HESPERIA
76
IDEA AND
(2OO7)
VISUALITY
Pages SSSS9S
IN HELLENISTIC
ARCHITECTURE
A Geometric
Temple
at
of
Analysis
of
A
the
Asklepieion
Kos
ABSTRACT
author uses analytic geometry
and AutoCAD
software to analyze
at Kos, revealing a circumscribed
the plan of Temple A of the Asklepieion
as the basis for the
and
Pythagorean triangle
plans design.This methodology
its results counter earlier doubts about the application of geometry to Doric
The
temple design and suggest the existence of an alternative to the grid-based
approach characteristic of Hellenistic
temples of the Ionic order. Appre
ciation of the geometric system underlying the plan of Temple A leads to a
consideration
of the role ofvisuality inHellenistic
architecture, characterized
inwhich abstract ideas shared by architects and scholars
here as the manner
conditioned
viewing
and influenced
the design process.
on the island of Kos was a
The Asklepieion
healing sanctuary and medi
some 4 km
cal school of great importance throughout
antiquity.1 It lies
southwest of the ancient polis of Kos, built on a terraced slope
commanding
sea.
views
of
the
In
its
the
state,
impressive
completed
complex consisted of
three separate terraces connected by stairways, each supporting structures
from various periods (Figs. 1,2).2
By the middle of the 3rd century b.c., the sanctuary's three terraces
were constructed.3 On the lower terrace, a
Doric stoa with ad
?-shaped
was built to enclose an
rooms
x 93 m
47
joining
approximately
space.4Major
architectural features on the middle terrace included an altar,
a
replaced by
more monumental
version in the following century, and temples dedicated
to thank Andrew
1.1 wish
for his
taking
which
constructive
an interest
criticisms
in my
are all the
versations.
stronger
I am indebted
Stewart
and for
arguments,
for our con
to Fikret
Yeg?l andDiane Favro for their de
voted
attention
inception
to
to this
completion.
to Erich Gruen
study from
I am also
and Craw
grateful
ford H.
Greenewalt
Jr. for their gen
?
American
School
The
of Classical
erous
encouragement
an initial
following
at an Art
my
arguments
Mediterranean
quium
of this
project
of
presentation
and
History
Collo
Archaeology
at the
of California,
University
Berkeley, inApril 2005. All drawings
and
are my
photographs
own.
2. For the history of the Koan
Asklepieion,
pp. 340-342,
Studies
see Sherwin-White
345-346.
at Athens
For
1978,
the devel
and
of the site,
opment
dating
Schazmann
and Herzog
1932,
see
p. 75;
Gruben 1986, pp. 401-410; 2001,
pp. 440-449.
3. Schazmann
pp. 72-75,
pis.
and Herzog
1932,
37,38.
4. A centrally placed propylon on its
north wing
served as the monumental
to the
entrance
Schazmann
sanctuary;
and Herzog
1932,
pp. 47-48.
556
R.
JOHN
SENSENEY
at Kos,
1.
Figure
Asklepieion
the middle
and lower
the upper
of the
Asklepios
restoration
the
terrace,
3rd-century
terraces
with
the
b.c.
of the altar
2nd-3rd-century
stoa
of
the
The
to
the
lower
terrace.6
first half of the 2nd century b.c. witnessed
upper
terrace
in a new
resulted
that
character
and additions
changes
for
the
as a
sanctuary
whole. To connect the upper terrace with the rest of the sanctuary below, a
new
a dominant central axis
a
grand staircase created
(Fig. 3).7 In addition,
new
marble
stoa
the
replaced
earlier
timber
structure.
In
the
center
of
the
50.4 x 81.5 m
approximately
temple of Asklepios
ple A
space enclosed by this stoa, a marble Doric
was
as
as 170 b.c.,
as
begun
early
today referred to Tem
to distinguish
it from the earlier temple of Asklepios
(Figs. 2-5)
on the terrace below.8
(Temple B)
placed before
Axially
the
middle
and
lower
terraces, Temple A became
overlooking
visual focus of the entire Asklepieion.
The
Doric
choice
of the Doric
stoas continued
through
order for Temple
to be common
the Hellenistic
A
fig. 74.
7. Schazmann
terrace, were
upper
this level. For these
pp. 22-24,
fig.
54.
45-48,
found
on
as well
features,
as the
monumental
altar,
2nd-century
see Schazmann
and Herzog
1932,
pp. 25-31,
pis. 12-14.
6. For
later marble
mann
figs.
34-39,
49-51,
60, 73,
is an archaism. While
and the nearby
5. Important
utilitarian
features,
as a
and wells
lo
springhouse
cated along the retaining wall for the
also
the dramatic
in all areas of the Greek world
period, Asia Minor
such
the staircase
down
islands reflect
62, 75,98,109,112,149,159,171,246,
and
18, pis.
8. Schazmann
pp. 3-13,
figs.
ple is oriented
and
3-14,
Herzog
10,11,
1932,
37-40,
1932,
Herzog
tem
1-6. The
pis.
25 degrees west
of north.
on a foundation
the
of limestone,
con
the
of
is
superstructure
temple
with
the
structed of marble
throughout
Built
the timber
and
portico
replacement,
and Herzog
1932,
15-17,
pi. 9; Coulton
its
see Schaz
pp.
14-21,
1976,
pp. 9,
of courses of poros
limestone
exception
blocks
in the interior walls
of the naos.
of
from
remains
Temple
(left), the 2nd-century
of
b.c.
and
(center),
a.d.
restoration
of the Temple of Apollo
to Asklepios
see
and Apollo
(Temples B and C, respectively;
Fig. I).5 On
the upper terrace, a TT-shaped stoa of timber construction
balanced the
view
(right)
IDEA
AND
IN
VISUALITY
HELLENISTIC
ARCHITECTURE
557
-C
2.
Figure
at Kos,
Asklepieion
view
:::?-%--S?:
;?:
?,',:R"?:?".
of the remains (in situ) of the upper
terrace
from
complex
the
southeast,
looking toward Temple A, with the
stoa
in the
foreground
!
Figure 3. Asklepieion
restored
plan
==J
0
at Kos,
of the upper
I
I
terrace
complex with Temple A
0
3W
a
for the Ionic order for temple architecture. As Vitruvius
predilection
bolstered this pref
such as Pytheos and Hermogenes
architects
indicates,
as its
erence with a theoretical
(Vitr. 4.3.1-2).9 Furthermore,
justification
was
measurements
traditional
in
its
omission
of
demonstrate,10 Temple A
to
and
Pytheos
Vitruvius
mentions
9. In addition
Hermogenes,
architect Arkesios,
to the 3rd century.
who
perhaps
For Arkesios,
the
dates
as well
as the
convincing
looked arguments
Vitruvian
the Doric
and
still much
over
the common
against
of a "decline"
conception
order in the 4th century
of
b.c.,
seeTomlinson
10. Schazmann
pp. 3-5,
pis. 2-5.
1963.
and Herzog
1932,
558
JOHN
R.
SENSENEY
??-?:-;
u ?;?:
i:
?:: :
?x??
::t:?i
r-?:?ii
:I
"'?ic??:r?
?-:
Figure
Temple
4. View
A
from
of the
the
remains
of
southwest
the kind of novel modifications
and "optical refinements" characteristic of
also
the
Foregoing
interesting and easily detectable schemes
of Ionic temples associated with Pytheos
and Hermogenes
(Fig. 6), the
seem to have been a
would
conventional
temple
strictly
reapplication of
the Parthenon.
order in the 2nd century b.c.
character of Temple A may represent only
the straightforward
a part of its story. As I argue below, a
measure
geometric
analysis of its
ments reveals the use of a compass in constructing
the interrelationships
of architectural
in plan according to circumferences.11 The di
elements
the Doric
Yet
ameters
share a simple arithmetical
relationship
a 3:4:5
of
proportions
Pythagorean
triangle,
of these circumferences
based on the whole-number
rather than amore
to irrational
strictly geometric
relationship pertaining
like v2 or v3, or their fractional approximations. The geometry
of the temple's plan is therefore very simple, and is not to be confused by
the analytic geometry
it.
required to substantiate
numbers
circumferences
concealed within
the
presence of theoretical
nature
raises
features
about
the
of
the
building's
interesting questions
Doric design process on aHellenistic
architect's drawing board. That such
an
is found in only a single (albeit prominent)
underpinning
example of
Greek temple architecture, as opposed to the more widespread
approach
of grid patterns, does not detract from its significance. As I will discuss,
the uniqueness
in a temple plan?as
of circumferential
op
relationships
to
the
kind of orthogonal
that temples of the Ionic
posed
relationships
The
to a dearth of specifically Doric temples during the
order permit?relates
inTemple A demon
Late Hellenistic
period. The interesting geometry
an important architectural
tenet that we might
strated here exemplifies
term "cryptomethodic,"
to
the
features
of the design
systematic
referring
process that cannot be appreciated
be recovered only through detailed
through
study.
casual observation,
but may
11. For
plans
berger
an excellent
in ancient
1997.
discussion
architecture,
of
see Hasel
IDEA
AND
IN
VISUALITY
HELLENISTIC
ARCHITECTURE
559
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4.368
4.435-1?
&
9.272
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18.075
Figure
state
5. Measured
plan
of
Temple A according to material and
trace
remains,
exposed
foundations
shown
limestone
without
masonry
the
of the
-?-
."" 1"...'".""H
-??-~~-*
10 rn
56o
R.
JOHN
SENSENEY
IDEALISM AND HELLENISTIC VISUALITY
a
turning to technical discussion,
that an ancient architect should design
Before
Iwill first address the very premise
on geometry that
building based
the final product.12 It is important to
a
does not correlate experientially with
state from the outset that architects of the Hellenistic
world thought about
their buildings in terms different from those used by architects today.We
that Greek architects called their plan, elevation, and
know from Vitruvius
to the notion that
perspective drawings i??ou (Vitr. 1.2.1-2), corresponding
uses
to
in reference
the transcendent ideas (or forms) that
Platonic idealism
are
to be the ultimate
thought
reality underlying the perceptible objects of
the everyday world. As Lothar Haselberger
has admirably observed, the
is
between the philosophical
and architectural meanings
correspondence
not casual,13 and the full implications of this correlation have yet to be
appreciated in studies of ancient architecture.
rhetorical manner
The
inwhich
Plato
sometimes
this ideal
discusses
can seem
our own way of
as when he
ist vision
quite foreign to
thinking,
can
presents Socrates' argument that couches manufactured
only
by artisans
a realm
an
our
in
imitate
couch
existing
beyond
archetypical
imperfectly
senses
(Resp. 10.596e-597e).
to these isolated metaphors
to reduce Platos
it is unfair
Yet
conception
and parables, and the lack of any clearly stated
our attention instead
unifying theory of ideas in Plato's work should draw
as amodel for systematic
to the more
of
mathematics
general importance
universe
to the ultimate realities of the
of penetrating
idealism. Perhaps the most articulate expression of this
methods
and hierarchical
in Plato's
is the well-known
way of understanding
passage inwhich Socrates, after
an uneducated
a
slave
that
geometric proof, concludes
through
guiding
in the world
eternal truths lie beyond our embodied experiences
(Meno
to
is
it
theoretical
rather
than
the
Platonic
the
model,
82b-86c). According
the sensory that is privileged.
