli (1624), the author of the Codex Huygens (c.1570)
and Coke (c.1720).
69. Perspectival effects caused by looking up from below (di sotto in su) in a
painting by Titian (London, National Gallery), a fresco by Francesco and
Bernardino Galliari (Bollate, Villa Castellazzo, c.1572), and in a treatise by Bosse
(1648).
70. Perspectival effects produced by looking down or up at human bodies in a
painting (Milan, Brera) and a fresco (Mantua, Camera degli Sposi) by Mantegna
and treatises by Cousin le jeune (1595), the author of the Codex Huygens (c.1570)
and Carlo Urbino (c.1570).
71. Perspectival effects caused by looking up (di sotto in su) at Luca Giordano's
Apotheosis of Sant'Andrea, Florence, Chiesa del Carmine and looking down (di su
in sotto) at a courtyard in Vredeman de Vries' treatise (1633).
72. Perspectival effects caused by looking up at a painted architectural ceiling in
the Marciana Library in Venice and a related engraving from Barozzi, il Vignola
(1583).
73. Related effects in Pozzo's ceiling in Il Gesù (Rome), in treatises by Pozzo
(1700), Has (1583), and an engraving by Escher (1947).
74. Perspective in inlaid wood (intarsia) in the Ducal Palace at Urbino and the
Cathedral at Todi.
75. Further examples of perspective applied to inlaid wood in a treatise by Stoer
(1567), in the Church of San Giovanni Evangelista in Parma and a writing desk
made at Augsburg (c.1560).
76. Links between chiaroscuro and perspective in paintings by Van der Weyden
and Van Eyck.
77. Perspective and chiaroscuro applied to architectural contexts in the Villa
Borghese (Rome) and the Pitti Palace (Florence).
338
78. Use of perspective to separate scenes in a painting by Uccello (Urbino), a
Boccaccio manuscript (Munich, BSB), the stage at Vincenza and the gardens at
Versailles.
79. Related effects in the Royal Palace at Caserta and in a stage set by Galli
Bibiena (1740).
80. Links between perspective, stage scenery and Venetian architecture in a
drawing by Serlio with parallels in Cesariano's edition of Vitruvius (1521) and a
painting by Canaletto (1726-1729).
81. Links between perspective and Roman ruins in Peruzzi and Serlio.
82. Colonnades as a recurrent motif in Cesariano's edition of Vitruvius (1521), a
drawing from the school of Bramante, treatises by Serlio (1583) and Barozzi, il
Vignola (1583), drawings by Benozzo Gozzoli and Donato Bramante (Uffizi) and
in a painting by the Master of the Barberini Panels (New York, Metropolitan
Museum).
83. The development of this motif in Annunciation scenes in Bellini's Sketchbooks,
paintings by Crivelli (London, National Gallery) and inlaid wood by Fra Damiano
di Bergamo.
84. Perspectival cutaway effects in Roman ruins by Serlio, Francesco di Giorgio
Martini, (based on) Brunelleschi and (attributed to) Donato Bramante.
85. Engravings by Pieter Stevens in Marolois (1633) of the Antonine Baths and
Emmaus, illustrating how perspective applies equally to archaeological record and
anachronistic reconstruction.
86. Idealized ruins in a detail from Mantegna's Saint Sebastian (1480, Paris,
Louvre) and engravings by Androuet Du Cerceau.
87. Idealized architecture in a treatise by Vredeman de Vries (1633) and in a
painting by Steenwyck II (London, National Gallery).
88. Perspective applied to make architectural features look closer at Caprarola, the
Capitoline in Rome and the Villa Frascati at Aldobrandini.
89. Perspective applied to make features of the landscape appear further at
Ryxdorp, Würzburg, Chenonceaux and Versailles.
90. The regimentation of Nature to fixed geometrical patterns to produce
perspectival effects in Dubreuil (1642-1649).
339
91. Other examples of the regimentation of Nature in drawings by Wolf Huber
(1526, 1511-1513), and treatises by Dubreuil (1642-1647) and Bosse (1648).
92. Perspectival gardens in treatises by Androuet Du Cerceau (1584) and
Vredeman de Vries (c.1600).
93. Perspective applied to the whole environment in a painting of Versailles (1668)
and in a treatise by Decker (1711)
94. Interplay of engravings by Vredeman de Vries (1560,1569) and Cock (1566)
showing imaginary buildings and real architecture of the Armoury at Wolfenbüttel
(early 17th c.).
95. Interplay of real architecture of the Uffizi in Florence, an engraving thereof as
if it were a stage set and actual stage sets in Torelli (1644) and Vasari Jr. (c.1594).
96. Interplay of real and imaginary architecture illustrated by a round temple that
serves as a Roamn ruin (Francesco di Giorgio Martini), a plan for a mausoleum
(Leonardo da Vinci), a temple in a painting of an ideal city (attributed to Giuliano
da Sangallo and Domenico Ghirlandaio), the Renaissance Tempietto in Rome
(Bramante) and an engraving thereof in a book on Roman ruins (Androuet Du
Cerceau).
97. Further examples of interplay between ideal and real, historical and imaginary
architecture: an engraving of the Temple of Jupiter by Androuet Du Cerceau and
the background to Raphael's Mystic Marriage of the Virgin (Milan, Brera); a
temple associated with Troy in Androuet du Cerceau (c.1540) and Bramante's Plan
for Saint Peter's; a view through the columns of the Palazzo del Te in Mantua and
Androuet Du Cerceau's (1551) engraving of an imaginary ruin.
98. Use of perspective in the interplay between Nature and artifice in a grotto by
de Caus (1620), a stage setting by Galli Bibiena (1740) and Le Lorrain's painting
of a sea port (Paris, Louvre).
99. Perspective in the interplay between reality and illusion: engravings of the real
Orangerie and Trompe l'oeil arch at Rueil and Galli Bibiena's (1740) illusionistic
scene of a garden and arch.
100. Trompe l'oeil figure and façade at the U.S. embassy in Paris.
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