What
systems
geometric
to bear on the question of underlying
in architectural plans is what J. J. Pollitt terms the
this discussion
brings
of the Hellenistic
"scholarly mentality"
Roman
12. The
considerations
following
to the ancient world,
only
pertain
to how
but more
culturally
generally
of the world
based understandings
discussion
of this
in which
objects
For
constructed.
idea
Cartesian
are
a
in the contexts
perspectivalism,
and 19th-century
painting,
see
Jay 1988, esp. pp.
phy,
early modern
photogra
16-17. A
definition of visuality offered by Nor
man Bryson (1988, pp. 91-92) has
recently been evoked by Jas Eisner in
his new
context:
structs
between
screen
in a classical
study of visuality
con
of cultural
"the pattern
that stand
and social discourses
the retina
through
which
and
a
the world,
... Greek
and
had
people
in the
originating
no choice
but
to
look and through which they acquired
not
the way
anticipate
viewed
and visually
age.14 Perhaps
(at least in part) their sense of subjec
I focus
tivity" (Eisner 2007, p. xvii).
texts
and what
here not on subjectivity
of
images
in the classical
how
Temple
were
tell us about
can
and
world,
but
visuality
rather on
of
underpinning
to ways
of seeing that
and socially
conditioned.
the geometric
A relates
culturally
13. Haselberger
and primary
92-94,
sources
esp. pp. 77,
and
secondary
Arendt
(1958,
cited. Hannah
p. 90) offers
articulation
to notions
1997,
an excellent
of how
of models
philosophical
ideas relate
Platonic
and measures,
which may be useful for framing the
conceptual
connection
between
ideas
and
of the
drawn
based
geometrically
in architecture:
into measures,
ideas
models
"For the transformation
is
Plato
helped by analogy from practical life,
it appears
that all arts and crafts
are also
guided
by 'ideas,' that is, by
the 'shapes' of objects, visualized
by the
inner eye of the craftsman
then
who
where
them in reality through
reproduces
imitation. This
enables him
analogy
to understand
ter of the
he does
the transcendent
ideas
in the
the transcendent
charac
same manner
existence
as
of
the fab
lives beyond
it
and
therefore
process
guides
can
for
become
the standard
eventually
its success or failure."
the model,
which
rication
14. See Pollitt 1986, pp. 13-16.
IDEA
----m
AND
VISUALITY
IN
HELLENISTIC
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.?j
I??j?I??h?-1|?H?|
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1,1.
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IB ?P
ARCHITECTURE
561
g?-^_||L?
ft
lE iB] f?fjf
loig,.?II_JiiL-JSIJ_lllll_?
[m
0
Figure 6. Restored plans showing the
grid systems of Pytheos's Temple of
Athena Polias, Priene (left), and
Hermogenes'
Magnesia
p. 70, fig. 23
Temple
After
(right).
of Artemis,
Coulton
1988,
10m
a taste for didactic
of the Library at Alexandria,
came to
displays of abstruse knowledge
strongly characterize Hellenistic
art and literature. A notable feature of works appears to have been the
deliberate potential for simultaneous appreciation from both common and
In architecture, in particular, this tendency is found in
erudite perspectives.
intellectual
ambience
as
Pytheos's Temple
examples such
inwhich the masses might marvel
knew
the building's proportions
of mathematical
precision.15
of Athena Polias at Priene (Fig. 6, left),
at its surface qualities, while those who
its plan as an expression
could understand
text depends
in part upon the writings
of earlier
Vitruvius, whose
insists
He
that
this
Hellenistic
architects, exemplifies
scholarly emphasis.
as
an architect's
in
and
like
geometry, music,
background
disciplines
tronomy is requisite (Vitr. 1.1.4, 8-10), a claim that he backs up at times
his eagerness to show
with pretentious displays of erudition. Sometimes
that he discusses, as
exceeds his command of the material
his knowledge
of the doubling of the square,
to the Pythagorean
which he follows immediately
theorem, without realizing that both of these theorems illustrate an identical
such limitations, he
(Vitr. 9.Praef.4-7).16 Despite
principle of proportion
when
15. Pollitt 1986, pp. 14-15.
16. See de Jong 1989, pp. 101
102.
he credits Plato with
the demonstration
with
an introduction
R.
JOHN
562
SENSENEY
*
5
,"i:.
?
, *
,,+
rt
.
~.: ",, !
I ,
,
,;
..~.~
.
,,
?,..
his scholarly quality in the context not only of general theory,
the plans of
but also of architectural design. His procedures for designing
both Latin and Greek theaters (Figs. 7,8) well illustrate this tendency, and
merit quoting at length. For the Latin theater, he writes (Vitr. 5.6.1-3):
demonstrates
Figure 7. Plan of a Latin theater
according
to Vitruvius's
description
to be constructed as follows.
plan of the (Latin) theater itself is
a line of circumfer
Having fixed upon the principal center, draw
ence
to be the perimeter at the bottom. In
equivalent to what is
it inscribe four equilateral triangles at equal distances apart and
The
as the
touching the boundary line of the circle just
astrologers do in
a
are making computa
figure of the twelve celestial signs when they
tions from the musical harmony of the stars. From these triangles,
side is closest to the scaena and in the spot
select the one whose
it cuts the curvature of the circle let the front of the stage be
located. Then draw through the center a parallel line set off from
that position to separate the platform of the stage from the space of
where
The wedges for spectators in the theater should
the orchestra....
run around the cir
so that the
angles of the triangles that
be divided
of the circle may provide the direction for each flight of
between
the sections up to the first curved cross-aisle. Above
steps
are to be laid out with aisles that alternate
the
this,
upper wedges
with those below. The angles at the bottom that produce the direc
tions of the flights of steps will be seven in number, and the remain
cumference
the arrangement of the scaena. In this
ing five angles will determine
center
in
the
the
way
ought to have the "palace doors" facing it
angle
and the angles to the right and left will designate the position of the
doors for "guest chambers." The two outermost angles will point to
the passages in the wings.17
17. Smith
S. Kellogg.
2003,
pp.
165-166,
trans.
IDEA
AND
IN
VISUALITY
I
I
HELLENISTIC
ARCHITECTURE
563
r
C
C
C
Ir
\ C?
r
-------?1---?--------??-,,,*,II,,,
(r
fr
C\CCI
*?
Y
r.f
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1,
r
Ir \t'
I I`rr \
I,II
"
r
r, i
r
Ir\ II'
( II
"'?'~''"""~""~"""'~~""""""'
rtt ''
r
r
\
'r
?I
1
,r
I\ c
rr
t Z
r
r
rrr
4\
rr
r
?r
t
.
rt ?
\
1.
tr r rr ,
r
?
r t
rr
I ?r
f
r
I? r
c r
t, r
\ ?I
I
Figure 8. Plan of aGreek theater
according toVitruvius s description
'4?
??r \
for the Greek
And
t
?-Ir
?) C
theater
C
(Vitr. 5.7.1-2):
theaters some things are done differently. First, in the bot
tom circle, while the Latin theater has four triangles, the Greek has
three squares with their angles touching the line of circumference.
In Greek
The
is determined by the line of the side of
limit of the proscenium
the square that is nearest the scaena and cuts off a segment of the cir
cle. Parallel to this line and tangent to the outer circumference of the
segment, a line is drawn that delineates the front of the scaena. Draw
a line
through the center of the orchestra and parallel to the direction
of the proscenium. Centers are marked where it cuts the circumfer
ence to the
at the ends of the half-circle. Then, with
right and the left
the compass fixed at the right, an arc is described from the horizontal
distance at the left to the left-hand side of the proscenium. Again,
with the center at the left end, an arc is described from the horizontal
distance at the right-hand side of the proscenium_Let
the ascend
as
as
of
between
the
of
far
the first
seats,
steps
up
ing flights
wedges
18. Smith
S. Kellogg.
19. For
1989.
For
2003,
the Greek
a discussion
pp.
167-169,
material,
trans.
see Isler
of
questionable
to match Vitruvius's
attempts
scholarly
of Roman
theater design
description
to later Roman
see Sear 1990;
theaters,
2006,
pp. 27-29.
curved cross-aisle, be laid out on lines directly opposite the angles
of the squares. Above the cross-aisle, the other flights are laid out
between the first.At the top, as often as there is a new cross-aisle, the
number of flights of steps is always increased by the same amount.18
are not easy to follow, and it would be
to
prescriptions
tempting
them as indicating a fussy outlook on the part of Vitruvius
if not
for the fact that these geometric constructions were applied in surviving
These
dismiss
Greek
and Roman
to a basic geometry
prescriptions pertain
or squares, rather than considerations
triangles
theaters.19 The
of forms such as equilateral
564
JOHN
R.
SENSENEY
based on irrational numerical
case of both theater types,
relationships. In the
not contribute to
the cryptomethodic
described
would
patterns
arguably
nor
most
ancient
visitors have
would
any visible harmonic relationships,
been likely to perceive them. Certainly, there are less theoretically grounded
and
the locations of radial stairways, boundaries,
ways of determining
on
seem more sensible to
it
forms
based
and
would
doorways,
design
simple
intuition and functional criteria. On the other hand, our very concern with
issues may be a consequence
of an inherently modern prerequisite
that the design process directly correlate with sensory experience. For the
world who could read and understand
privileged few in the Hellenistic
these
such passages,
there was value of a different
to aworld
for material
Furthermore,
dence of underlying
kind: the value of discourse.
pertaining
ideas, our own privileging
in the final built form is arguably misplaced.
that validates
the indepen
of the tangible properties
Vitruvius's
reference to the drawings of astrologers reveals a signifi
cant interdisciplinary
issue at work in such architectural ideas. Given the
interests
of Hellenistic
architects, there is no reason to believe that
scholarly
in reference solely to the
the practice of architectural drawing developed
construction
Another
drawn
that Vitruvius describes
of
designs
buildings.
avaXrijiua, which was the graphic reference for solar
declensions
that served as the basis for sundials (Vitr. 9.1.1, 9.7.2-7). He
recon
an
algorithm for the drawing, which has allowed for its
provides
in detail
is the Greek
struction as amarkedly circumferential design (Fig. 9).20 In this curvilinear
the cir
quality, the analemma provides intriguing general comparisons with
cumferential geometry underlying the design of Temple A at Kos proposed
Interestingly, Berossos the Chaldean, whom Vitruvius credits with
to Kos and established
the invention of the semicircular sundial, moved
the Great s conquest of
there a school of astronomy following Alexander
In the course of the 3rd century, Berossos s
(Vitr. 9.2.1,9.8.1).
Mesopotamia
school amalgamated with elements of the Koan medical school to establish
below.
the discipline of medical astrology, concerned particularly with the moment
of conception as the basis for casting nativities (Vitr. 9.6.2).
I do not argue that there was any symbolic connection between Tem
and the analemmay let alone some sort of mystical value. The study
A
ple
is an inexact science, and we cannot lose
of architectural
iconography
we deal with a design that pertains solely to the
sight of the fact that here
architect s drawing board; it is only the circumferential
approach that is
of
of
shared
the
(and
ways
similar, underscoring
envisioning
possibility
?izz?ary drawing) forms among architects and those concerned with astral
as well as geometry. As I demonstrate
below, the curvilinear
phenomena
of Temple A pertains not to solar declen
element in the underpinning
to
sions, but rather to a Pythagorean
triangle. In this aspect, it is similar
the ways inwhich Greeks and Romans began their theaters with squares
an outlook characteristic of the ways in
or
triangles, and consistent with
the drawn
which educated men of the Hellenistic
period thought. While
an eternal and abstract form of the idea, the final built form
plan expresses
into presence inways that need not readily unveil its un
idea
that
brings
truth to the senses.
mathematical
derlying
then, visuality in architecture was consti
of the casual viewer, but also by the
solely by the perceptions
In the Hellenistic
tuted not
period,
20.
trations
Howes
e.g.,Thomas
in Howe
and Rowland
See,
pp. 288-289, figs. 114,115.
illus
1999,
IDEA
Figure
9. The
analemma
according
AND
VISUALITY
IN
HELLENISTIC
ARCHITECTURE
565
to
Vitruvius's description
spon
certainty of geometry. Framed by a monarchically
ac
agenda and the resulting practices of visualizing form
to geometry, modes of visual representation established the starting
cording
for
form in disembodied
abstractions
that were subject to math
point
epistemological
sored scholarly
rules or norms.
ematical
In this way, the squares underlying
the placement
were
of empirical features within
the curvilinear Greek theater
patently
mea
real. Similarly, the circles (and the Pythagorean
triangle that gives
sure to their
of
the
rectilinear
forms
underlying
experiential
proportions)
relate to a primary consideration:
the
that defines the visuality of the building by constructing
its
geometry
eternal idea. The square, circle, triangle, and other shapes are the ideas of
nature that engender the visible things in the world, be they a theater, a
or even a human
temple,
body (Vitr. 3.1.3). As in Vitruvius's discussion
Temple
A
at Kos discussed
below
of theaters, the drawing of a building may begin with geometry alone, and
only through the process of design arrive at the final form. In further sup
I argue that the design for the plan of Temple
port of these observations,
a
similarly began with the drawing of Pythagorean
triangle, from
the design and construction
which
evolved into a completed expression
that continues to reflect its origin, however imperfectly.
A at Kos
QUESTIONABLE METHODOLOGIES
very suggestion of a hidden system within an architectural
to touch a raw nerve among archaeologists
and architectural
The
plan tends
historians
alike. Far from striking an innovative note, such an approach falls squarely
a tradition that has so tried the
one
patience of readers that itmay
within
day risk outright exclusion from mainstream
scholarly research. Before
to
it
is
circumstance.
address
this
necessary
briefly
proceeding,
566
R.
JOHN
SENSENEY
In a penetrating essay on the Parthenon, Manolis Korres offers amark
assessment of efforts to present that celebrated building as an
edly negative
expression of ideal numerical relationships and harmonious proportions.21
such studies as "pseudo-science," Korres notes the disturb
that contradict the reality of the building.
ing tendency
error in the
to him,
According
approaches include impudent suggestions of
Characterizing
to argue theories
the reliance of proposed
temple's construction and published measurements;
on inaccurate, small-scale drawings rather than the
theories
geometric
found in the actual building; the inability to credibly
degrees of magnitude
the proposed geometric
shapes with analytic geometry; and the
or even
that may underlie such studies in
motivations
mystical
like these have articulated and, justifiably,
the first place.22 Observations
correlate
obsessive
even reinforced
general reservations about the rigor and value of
studies of architecture in various periods and
and
geometric
metrological
world.23
locations in the ancient Mediterranean
perhaps
to future stud
Although Korres's remarks may provide salutary caution
of geometric
ies, we may not entirely benefit from severe marginalization
one thing, the Parthenon
antedates
For
in
Greek
analysis
temple design.
the use of scale drawings in architectural planning.24 In buildings of the
were used
con
Hellenistic
(Fig. 6), questions
period, when such drawings
more
of
become
basis
the
considerably
applicable.25
cerning
geometric
plans
at the close of the Hellenistic
(1.2.1-2)
clearly
period, Vitruvius
Writing
describes Greek temple design process in terms of Tragic, or the creation
of a quantitative geometric
system, and SiaGeGi?, the placement of archi
Vitru
tectural elements according to that established geometry.26 While
vius's comments
statements
21. Korres's
pp. 79-80)
going back
(1994,
on Greek
scholarship
not be aware of the
might
attached
of esteem
degree
and his views,
to Korres
own
my
referenced
2005).
"genius" (Hurwit
the remarks of Korres
In
tically incisive,
that I invoke as a
and their implications
used
for
the
methodology
background
A at Kos. To
in my
of
analysis
Temple
be clear, I in no way draw any meaning
ful comparison between Temple A and
greater
of a different
era. The
environ
architectural
(1972), in
of the Asklepieion
analysis
both a proper
trigono
Lacking
and convincing
identi
analysis
metric
of salient
fication
structures
to relate
tended
features
architectural
to his
geometry,
proposed
that the sanctuary's
suggests
eras were
in
from various
lines
to one
established
another
at
through
related
angles
sight
to the
section." He does not
"golden
an
A. See
of Temple
attempt
analysis
Doxiadis
1972, esp. pp. 125-126,
fig. 77.
its markedly
and
sophistication
is an expression
the Parthenon
details,
of a completely
different mentality
from what we find in Temple
A, and
the product
Similar
pp. 79-80.
toward the
be directed
his
pertaining
Doxiadis
are characteris
study
and it is these remarks
in this
in execution
may
of Greek
cluding
at Kos.
to
With
1994,
to method
carry
ments by C. A. Doxiadis
view,
the Parthenon.
22. Korres
practice,
implications
of ancient
analysis
and not to the
temple architecture,
of the Parthenon
architecture
per se.
study
referred
Jeffrey Hurwit
ological
for any geometric
that
criticisms
that comes
something
set
across
in less formal
particularly
a recent
In an aside during
public
tings.
in Chicago,
Institute
lecture at the Art
for example,
as a
Korres
pertains
issues
(1923a, 1923b). Readers
architecture
discussion
lowing
similar misgivings
at least as far asWilliam
with
represent Hellenistic
comprehensively
reflect
Bell Dinsmoor
less familiar
cannot
fol
is
advocates
"a general
architects
exploited
rule
[that]
geometry
... but not
details
for the
unless
of whole
buildings
composition
or
con
were
concentric
they
partially
own
in
Wilson
centric
Jones's
plan."
of such complex
geometry
acceptance
and numerical
ings and other
in turn, elicited
to material
in circular
systems
structures
(2000b)
doubts
extending
of the Roman
2001.
e.g., Yeg?l
24. A particularly
in favor of detailed
period;
forceful
architectural
build
has,
even
see,
argument
draw
for at least one Classical-period
ings
Athenian building, the Propylaia, is
Dinsmoor
on
the
plans
Jr. 1985.
introduction
in Greek
1997,
berger
25. For
For
and
views
opposing
role of drawn
architecture,
p. 83.
the development
see Hasel
of scale
plans during theHellenistic period
and alternative
design
In support of his theory for
in the 5th
"facade-driven"
Doric
design
b.c., Mark Wilson
(2001,
Jones
century
23.
p. 678)
ancient
for resolving
in earlier
modes
periods,
pp. 51-67.
26. For
complexities
of architectural
see Coulton
1988,
Vitruvius's
use
in this passage,
p. 217.
of Greek
arising
from
terminology
see Fr?zouls
1985, esp.
IDEA
AND
VISUALITY
IN
HELLENISTIC
ARCHITECTURE
567
his stated reliance upon Greek architectural writers arguably merits con
into the geometric
of Hellenistic
tinued investigations
underpinnings
to
In
Vitruvius's
adherence
addition,
ap
apparent
grid-based
buildings.
proaches in Ionic temple design27 might elicit inquiry into procedures that
he does not elaborate upon: in the Doric order, where intercolumnar spatial
contractions do not lend themselves to an orthogonal grid, how might the
of taxis differ?28
geometric constructions
a
the Parthenon will continue
furthermore,
privileged monument,
to be a favored object of attention for numerous
lines of inquiry despite
of particular approaches. Dating
from the 19th century
condemnations
are
re
too
volumes
of
onward, however,
many
archaeological
published
we
ports with scientific measurements
pertaining to buildings about which
As
still know
relatively
electronic
little. To allow these to gather dust or occupy unused
space, instead of reaping what the laudable efforts of
storage
their excavators can tell us about ancient
design, will benefit
nor architectural historians. Furthermore,
accusa
neither archaeologists
tions of "intellectual totalitarianism"29 directed at proponents of geometric
architectural
serve
only to curtail productive discussion.
analysis could
as ra
Rather than framing various outlooks as scientific or mystical,
tional or obsessive, we might
instead see observations
such as those of
to reevaluate the methodologies
in
Korres as an opportunity
employed
and geometric
analyses. In addition, an inclusive view may
proportional
us
to methods
that allow for scientifically sound analyses that, in turn,
open
a
our
of Hellenistic
solidify
understanding
temples. Finally,
responsible,
and
mathematically
rigorous,
computer-based
approach to geometric
us build upon and refine the criticisms,
analysis will help
tations of similar studies.
rules, and expec
The present study uses analytic geometry and vector-based AutoCAD
of the design of
(or CAD) software to analyze the geometric underpinning
at Kos. In the course of this analysis, I also consider
Temple A
questions
the perceived
limitations of studies that attempt to unveil
surrounding
hidden numerical and geometric
systems. In order to avoid the inevitable
distortions of proportional
and geometric
that look correct
relationships
on
a plan drawn to reduced scale, my
only when overlaid
study instead
on the
measurements.
relies
In
other words,
directly
buildings published
27.
Howe
the comments
See
in Howe
pp. 5,14,149.
28. See Vitr.
expresses
tradition
his
of Thomas
and Rowland
1999,
where
4.3.1-8,
indebtedness
he
to the Ionic
of
by charac
as deficient,
interaxes
issue of columnar
Hermogenes
the Doric
order
terizing
leaves the
on elevations
and focuses
unexplained,
at the expense
of any discussion
of
of
Jones's related notion
plans. Wilson
"facade-driven"
Doric
design
(2000b,
pp. 64-65; 2001) is discussed below; see
also n. 23,
above.
29. Korres
1994,
p. 80.
the proposed geometric system is now mathematically
verifiable rather than
we
is
in
and
So
that
intuitive,
may furthermore
computation.
grounded
ensure both mathematical
accuracy and the relationship between the nu
systems and the concrete, graphic form of the revealed geometry,
the calculations have been verified through the use of AutoCAD.
CAD
is not a requisite for this study, but merely a convenient
tool that may
merical
allow
researchers
and
readers
a
simpler
recourse
to
the measurements
of
in an architectural
proposed relationships
tions themselves that demonstrate
form; it is ultimately the calcula
the geometry. This combined Cartesian
carries the potential of standardization
and computer-based
method
for
future studies, allowing for a truly scientific approach inwhich results may
be replicated to confirm their veracity. Provided that an analysis such as
this one relies upon previously published numbers rather than ones own
we may now set aside
measurements,
suspicions of personal agenda and
in the objectivity of the process.
have confidence
R.
JOHN
568
SENSENEY
ANALYSIS OF THE BUILDING
The
Metrology
Before
dimensions
revealed through analy
discussing the nonorthogonal
should consider the temple s general measurements.
From the 5th
was
a
common
rule of thumb that the width:length
century onward, it
ratio of a Doric
should match
temples plan (including the euthynteria)
sis, we
on the short and
long sides of its peristyle.30 With
rear and eleven along its flanks,
its
front
and
along
Temple A
no
appears to be
exception (Fig. 10). In plan, the temple's overall dimen
sions are 18.075 x 33.280 m,31 a differential of only 0.4% from a proper
the number
of columns
six columns
as a 0.143 m reduction of the overall
simple adjustment, such
or a 0.078 m increase in the width, would result in a
length
perfect whole
6:11 ratio. A
ratio.
number
in
Scholars usually account for such "errors" by citing constructional
as well as centuries of exposure to the ele
exactitude and adjustments,
ments.32 Other
the temple might
slight irregularities found throughout
the theoretical design and
support this notion of a difference between
the actual built form (Fig. 5). For example, there are slight variances in
the thickness of the eastern and western naos walls (1.028 and 1.016 m,
to the
respectively) and in the distances from the exterior of these walls
edges of the stylobate (3.313 and 3.380 m, respectively).33 As
naos is not centered on the
stylobate.34
a result, the
over
and deterioration
factors such as imperfect masonry
Although
for such disparities,
additional
consid
time are plausible explanations
erations deserve emphasis. If it is the architect's design to begin with a
6:11 plan, other features might
the maintenance
of
complicate
as the construction progresses.
in
the
final
built
form
perfect proportions
In the end, there will be a set of measurements
that are necessarily inter
as
of
the
and
the overall dimensions of
such
the
widths
related,
krepidoma
proper
30. See Coulton
Wilson
1974,
on
pp. 62-69;
Jones 2001, p. 694.
31. Schazmann
and Herzog
1932,
in courses
pi. 2.
32. For
ence
the architect
Wilson
and
the final
see
product,
Jones 2000b, pp. 11-14; Dwyer
p. 340.
33. Schazmann
2001,
pi.
and Herzog
1932,
34. The
reason
result
excavators
of Temple
A
is a
lack of symmetry
of earthquakes
that have shifted
that
the entire
an
and pronaos
eastward,
that I find unconvinc
explanation
see Schazmann
ing;
and Herzog
1932,
on
on-site
there
6.
Based
p.
my
analysis,
are differences
in the limestone
foun
dations
sides
on
the eastern
of the naos. While
and western
the masonry
that are roughly perpendic
In addition,
the
continue
tendencies
divergent
raised foundations
where
of the naos
the
separate
ing the
should
crews were
limestone
indicate
responsible
foundations
that
for
lay
on either
than
side of the temple. More
plausible
the eastward
shift of the entire celia is
that one
in
crew
establishing
or
stylobate,
resulting
committed
the eastern
possibly
in a distance
a minor
limit
error
of the
the euthynteria,
from the celia
is
edge of the euthyn
and southern
sides,
to 4.368 m on the eastern
the western
m was
the eastern
would
celia
axis of the
central
that
originally
side as well,
be a more
if the entire
difference
on
to the outer
opposed
side. If we maintain
4.435
itself,
that found
less than
side. This
as
into
m
interpretation
distances
supported
by the nearly equal
of 4.43 and 4.435 m from the naos
teria on
the two separate
approaches
at a line west
of the central axis
The
is 0.067
the western
walls
of the naos.
this
naos
that
on the western
side are tighter
joints
than those toward
the east. These
meet
2.
in courses
to these walls.
ular
the problem
of the differ
the abstract vision of
between
side runs
the eastern
of
that are parallel with
the long walls
the naos, that on the western
side runs
approximately
intended
for
the result
balanced
originally
than
design
on the
lay
in its present
temple
I therefore
favor
dimensions.
human
causes for
to natural
opposed
in the
the lack of symmetry
temple's
measurements.
Such errors can and do
error
occur
as
in the
laying of foundations,
of elements
the placement
affecting
the superstructure.
in
IDEA
AND
VISUALITY
IN
HELLENISTIC
ARCHITECTURE
569
14.666 M = 45 F = 24 T
4^
i-4
o
Uh
10m
Figure 10. Restored plan ofTemple A,
with
axes
measurements
(M
=
meters,
of the colonnade
F = Doric
T = triglyph width modules)
feet,
SENSENEY
R.
JOHN
57?
in turn relate to the sizes of the paving slabs and the
the stylobate, which
area where the relative propor
spacing of the columns they support. The
is the conversion from
tions of the various parts are subject to modification
the abstract units of the drawing board (such as 6 x 11) to actual metric
must be privileged
values. In determining
specifications, certain distances
while others must be adjusted to the space allotted them. Considerations
of the paving slabs, for example, may
such as the specific measurements
a
ultimately result in slight departure from the integral proportions of the
s
architect
original drawn plan.
One method of accounting for the overall and individual dimensions
of a building is a metrological
analysis. A recent study proposes that the
architect of Temple A first worked out the overall dimensions
according
were the usual corner
to a specific metrological
system.35 Only thereafter
to
of the Doric order worked out, resulting in adjustments
contractions
of the theoretical plan. This theory, however, relies upon
the dimensions
the
the identification of a 0.305 m "foot" as the common unit underlying
no such unit of
system. Simply put, there exists
temple's metrological
measurement
in the ancient Greek world, a fact that the theory's authors
in our understanding
of
contend with by advocating greater flexibility
Greek metrology.36
Instead of suggesting
issue of commensuration.
we may consider the
Jones
specifically, Wilson
new units of measurement,
For Doric
temples,
exam
system, at least for 5th-century
a
to this theory, the width of
standard triglyph expresses
ples.37 According
the module that establishes commensurability
throughout various elements
itself commonly corresponds to a
of the building.38 The triglyph module
a standard foot (e.g., 25 or 30), with a dactyl equal to
5-dactyl multiple of
standards.39
1/16 of a foot in accordance with Greek metrological
makes
a detailed
case for amodular
for the remains in situ are available for the
InTemple A, measurements
western half of the columns on the rear
the
and
central columnar interaxis
of the stylobate, aswell as four columns along the western lateral colonnade
m for the missing
eastern half
(Fig. 5). At the rear, the addition of 5.793
+
m
+
a
14.666
for
in
of
the entire
results
3.080
5.793
m)
(5.793
length
axis (Fig. 10). For the long sides, the temple's excavators posit columnar
of
interaxes of 3.05 m based on the remains in situ and a consideration
0.61 and 0.915 m, respec
the triglyphs and metopes, which measure
one
of 3.034 m (see Fig. 5)
interaxis
the
Thus
preserved
tively (Fig. II).40
would represent an unintended departure from the theoretical constant of
3.05 m, and we may thereby restore the theoretical lateral axes, excluding
the contracted corners, to a length of 24.4 m (8 x 3.05 m), as in Figure 10.
and the 14.666 m
the 24.4 m axes of the lateral colonnades
Therefore,
axes of the front/rear
respectively,
would
of a value equal to 0.61 m
35. Petit andDe Waele
36. Petit
colonnades
and De Waele
37.Wilson
1998.
1998,
esp.
an earlier essay, J. J. de
Jong
p. 62. In
to have
the measure
claims
analyzed
ments
of Temple
A, but offers no dis
or results
to his anal
cussion
pertaining
ysis;
see de
Jong
1989,
equal 40 and 24
(Fig. 10).41
esp. p. 104, fig. 3.
the possibility
have endured
author's
response
integral units,
Jones 2001. Regarding
that
into
comments
to Coulton
such
a
could
system
see the
later periods,
on p. 697, n. 107 (in
Jones 2001.
39. Wilson
Jones
2001,
frieze;
1932,
0.611
esp. p. 690.
measurements
are based
of the
surviving
fragments
see Schazmann
and Herzog
three
pp.
10-11.
41.24.4/40
1983).
38.Wilson
40. These
on
m.
= 0.610 m; 14.666/24 =
IDEA
AND
IN
VISUALITY
HELLENISTIC
ARCHITECTURE
571
.345fr
.960
v
*
1.5r
? .610 *
.803
\\\\ \ MI
<--1.056-5>j
IM I M
Hl
3.05 = 5 T
<?1.270-->
HS?1.515-3H<S-1.535?-3H
.358'
.355
5m
0
Figure 11. Restored elevation of
lateral colonnade of Temple A, with
measurements
in meters
width modules
(T)
and
also measure
0.61 m.42 A
Significantly, Temple As triglyph widths
shows that this value equals 30 dactyls of a 0.325 m
simple calculation
triglyph
"Doric"
shares a 2:3 relationship with
the
triglyph width
a 1:5 ratio with the average interaxial
of
the
spacing
and a 1:24 ratio with the axis of the facade colonnade?
foot.43 This
standard metope,
lateral colonnades,
all typical proportional
relationships
is
It
also
10,
ll).44
(Figs.
interesting
42.
pp.
and Herzog
Schazmann
combined
1932,
10-11.
43.0.610
from
m/30
= 0.02033
m.
Since
foot divides into 16 dactyls, 0.02033 m
x 16 = 0.325
m.
Varying
between
0.325
and 0.329 m, the Doric foot has been
known
since Wilhelm
study
D?rpfeld's
of
the late-5th-century
(1890)
inscrip
tion relating
in
the expenses
involved
the construction
of the Erechtheion,
a
and
with
measurements
various
buildings
Attica.
throughout
tions ofWilliam
who
coined
firmed
Wilson
Bell Dinsmoor
term Doric
of 0.326
m.
(1961),
con
foot,
See
also
Jones 2000a, p. 75; 2001,
p. 689. The
Salamis,
sent a
the
a value
taken
on the
Acropolis
The
investiga
metrological
previously
system based
relief
from
to repre
thought
on a 0.322 m foot
according toWilson
that these distances
Jones's study
of 40 and 24
to the measurements
according
of
Ifigenia Dekoulakou-Sideris
has now
Wilson
system
been
(1990),
shown
convincingly
by
Jones (2000a) to represent a
based
on a 0.3275
to 0.3280
Doric foot. For the divisibility of
the triglyph module into 20,25, 30,
etc., dactyls,
p. 690.
44.Wilson
seeWilson
Jones
Jones 2001.
2001,
m
JOHN
572
R.
SENSENEY
to precisely
75 and 45 Doric
feet.45 In
triglyph modules
correspond
to
of
the
actual
dimensions
the
drawn
the
building and
translating
plan
its features, then, it is reasonable to theorize that the architect may have
the colonnades
of the facade and rear, establishing
their axes
privileged
a
of 45 Doric feet. Through
this magnitude,
3:5 ratio finds the 75-foot
for the axes of lateral colonnades
measurement
(Fig. 10). This latter di
each of which
subdivides
into eight intercolumniations,
two
into two half triglyphs, one whole
and
metopes
triglyph,
(Fig. 11).
the distance separating the end columns of these axes es
Furthermore,
tablishes the measurements
for the contracted corners, and the remaining
mension
divides
of the facade and rear colonnades
three interaxial distances
to the criterion
according
the dimensions
of incremental widening
could be set
toward the center. In
slabs in accordance with
of the individual
paving
of the stylobate are es
spacing, the total dimensions
of
the
and
and
the
widths
stereobate
tablished,
euthynteria are set according
to the remaining distance necessary to maintain
the 6:11 ratio of the over
varying
this irregular column
all plan.
To insist upon this explanation, however, is to treat Temple A as we
one more
have the Canon of Polykleitos,
plausible theory
resulting in yet
that can never be proven. There are too many types of metrical units, too
and too many rationales for us to induce conclu
many ways of measuring,
a
sively
guiding metrological
is not so much a reasonable
system. What
is lacking in such approaches
to a pattern of numbers, such
correspondence
ratios, but rather something outside of the buildings
themselves that might verify the significance of those numbers, such as a
source or a basis in Euclidian geometry. While
Vitruvius validates
primary
as whole-number
the case for how this system relates
of the triglyph module,
to large-scale distances must remain provisional;
in this regard, we may
40
units
of
the lateral colonnades
for
the
wonder,
integral
example, why
as
corner
In
the
modular
interaxials.
exclude the
addition,
theory
applied
to Temple A cannot address a central aspect of design that is unrelated
to the trabeation: the placements of the walls of the naos and pronaos in
of
relation to the overall plan. We must therefore explore other methods
the relevance
analysis
in seeking
buildings
design.
The
Theoretical
to substantiate
Plan
a theory for the
underlying
and
Standards
for
logic of the
Accuracy
it is not enough to merely draw geometric
shapes
emphasizes,
to a scale of 1:100.46 Instead,
over the features of a
proposed
plan reduced
must be verified through analytic geometry.
In other
geometric
shapes
to
a
the elements they
words,
drawing should correspond
superimposed
As Korres
co
not
through Cartesian
overlap
only visually, but also mathematically
and
with
lines
ordinates with
expressed algebraically,
interrelationships
described in terms of slopes and curves with coefficient-based
formulas,
such a strict standard places a damper on continued
for example. Naturally,
to
ancient architectural plans, but the gains in
about
theorize
attempts
are arguably well worth the endeavor.
credibility
45.14.666 m is only 0.026 m
(or 0.18%)
in excess
of 14.640
m.
14.640/24 = 0.610 m; 14.640/45 =
0.325 m; 24.4/40 = 0.610 m; 24.4/75 =
0.325
m.
46. Korres
1994,
p. 80.
AND
IDEA
IN
VISUALITY
ARCHITECTURE
HELLENISTIC
573
a
point of emphasis has been that the degree of accuracy in
must
in
the
actual
the
tolerances
theoretical
geometry
approximate
plan's
the accuracy of the built form, however, elicits
construction.47 Determining
a bit of circular reasoning, since many of its elements must be measured
Another
same theoretical
to
plan that its author attempts
support.48
against the very
This need not be the case for every feature, however. In Temple A, for ex
columnar interaxes
ample, there exist slight variances in the noncontracted
such as 3.050 m and 3.034 m,49 that are likely to
of the lateral colonnades,
relate to a theoretical constant rather than an intentional irregularity.
On a larger scale, we may note that Temple As naos (9.272 m wide,
not in the exact center of the stylobate (15.965 m
including itswalls) lies
0.067 m off axis (Fig. 5).50 Given
the gen
wide), but an imperceptible
for symmetry even in conjunction with "optical refine
eral predilection
one
be hard-pressed to argue the plausibility of this feature as
would
ments,"
intentional. From the outer wall to the edge of the stylobate, the dis
sides of the naos measure
tances on the western
and southern
3.375 m,
and the diverging measurement
eastern
respectively,
side
an
represents
error
of
ca.
3.380
and
of 3.313 m on the
1.98%.51
Still, it may be inadvisable to isolate this error in the eastern pteron,
since the final built form is the product of multiple
interrelating compo
nents. The most conservative approach would be to calculate the percentage
of tolerance according to the entire width of the stylobate. This calculation
should pertain to the theoretical plan rather than the actual plan, with the
m from the eastern
only difference being the addition of the "missing" 0.067
side of the temple, resulting in awidth of 16.032 m for the stylobate and
an overall width of 18.142 m (see
the
1). In order to maintain
Appendix
strictest possible tolerance in my analysis of this theoretical plan, I will
cap the standard for accuracy at 0.42%
discussed here.52
in accordance with
the divergence
in the
It is important to emphasize
that this addition to the width
not
is
in
"stack
the
deck"
for
the
and
does
any way
slight,
plan
results of the analysis that follows. Instead of adding 0.067 m to the nar
rower side, we may be justified in adjusting for symmetry in the theoretical
the actual width and shifting the naos to the
plan either by maintaining
center (see Appendix
2),53 or by reducing the width of the naos by 0.067
m in order to balance the sides
3). As the calcula
evenly (see Appendix
2 and 3 demonstrate,
the results for each of
tions provided inAppendixes
theoretical
these alternative
47. Korres
48.
80),
theorists
methodological
to which
degree
(whether
whatever)
p. 79.
words
(1994, pp. 79
"refuse to be bound by the
that the
requirement
1994,
In Korres's
a theoretical
metrological,
approximates
should be no
definition
or
geometric,
to the actual
less than the de
building
the build
of accuracy with which
was constructed
in any
(which
ing itself
gree
case
such
theorists
ceiving)."
49. Schazmann
pi.
theoretical
are
plans
of con
incapable
surements
and Herzog
1932,
plane of the walls
51. 0.067/3.380
the strict tolerance
see
and others,
and Herzog
m
52. 0.067/16.032
53. This
and Herzog
1932,
this and all of the follow
Schazmann
p. 6, pi. 2. For
measurements
ing
naos, dimensions
under
Schazmann
2.
50.
remain well
of the naos
and pro
to the outside
relate
rather
m.
than
For
the
socle.
these mea
tent with
vators,
who
the result
the entire
solution
the views
Fig.
1932,
= 0.42%.
would
5, and
pi.
2.
be consis
of Temple
A's exca
as
the displacement
explain
of an
that shifted
earthquake
and
celia; see Schazmann
1932, p. 6. For the problems
Herzog
with
this theory, see n. 34, above.
574
R.
JOHN
SENSENEY
of 0.42%, and in fact produce results closer to 0% in the case of several
dimensions. The rationale for privileging the theoretical plan inAppendix
1,
not
to
most
to
is
the
rather
but
therefore,
convincing analysis,
adjust
provide
for symmetry in away that most thoroughly relates to the measurements
of
the actual plan; when 0.067 m is added to the eastern side of the stylobate,
the eastern and western
sides of the plan equal one another as well as the
side behind the southern wall of the naos.54
The theoretical plan of 18.142 x 33.280 m solves one problem but
leaves another unresolved. On the one hand, our expectation for integral
in the overall plan is satisfied, since the theoretical plan results
proportions
in a nearly perfect 6:11 form.55 On the other hand, the rationale for the
naos and pronaos remains unclear. While
the distance of
placement of the
an equal
the walls of the naos from the edge of the euthynteria maintains
1:1:1 ratio on the sides and rear, the space before the antae of the pronaos
shares no integral relationship with these distances.56 Nor
in the
discern any meaningful
proportional
relationship
dimensions
of the naos and pronaos.57 As I argue below,
a
servable correspondences
pertains to process of design
arithmetical
may we
readily
length-to-width
this lack of ob
grounded not in
but rather to a
relationships
orthogonal dimensions,
procedure executed with the rule and compass. This geometry
between
geometric
is quite simple, though it requires some detail and rigor to substantiate
it. In the following
section, I demonstrate how we may recover the plan's
specific design process
through
analytic geometry.
Analysis
Geometric
To properly analyze the plan, I rely on simple calculations based on the
of Temple A, with the only adjustment being a
published measurements
centered naos, flanked on either side by equal distances of 0.380 m from
of the naos to the edges of the stylobate.58 All relevant di
in the plan are mathematically
verified and expressed
agonal relationships
in the footnotes with reference to a single quadrant of a two-dimensional
1-3 with accompanying Fig
coordinate system. In addition, Appendixes
ure 23
the
and
tolerances
that demonstrate
equations,
provide magnitudes,
the outer walls
measurements
for all three theoretical plans
proposed geometry according to
described in the prior section. Whenever
relevant, the location of features
will be given as Cartesian coordinates, inwhich the southeastern corner of
the euthynteria's outer edge is at the origin 0,0, and the extreme northwest
54. The
m
4.430
the exterior
of the naos
wall
euthynteria,
to the 4.435
side measures
southern
from
to the outer
which
56. The
face of the
edge
of the
is
essentially
equal
measurement
of the west
ern side (see Fig. 5). Adding 0.067 m to
the narrower
bate,
eastern
therefore,
ratio
side of the
produces
for all three sides.
a
stylo
1:1:1
nearly
of only
0.02 m
33.280 m length.
naos
to the outer
teria
is 6.797
find
from
the plan's
distance
and
the pronaos
it preserved
be
Here,
the pro
whose
tolerance
would
from
integral
relationship
rear distances
ratio
I can
between
the
to the
euthyn
teria (4.435 m) and that of the front
m), with
(6.797
ance of 2.1%.
an
implausible
overall
57. The
naos
and pronaos
the closest
edge of the euthyn
m. Of these two measure
the closest
is a 2:3
were
facade,
m. The
ments,
from
edge,
5.742
lateral
55. (18.142/6) x 11 = 33.260, a dif
ference
distance
to the
stylobate
on the northern
toler
acceptable.
58. Thus,
the exterior
long
4.435
outer
m,
and 4.435
above.
integral
of 1.9%
the distances
m;
x 22.053
ratio
is again
and each
of the euthynteria
than the present
see
Fig.
m.
is 3:7,
un
between
of the naos
walls
edge
rather
of the
dimensions
are 9.272
5. See
equal
4.368
also n. 34,
AND
IDEA
IN
VISUALITY
m
Figure 12. Restored theoretical plan
of Temple A with geometric under
ARCHITECTURE
HELLENISTIC
575
M,M,M,UP
I II
pinning
corner at 18.142,33.280.
In addition to consulting the calculations provided
here, readers may replicate the proposed findings using CAD software. The
results of the following analysis were verified with AutoCAD.59
A significant result of this analysis emerges from the location of a
the outer corners of the antae and
theoretical central point from which
corners
are
the outer back
of the euthynteria
and thereby
equidistant,
The
of this cir
share a theoretical circumference
12).60
pertinence
(Fig.
cumference to the design process is supported by the rational relationships
it shares with other features. The overall width of the temple shares a
3:5 ratio with the diameter of the theoretical circumfer
whole-number
ence, with a tolerance of less than 0.1%.61 If caution advises us to consider
this ratio a possibly
59. For
all magnitudes
consistency,
to the millimeter.
are rounded
60. From
plan's
long
a
located on the
point
central axis at [9.071,
12.101], a theoretical line to [0, 0]
measures
is the square
root of the sum of the squares of 9.071
and
12.101.
15.123
From
m, which
the same
coordinates
on
the central
corner
sures
m.
nal
15.124
corner
a theoretical
axis,
the external
result, there is an additional whole-number
fortuitous
of either
line
to
anta mea
the exter
Specifically,
anta is at
of the western
[13.749,26.483]. Through simple sub
traction,
distances
from
we
find
of 4.678
[9.071,12.101].
these
m
at
coordinates
and
The
14.382
m
sum of these
+ 15.124 m) finds a
figures (15.123 m
theoretical
diameter
of 30.247
see
m;
Appendix 1.
61. (30.247 m/5) x 3 = 18.148 m,
a difference
overall
plans
therefore
of only
width
a tolerance
seeAppendix
1.
6 mm
from
of 18.142
m,
of less than
the
and
0.1%;
576
JOHN
R.
X/
SENSENEY
_'
I-'
~
r
r
_
....
__
0__
<'^)
_--_
~~~10m 0
that should give pause to our skepticism: the distance from
proportion
to the plans southern edge and the overall
the theoretical circumcenter
width of the temple share a 2:3 ratio, again with a tolerance of less than
with a baseline x-x
of
0.1%.62 We may illustrate this correspondence
3 units drawn across the entire width of plan at the ordinate correspond
a line
center point of the circumference,
along with
ing to the theoretical
y-y
of 2 units drawn from the circumcenter
to the edge of the euthynteria
(Fig. 12).
Figure 13. Restored theoretical plan
of Temple A with geometric under
pinning
62. (18.142 m/3) x 2 = 12.095 m,
a difference
ordinate
tolerance
of only 6 mm
from the
at 12.101 m, and therefore
63. The
we may express this
Geometrically,
relationship through the algorithm
of two circumferences with a radius of 2 units, each centered on either
terminus
of baseline
centered
at the middle
x-x
is
(Fig. 13). The larger circumference, which
of x-x\ intersects with the smaller circumferences
outer corners of the euthynteria. Both the
exactly at the points of the
are
for
and
mathematical
significance of these intersecting points
proof
ratio
of
of
the diameters
the smaller and
revealed by the whole-number
a tolerance of less than 0.1%.63 When
larger circles, equaling 4:5 with
in relation to the overall width of the temple (the 3 units of
conceived
this final dimension
x-x),
brings the geometric
principle underlying
the architect's
system
into striking
clarity:
the 3:4:5
dimensions
of a
a
of less than 0.1%.
diameter
theoretical
circumference
larger
(see n. 60, above),
equals
which
has
of the
30.247
m
a ratio
of 5:4 with 24.202 m (the diameter cor
to the radius of 12.101 m in
responding
x-x
from the baseline
the y dimension
to either back corner of the
euthynteria
at [0, 0] and [18.142, 0]), with an error
of less than
0.1%
calculated
by the
difference divided by the magnitude:
=
(30.247 m/5) x 4 24.198 m, a dif
ference
of 4 mm
from
24.202
m.
=
(24.202 m/4) x 5 30.253 m, a differ
ence
of 6 mm
from
30.247
m.
IDEA
AND
IN
VISUALITY
HELLENISTIC
ARCHITECTURE
577
X
0
-0-__
0
Os__
Figure 14. Restored theoretical plan
of Temple A with geometric under
pinning
_
1~~~~~010m
K^)0~~~
circumscribed
Pythagorean
triangle.64 In effect, this geometric form ABC
lies at the heart of the design, with the compass centered midway
along
its hypotenuse
and the circumference
coinciding with its angles and lines
(Fig. 14).
We
should understand
as
based construction
this geometric underpinning
interdependent. Even in the Roman
and its compass
period, architects
a square, let alone aT square. Instead, the method
of
a
lines
with
the
rule
producing perpendicular
highest precision employed
and compass, with straight lines drawn through circumferential
intersec
tions in the same manner
that is revealed through this analysis of Tem
ple A.65 It has already been observed that Roman buildings such as amphi
theaters would commonly begin with a Pythagorean
triangle, and arrive at
did not work with
the final design using the compass through various stages.66 This Roman
use of the
similar manner of
Pythagorean
triangle recalls a conceptually
64. The
theoretical
circumference
diameter
of the
30.247
m
larger
equals
of
(see n. 60, above). The magnitudes
or
18.142 m (the plan's overall width,
baseline
24.202 m (the diameter
x-x),
to the radius of 12.101
corresponding
in the y dimension
from the baseline
x-x
to either
back
corner
m
of the euthyn
teria at [0,0] and [18.142,0]), and
30.247
m
=
3:4:5, with
a maximum
error
in any dimension
of less than 0.1%.
65. See Roth Conges 1996, pp. 370
372; Taylor 2003, p. 38.
66.Wilson Jones 1993, pp. 401
406,
figs.
13,15,16.
57?
JOHN
-- ------ -- ----- ------
R.
SENSENEY
--l ------ --------
Figure 15. Proposed general con
struction of a 3:4:5 Pythagorean
to circumferential
triangle
according
with
intersections,
dashes
indicating
the baseline
Ionic column bases that was familiar to Greek architects as
constructing
as the Archaic
early
period.67 The transparency of the plan of Temple A
us
to
allow
understand
how aHellenistic
architect might construct the
may
a
Pythagorean
triangle itself. The formula appears to consist of baseline of
6 units, upon the center of which a compass with a radius of 5 units is set,
and on the ends of which are set compasses with radii of 4 units. By these
could be joined to form the perpendicular
lines
means, the intersections
of the triangle's sides as well as the diagonal of its hypotenuse
(Fig. 15).
In the case of Temple A, it appears that the larger circumference
of this
to
construct
extent
in
remained
define
the
of
the
pronaos
geometric
place
at the antae (Fig. 14).
To dismiss these results would
now
us to
a confluence
require
posit
of three separate coincidences
of whole-number
(3:4:5) with
proportions
a maximum
error that is consistent with the strictest possible
standard
in the actual building, along with a fourth (and
an inte
more
that these proportions
coincidence
engender
conspicuous)
to
Greek
of
central
mathematics.
More
form
gral geometric
significance
a
the
of
over,
circumscription
triangle graphically expresses
Pythagorean
bisectors meet at a circumcenter
Tha?es' theorem: three perpendicular
of tolerance
observable
located on the hypotenuse, which runs the length of the circle's diameter
that the Pythagorean
triangle
(Fig. 16).68 In turn, the basic proportions
center point and the di
of
establish
location
the
theoretical
the
yields
ameters
(Fig. 15). In the face of these internal
to Euclidian geometry, the balance
their
and
pertinence
correspondences
on the side of in
form
this
concerning
obviously falls heavily
resulting
of the circumferences
design rather than chance.
There is yet another integral proportion that completes the geometric
of the temple's plan. The diagonal across the naos from
underpinning
67. For
and
column
pp.
126-129.
a
68. By definition,
Pythagorean
see Eue.
is a
triangle
right triangle;
Elem.
3.31.
69.Width
tentional
a 1:1
correspondence
including its external walls shares
a
difference of only 0.1%.69 From
with the total width of the temple, with
a theoretical central point located on the cross-axes of the naos, therefore,
corner to corner
the distance to either edge of the temple's width and each of the external
a circum
corners of the naos is essentially
equal. This congruency suggests
to the design of the naos, whose diameter shares a
ferential underpinning
the Pythagorean
triangle
see Gruben
bases,
1963,
including
15.572 m,
and length of naos
its walls
equal
respectively.
9.272
According
and
to
theorem,
then, we
Pythagorean
and
find
the
each
square
square root
the
of their
sum,
thus finding
18.123
m.
Ifwe take the 0.019 m difference
between 18.123 and 18.142 m (the
total adjustedwidth of the temple) and
divide by either 18.123 or 18.142 m, we
find
a difference
of 0.1%.
IDEA
AND
IN
VISUALITY
HELLENISTIC
010
ARCHITECTURE
579
0
Q
---=- --S---- ----
X
'-0^~~
:-
-~
-c
=- L d
- m
m
"S^~~~loZZ
Figure 16. Restored theoretical plan
of Temple A with geometric under
0
10~~~~~~~~~~~~~~~~~~~1
0 0t
pinning
the diameter of the large circle, with a toler
we
as a
If
accept these circumferences
(Fig. 17).70
guiding
method for the placement of features within the plan, their ratio would call
tomind Vitruvius s formula of 3:5 circumferences for the main proportions
whole-number
3:5 ratio with
ance of 0.1%
of plans in peripteral round temples (Vitr. 4.8.2).
One indication that the circumferences
here
geometric
underpinning
the ordinates
suggest
an intentional
is their planar interrelationship.
The distance
of their theoretical center points is 0.115 m.71 In
separating
a scale
are
plan, special markings
required to make this separation percep
tible (Fig. 18). Before considering why the architect might have centered
his compass at different points a hair swidth apart in his design, we might
consider
this separation in relation to the theoretical proportions
and ac
to which
it corresponds: the separation of these ordinates
tual dimensions
70. (30.247 m/5) x 3 = 18.148 m,
a difference of 0.1% from 18.123 m;
=
(18.123 m/3) x 5 30.205 m, a differ
ence
of 0.1%
71. The
cal center
from
30.247
coordinates
point
of the
m.
of the theoreti
larger
circle
are
[9.071,12.101]
the
smaller
(see n. 60,
above).
For
of the
circle, the coordinates
are [9.071,12.216].
center
The
point
sum
ordinate
here is determined
by the
of the center point of the naos and the
distance
of the naos from the south
outer
(15.572
edge of the euthynteria:
+ 4.43 m. For the distance
sepa
center
of
rating the theoretical
points
the larger and smaller circles: 12.216
= 0.115 m.
12.101
m/2)
580
-
R.
JOHN
--
SENSENEY
--
-0
--------\
---- - ---_
^=
=
Y-.
BiaS~~iiiiff~~ia1Q
lo
Figure 17. Restored theoretical plan
of Temple A with geometric under
pinning
represents a 0.38% difference, sowe remain within the strictest standard for
theoretical tolerances of 0.42% calculated according to the constructional
inexactitude found in the actual building.72
On
the other hand, the applicability of this standard here is dubious.
we cannot
the precise metrological
sys
Although
conclusively determine
tem
the
remains
fact
that
the architect or builders
underlying Temple A,
would have needed to convert any conceptual circumferential
geometry
to actual measurements
for orthogonal distances. After all, we cannot ex
pect masons to have laid out the building according to invisible circles with
an eye to
a shared theoretical center
maintaining
point. Due to such nec
in
the
essary adjustments
planning and building process, it is natural that
from original design elements are bound to occur. Since we
lack secure access to this intermediary
the
stage of metric
specification,
relevance of a precise calculation for the percentage of error in a common
deviations
center point (such as 0.38%) may be limited. Instead, we may conceive of
the divergence inmore experiential terms: in a building over 33 m
we
long,
find the two theoretical circumcenters
of the integrally proportioned
cir
cumferences
child's hand
at points only 0.115 m apart, or less than the
a
length of small
in relation to the distance from floor to vaults in the cathedral
72. As
relating
the widths
tion
bate),
of error
in the calculation
to the difference
of the ptera
to the entire width
the difference
of 0.67 m
(0.42%
of the
is here
in
in rela
stylo
calculated
to the
geometry,
according
complete
as
of
represented
by the diameter
the larger theoretical
circumference:
m = 0.38%.
0.115/30.247
IDEA
AND
IN
VISUALITY
1
?-DII
ARCHITECTURE
HELLENISTIC
zzzzzz
~-Q-)
I
--Q" /
EEEEz
\>QZ
581
oizzzzzzziq-;
Figure 18. Restored theoretical plan
of Temple A with geometric under
and
pinning
circumcenters
indicators
marking
iii
i
the
fc\7)
i
i
i
i
*
i
i
i
i^~^ i
10m
0
in Paris. In a structure where even the width of the stylo
of Notre Dame
bate is off by 6.7 cm, an additional inexactitude of 4.8 cm for an invisible
feature is insignificant, particularly when that feature was no longer relevant
during the actual building process.
The
Schematic
Plan
affords, I will
justification
Leaving aside the security that mathematical
now suggest
to
in
the
Hellenistic
which
this
relates
geometry
possible ways
the theoretical demon
architect s process of designing Temple A. Unlike
stration above, the following analysis takes into account the proportions
intention here is to explore further questions
of the actual building. My
to
the
design process, integrating what I hope is well-grounded
relating
the results of the above geometric analysis.
with
speculation
In designing Temple A, the architect would have needed to harmo
nize the 3:4:5 triangle underlying
the placement of the naos and pronaos
inmind how a compass is
with the 6:11 ratio of the overall plan. Keeping
that the simplest way of working with
centered, it isworth emphasizing
the tool is to conceptualize
circumferences
in terms of radii rather than
582
JOHN
'
R.
'
'
?'i K')l I?I tV
i
i
i ;
i ;
i ; r
SENSENEY
i ; i
i,
I?I
?
In this way, one need not resort to half-number
divisors, such
as 2.5, in order to create a whole-number
diameter such as 5 units. In
radii of 3, 4, and 5 on a baseline of 6, therefore, the architect
producing
would have created a 6:8:10-unit
this same divisor
triangle. Extending
to the overall plan, an additional 3 units in the y dimension
produces the
final 6:11 ratio of the temples plan, which repeats the 6 x 11 number of
columns for the intended colonnades and simplifies the process of
drawing
diameters.
by maintaining
integers.
This demonstration
of the architect
to circumferences
Figure 19. Restored theoretical plan
of Temple A overlaid with intersec
tions
of circumferences
with
3 units
s method
of locating the wall
still does not explain the rationale
termini according
behind where they were placed along those circumferences.
It is tempting
to suggest a
circumference-based
the architect
simple
algorithm whereby
out
x-x
have
worked
these placements. On the baseline
of 6 units,
might
center the compass on the termini and center,
drawing
radius. Repeat this procedure three times, each with
three circles of equal
radii of 3, 4, and 5
according to the cir
units, finding the location of the walls and corners
cumferential intersections (Figs. 19-21). Despite
the appeal of the resulting
to
it
would
be
inadvisable
this
plans, however,
procedure. As Korres
adopt
we cannot draw conclusions
on the basis
recognizes,
concerning geometry
of how that geometry appears to coincide with features when overlaid on a
scale plan.73 Rather, we must replicate such results mathematically.
Unlike
73. Korres
1994,
pp. 79-80.
radii
of
IDEA
AND
-NIo--
C-:o
/
/
/111.~-^
VISUALITY
-
IN
HELLENISTIC
_1_1...
~ I Ii I
..'. ..
-
/
.
I. . I
I
?
0^J)~~
tions
of circumferences
with
radii
of
4 units
583
\s
0 \
Figure 20. Restored theoretical plan
of Temple A overlaid with intersec
ARCHITECTURE
~lo10m
the case of the underlying geometry demonstrated
above, calculations do
away that satisfies the strictest
not verify the hypothesis
in
here
suggested
possible tolerance of 0.42% in the actual building.74
Still, even in cases where proposals hold up to such scrutiny, one
deserves recognition. There is, of course, a gap between our
of verifying the plan through analytic geometry and the ancient
of converting
the location of its features into magnitudes
for
consideration
method
method
74.
In the case of the 3-unit
radii
that
the naos
the cross-axis
from
are set 9.062
m
at [9.071,12.216].
we
corner
at [4.435,4.430]
dimensions
of 4.435
andjy
to calculate
a
m
of
diagonal
a difference
of 1.1%
showing
from the
9.062 m.
expected
In the case of the 4-unit
radii
8.961
m,
we may
reference
the line of
(Fig. 20),
either
wall.
That
of the
long pronaos
western
intersects with
wall
the central
m
of 4.636
erance
of the plan to the external
and the 12.101 m ra
a distance
in
resulting
the baseline
of 11.178
m
to the
intersection
in
= 4.6362
+
dimension
(12.1012
they
y2).
intersection
The western
wall's
with
the
lateral
as
23.360],
of 4.435
occurs
circumference
m
given
from
by
the outer
and
the 12.101
euthynteria
resulting
the baseline
at [13.707,
the wall's
in a distance
to the
distance
intersection
in the y dimension
is a tol
of 0.7%.
In the case of the 5-unit
radii
of the central
(Fig. 21), the intersection
anta
circle and the western
exterior
corner
is at [13.749,26.483],
of 15.124 m from
in a radius
(see n. 60, above)
12.101]
resulting
[9.071,
and a dis
tance of 14.382 m from [13.749,
If the circle with
12.101].
m
a radius
of
15.124
m
12.101], itwill intersectwith the line of
from
in the
theoretical
the anta
is centered
at the end of the
of the
edge
m radius,
of 11.259
m
of 0.081
from
of the naos
from
x
find
and 7.786
distance
given by
the midpoint
dius,
corner
sidered here: from [0,12.216] to the
naos
the distance
wall
the plan is symmetrical,
only
to be con
of the naos needs
Because
one
corners
as
at [13.707,23.279],
circumference
(Fig. 19), it has already been established
baseline
x-x
at [13.749,26.573],
at [18.142,
a differ
=
y dimension (12.1012 4.4352 + y2).
ence of 0.09 m from [13.749,26.483],
The
or an error of 0.6%.
difference
of these
intersections
584
JOHN
R.
SENSENEY
--r
I
I
rI
I
10om
the actual building. We might,
scale
therefore, ask how an architectural
in
would
have
been
created
the
Hellenistic
This
drawing
question
period.
is especially relevant to the planning of Doric
temples, where interstitial
contraction precluded convenient
slabs that ensure conformity to a grid-based
A reasonable answer in the case of Temple
intuitive process that begins with the initial
columnar
repetition
of uniform
paving
plan.
A, I suggest, lies in a simple
schematic sketch before the
the smaller
of the detailed drawing (see Fig. 22): (1) within
completion
rear
naos
at
set
exterior
of
the
the
lines
of
the
walls
the
and sides
circle,
with approximately equal distances to the outside edges of the overall plan
in accordance with the principle of symmetry; (2) where the lateral lines
same circle, set the spur walls
again intersect with the circumference of this
naos
and pronaos; (3) in conjunction with these same lateral
separating the
lines, set the antae at the intersection with the circumference of the larger
circle. In the drawing process itself, this result is most easily achieved in
away that is similar to what I describe above: first set the locations of the
s
corners and the antae
by establishing equal distances from the plan edges,
and then mark these points with the compass set on the termini and center
of the baseline x-x. In these ways, the logic of the overall design maintains
that are circumferential, which is in keep
symmetry with interrelationships
a process of
relies upon the rule and compass.
with
that
ing
drawing
Figure 21. Restored theoretical plan
of Temple A overlaid with intersec
tions
of circumferences
5 units
with
radii
of
IDEA
AND
IN
VISUALITY
-
HELLENISTIC
I- - -
I \
ARCHITECTURE
I
--1
585
--
Figure 22. Proposed geometric
underpinning of Temple A
If we
of a modular-based
again consider the hypothesis
metrology,
we can
on one manner
s
in
which
the.
speculate
plan designer might have
established
scale. Since the placement of features depends upon circum
considerations, while the production of elements such as paving
slabs must be related to orthogonal dimensions,
itwould appear that the
a fixed
in
the
the
scaling
drawing precedes
following way. In privileging
as 45 Doric feet for the colonnade axes of the front and
such
magnitude
ferential
the remaining elements in the drawing
rear, the architect could measure
and placements
of the walls and the varying
(such as the dimensions
of the individual slabs that make up the stylobate and steps)
dimensions
against these established distances and fix their sizes according to scale.
By its nature, this procedure would be inexact for two reasons. In the first
place, the expectation of symmetry in the final built form would dictate
naos walls to the
equal values for the distances from the exterior
edge of the
at
in
both
the
sides
when
and
fact
the
of
the drawn
rear,
geometry
stylobate
form would
show a very slight discrepancy between the lateral and rear
indeed, the separation of 0.38% in the centers of the theoretical
distances;
circumferences
75. Two
tect could
in which
ways
resolve
this
the archi
issue would
be
for the
(1) to center the compass
at a
smaller circumference
slightly dif
ferent location
discussion
(see
above),
a result of this very consideration.75
(Fig. 18) is likely to be
to measure
the
would
need
the features on the
Secondly,
plans designer
the
drawing surface by hand and convert them to varying values. Unlike
case with Ionic
a
the
varied
in
of
columns
Doric
temples,
spacing
temple
such as that at Kos dictated
that individual slabs could not repeat an
therefore, would need to be subdivided
prototype. Distances,
into varying units for the paving slabs in accordance with
the spatial
or (2) to
a
verbally
designate
larger
numerical
distance
for the area behind
established
the naos,
contractions.
and
subtract
this distance
the length of the walls
latter solution
pronaos. The
from
more
practical
especially
of verbal
of the
seems
both
and more
considering
probable,
Greek
traditions
in
specification
"incomplete
as discussed
preliminary
planning,"
by
Coulton
In either case the ad
(1985).
is very small, both
in relation
justment
to the
in
of 0.42%
tolerance
expected
the final
built
form
cal distance
it would
the original
scale
and
in the theoreti
correspond
drawing.
to in
dress
In the end, therefore, the measurements
would have needed to ad
the individual paving slabs in addition to the overall size of the
or
steps in this process,
stylobate
euthynteria. Because of the multiple
and the slight modifications
bound to occur in each of these steps, it is
not reasonable for us to theorize intended values for each element and
of the plan, given asmeasurements
down to the dactyl. Instead,
the significant result of this study remains the revealed correspondence
of the overall form to a rational, theoretical geometry
in which
the per
error
of
remain
within
the
strictest
centages
possible tolerance found in
dimension
the
actual
construction.
586
JOHN
R.
SENSENEY
CONCLUSIONS
at Kos suggests
A metrological
analysis of Temple A in the Asklepieion
that the triglyph module theory proposed byWilson
Jones for 5th-century
Doric temples may be applicable to this Hellenistic
example. This theory
cannot, however, account for the locations of features not associated with
the temples trabeation, such as the walls of the naos and pronaos. Since
was created in an era when the kind of drawn
plan described
Temple A
in Ionic temples,
is likely to have been already commonplace
by Vitruvius
we are
in
its
how
address
the
considerations
of
asking
justified
plan might
design particular to the Doric order, where transparent orthogonal relation
a
were not
grid
possible. A geometric analysis that
ships established with
to the methodological
issues
addressed by Korres demonstrates
responds
a
that
circumscribed Pythagorean
triangle forms the basis of Temple As
the placements
of the plans
of
the
problem
verifying
principal
rests
for
this
modular
the
evidence
system
geometric
solely upon
theory,
the internal, measurable correspondences
that conform to Euclidian norms.
Furthermore, we can replicate these results both by calculation and with
design,
in which
determine
circumferences
features. Unlike
the more
difficult
with the modular theory, we can speculate
axes
scale in the
that the colonnade
may have played a role in establishing
into
drawn plan, by allowing for the conversion of relative dimensions
CAD
software.
In combination
actual values for the building. The full implications of the results of this
a few observations
analysis cannot be explored in the present study, but
merit brief comment.76
the design process proposed here runs counter to the
cur
as well as
differing from
simple grid approach used in Ionic temples,
rent ideas about the way in which Doric temples were designed. Wilson
In its details,
Jones insists on the principle of "facade-driven" design for Doric temples,
in contrast to the "plan-driven" design for Ionic temples.77 In other words,
architects designed Doric temples strictly according to the commensuration
of elements in the facade, as opposed to the creation of a guiding plan that
the layouts of Ionic temples. Yet given the mixing of the archi
determined
tectural
orders
as
early
as
the
5th
century
b.c.?most
famously
witnessed
might question such categorical notions of mutual
exclusiveness, particularly in buildings as late as the Hellenistic
period. As
discussed above, it appears that the triglyph module may very well have
in the Parthenon?we
a
significant role in the design of Temple As facade. One might
played
wonder, however, why ancient architects who are likely to have been trained
in the details of both orders should necessarily have repressed planning
of a particular module. After all,
tendencies solely due to the employment
the very notion of mutu
demonstrated
has
Rowland
convincingly
Ingrid
an
to
of Vitruvius's
modern
transformation
be
"orders"
early
ally exclusive
notable
accommodate
like ancient buildings
themselves,
genera, which,
a discussion
omit
should
Vitruvius
That
of
interchangeability.78
degrees
of taxis in relation
traditions
to Doric
temples probably reflects his bias toward the
that formed the core of his architectural train
of Ionic design
s
ignorance
ing.79 If Vitruvius
of Doric
taxis stemmed
from
this limited
76.
In an article
in prog
currently
the results of the present
other considerations
analysis
along with
of ancient Greek
in the larger context
I assess
ress,
architectural
77.Wilson
2001.
78. The
rigidly
Jones 2000b, pp. 64-65;
notion
of the "orders"
defined
begin with
the milieu
continuing
tools,
drawing, masonry
of planning.
and methods
categories
Renaissance
of Raphael
later with
appears
thinkers
as
to
in
and Bramante,
Serlio,
Palladio,
and Vignola; see Rowland 1994; Howe
and Rowland
1999,
79. See Tomlinson
p. 15.
1963.
IDEA
AND
background,
extending
With
IN
VISUALITY
HELLENISTIC
ARCHITECTURE
587
there is no reason why we should perpetuate his ignorance by
to Hellenistic
it retrospectively
architects and their buildings.
support from the results of this analysis, it is even worth specu
a
on the
higher degree of
special potential of the Doric order for
in
in the case of
At
the
least
design process.
drawing-board
sophistication
a
in
in
columnar placements
Doric temple might
Temple A, the variations
lating
an alternative
approach to the location of the internal
the plan.80What
appears to have resulted was a system
more interesting than the
characteristic
arithmetical
simple
relationships
one
was
too
innovative
that
for reuse and
of the grid plan, but also
perhaps
have motivated
features within
partly for this reason, and partly because
of Doric temples altogether, the possibly
in Temple A may have disappeared
from
continued development.
Perhaps
of the "decline" in the production
Doric-related
method
found
common
practice well before Vitruvius picked up his pen. Yet Temple A
was not the final instance of this
approach, which appears to have extended
even
and
into aHellenistic-Roman
the
Doric
order
context, where
beyond
to
demonstrate
the application of the Pythagorean
temple plans continued
as their
guiding geometry.81 Ultimately,
triangle and 3:5 circumferences
of
form
of Temple A might have its
the
characteristic
however,
geometry
not
most recognizable
in
the
taxis of the architect's
legacy
cryptomethodic
in
the
caementicium
but
that
Roman
drawing board,
shapes
opus
finally al
lowed for permanent expression in three dimensions. Framed in this way,
the fully experiential
rise to a new aesthetic
80. In Temple
interaxes
A, the lateral corner
ca. 2.7 m,
measure
as
to the other average
opposed
axes of ca. 3.05 m. In the facade
rear colonnades,
interaxes measure
the corner
and central
sure 3.065
and 3.080
pi.
2.
and
column
ca. 2.7 m, while
the second
see Schazmann
inter
interaxes
m,
and Herzog
81. These
found
geometric
approaches
in two of the earliest
hellenizing
respectively;
1932,
have been unimaginable
are
temples in Italy during the Republican
period: theTemple of Juno atGabii of
ca. 160
b.c.
ca. 120-100
mea
that would
and
the round
b.c.
in Rome's
temple
Forum
of
Boa
rium. For
of Juno
of the
the geometry
Temple
see
at Gabii,
Almagro-Gorbea
1982; Jim?nez 1982, esp. pp. 63-74;
Almagro-Gorbea
give
in the Hellenistic
theory of Vitruvius.
architectural
column
of the idea and its reflection would
intersection
and Jim?nez
1982;
Coarelli
1987, pp. 11-21. For the round
see Rakob
1973.
and Heilmeyer
temple,
An
elaborated
of
such
geom
analysis
etry, its significance,
tions between
these
and
the connec
and the
examples
at Kos discussed
in the present
work
are themes
in a
that I explore
study
article
focused
(in
follow-up
progress)
on Roman
architecture.
APPENDIX
1
THEORETICAL
PLAN A
Select
and equations for theoretical
locations, coordinates, magnitudes,
are given below. The coordinates
A
in
correspond to measurements
plan
meters taken by Schazmann
to
and Herzog
converted
here
(see Fig. 5),82
an 18.142 x 33.280
0 and limit 18.142, 33.280 at
with
0,
origin
quadrant
the southeastern
and northwestern
extremes, respectively
(Fig. 23). For
additional equations, see text and notes above.
Location
Relevant
Coordinates
Circumference
1 A
1
B
1
C
0,0
18.142,0
24.202
D 2 4.435,4.430
E 2 13.707,4.430
F 2 13.707,20.002
G 2 4.435,20.002
H 1 13.749,26.483
I 1 4.393,26.483
Circumference
(Circumcenter
1
9.071,12.101)
Definitions
= Radius 1 + Radius 2
AC = Diameter
=
to A
Radius 1 distance from circumcenter
to H
Radius 2 = distance from circumcenter
Magnitudes
X, Y distances from circumcenter
= 9.071
XI: 9.071-0
= 12.101
Yl: 12.101-0
X, Y distances from circumcenter
9.071 = 4.678
X2:13.749
= 14.382
Y2:26.483-12.101
(or B)
(or I)
to A
to H
82. Schazmann
pi. 2.
and Herzog
1932,
AND
IDEA
IN
VISUALITY
HELLENISTIC
ARCHITECTURE
/ ^ID
EIL
G
F_
,-_
- 1^
L
__
_
0
_~
O-
O
_
0
I
Figure 23. Restored theoretical plan
of Temple A with geometric under
pinning
responding
and
indicated
to Cartesian
locations
cor
~10m
lomo
0WJ~
coordinates
Equations
Radiusl2
Radius
=Xl2
inMagnitudes
Differences
= 0.042
30.247-30.205
= 0.025
18.148-18.123
+Yl2
Radius
12=9.0712+
1 = 15.123
Radius
22 =X22 +Y22
0.042
/ 30.247
Radius
22=4.6782+14.3822
2 = 15.124
0.025
/ 18.123
12.1012
Tolerances
Radius
AC
= 15.123
+ 15.124
= 30.247
Pythagorean
Equations
Circumference
(Circumcenter
2
hypotenuse2
hypotenuse2
9.071,12.216)
hypotenuse
Diameter2 = (DE)2 + (EF)2
Diameter2
Diameter
6:10 Ratio
Equations
= 9.2722+
= 18.123
=
(18.123 / 6) x 10 30.205
=
(30.247 / 10) x 6 18.148
Triangle
=AB2 +
(Yl x 2)2
= 18.1422 + 24.2022
= 30.247
inMagnitude
Difference
AC
hypotenuse
30.247
30.247 = 0
15.5722
of Circumferences
= 0.1%
= 0.1%
1 and 2
Tolerance
0 / 30.247 = 0%
589
APPENDIX
2
THEORETICAL
PLAN B
Select
and equations for theoretical
locations, coordinates, magnitudes,
are
B
below.
The
in
coordinates
given
plan
correspond to measurements
meters taken by Schazmann and Herzog
(see Fig. 5),83 converted here to an
at the
18.075 x 33.280 quadrant with origin 0,0 and limit 18.075,33.280
a
southeastern and northwestern
and
extremes, respectively,
symmetrically
and
centered naos (see Fig. 23, scaled for the slightly differing dimensions
coordinates of Appendix
1).
Location
Relevant
Coordinates
Circumference
1 A
1
B
0,0
18.075,0
C 1 18.075,24.224
D 2 4.402,4.430
E 2 13.674,4.430
F 2 13.674,20.002
G 2 4.402,20.002
H 1 13.716,26.483
I 1 4.360,26.483
Circumference 1
9.038,12.112)
(Circumcenter
Definitions
= Radius 1 + Radius 2
AC = Diameter
=
to A
Radius 1 distance from circumcenter
to H
Radius 2 = distance from circumcenter
Magnitudes
X, Y distances from circumcenter
0 = 9.038
XI: 9.038
= 12.112
Yl: 12.112-0
X, Y distances from circumcenter
9.038 = 4.678
X2:13.716
Y2: 26.483
12.112 = 14.371
(or B)
(or I)
to A
to H
83. Schazmann
pi.
2.
and Herzog
1932,
IDEA
AND
Equations
Radiusl2
Radius
IN
VISUALITY
=Xl2
12=9.0382+12.1122
1 = 15.112
Radius
22 =X22 +Y22
Radius
22=4.6782+14.3712
2 = 15.113
AC
= 15.112
+ 15.113
ARCHITECTURE
inMagnitudes
Differences
30.225
30.205 = 0.020
= 0.012
18.135 -18.123
+Yl2
Radius
Radius
HELLENISTIC
Tolerances
= 30.225
0.020
/ 30.225
< 0.1%
0.012
/ 18.123
< 0.1%
Pythagorean
Equations
Circumference
(Circumcenter
2
hypotenuse2
hypotenuse2
9.038,12.216)
hypotenuse
Diameter2 = (DE)2+ (EF)2
Diameter2
Diameter
6:10 Ratio
Equations
= 9.2722+
= 18.123
15.5722
of Circumferences
=
(18.123 / 6) x 10 30.205
(30.225 / 10) x 6 = 18.135
Triangle
= AB2 +
(Yl x 2)2
= 18.0752+ 24.2242
= 30.224
inMagnitude
Difference
AC
hypotenuse
30.225
30.224 = 0.001
1 and 2
Tolerance
0.001
/ 30.224
< 0.1%
59I
APPENDIX
3
THEORETICAL
PLAN C
Select
and equations for theoretical
locations, coordinates, magnitudes,
are
in
C
The
coordinates
below.
plan
given
correspond to measurements
meters taken by Schazmann
to
here
and Herzog
converted
(see Fig. 5),84
an 18.075 x 33.280
0 and limit 18.075, 33.280 at
with
0,
origin
quadrant
the southeastern and northwestern
extremes, respectively, with the width of
the naos reduced
.067 m in order to provide symmetry (see Fig. 23, scaled
dimensions
and coordinates of Appendix
1).
for the slightly differing
Location
Relevant
Coordinates
Circumference
1 A
1
B
C
D
E
F
0,0
18.075,0
1 18.075,24.224
2 4.435,4.430
2 13.640,4.430
2 13.640,20.002
G 2 4.435,20.002
H 1 13.682,26.483
I 1 4.393,26.483
Circumference 1
(Circumcenter
9.038,12.107)
Definitions
= Radius 1 + Radius 2
AC = Diameter
=
to A
Radius 1 distance from circumcenter
to H
Radius 2 = distance from circumcenter
Magnitudes
X, Y distances from circumcenter
= 9.038
XI: 9.038-0
= 12.107
Yl: 12.107-0
X, Y distances from circumcenter
9.038 = 4.644
X2:13.682
12.107 = 14.376
Y2: 26.483
(or B)
(or I)
to A
to H
84. Schazmann
pi. 2.
and Herzog
1932,
IDEA
AND
Equations
Radiusl2=Xl2
Radius
IN
VISUALITY
12=9.0382+12.1072
1 = 15.108
Radius
22 =X22 +Y22
Radius
22=4.6442+14.3762
2 = 15.108
AC
= 15.108
+ 15.108
ARCHITECTURE
Differences inMagnitudes
30.216
30.148 = 0.068
= 0.041
18.130-18.089
+Yl2
Radius
Radius
HELLENISTIC
Tolerances
= 30.216
0.068
/ 30.216
0.041
/ 18.089
Pythagorean
Equations
Circumference
(Circumcenter
2
hypotenuse2
hypotenuse2
9.038,12.216)
hypotenuse
Diameter2 = (DE)2+ (EF)2
Diameter2
Diameter
6:10 Ratio
Equations
= 9.2052+
= 18.089
15.5722
of Circumferences
(18.089 / 6) x 10 = 30.148
(30.216 / 10) x 6 = 18.130
= 0.2%
= 0.2%
Triangle
= AB2 +
(Yl x 2)2
= 18.0752+ 24.2142
= 30.216
inMagnitude
Difference
AC
hypotenuse
30.216
30.216 = 0
1 and 2
Tolerance
0/30.216
= 0%
593
594
SENSENEY
R.
JOHN
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