SOURCES - page 1
SOURCES IN RECREATIONAL MATHEMATICS
AN ANNOTATED BIBLIOGRAPHY
EIGHTH PRELIMINARY EDITION
DAVID SINGMASTER
Copyright ©2003 Professor David Singmaster
contact via http://puzzlemuseum.com
Last updated on 9 March 2016.
This is a copy of the current version from my source files. I had intended to reorganise
the material before producing a Word version, but have decided to produce this version for
G4G6 and to renumber it as the Eighth Preliminary Edition.
A version from early 2000 was converted into HTML by Bill Kalush and is available on
www.geocities.com/mathrecsources/ and another version is at
http://members.it.tripod.de/catur/singmast/intro.htm .
If I have perchance omitted anything more or less proper or necessary, I beg indulgence,
since there is no one who is blameless and utterly provident in all things. [Fibonacci,
translated by Grimm.])
INTRODUCTION
NATURE OF THIS WORK
Recreational mathematics is as old as mathematics itself. Recreational problems
already occur in the oldest extant sources -- the Rhind Papyrus and Old Babylonian tablets.
The Rhind Papyrus has an example of a purely recreational problem -- Problem 79 is like the
"As I was going to St. Ives" nursery rhyme. The Babylonians give fairly standard practical
problems with a recreational context -- a man knows the area plus the difference of the length
and width of his field, a measurement which no surveyor would ever make! There is even
some prehistoric mathematics which could not have been practical -- numerous 'carved stone
balls' have been found in eastern Scotland, dating from the Neolithic period and they include
rounded forms of all the regular polyhedra and some less regular ones. Since these early
times, recreations have been a feature of mathematics, both as pure recreations and as
pedagogic tools. In this work, I use recreational in a fairly broad sense, but I tend to omit the
more straightforward problems and concentrate on those which 'stimulate the curiosity' (as
Montucla says).
In addition, recreational mathematics is certainly as diffuse as mathematics. Every main
culture and many minor ones have contributed to the history. A glance at the Common
References below, or at almost any topic in the text, will reveal the diversity of sources which
are relevant to this study. Much information arises from material outside the purview of the
ordinary historian of mathematics -- e.g. patents; articles in newspapers, popular magazines
and minor journals; instruction leaflets; actual artifacts and even oral tradition.
Consequently, it is very difficult to determine the history of any recreational topic and
the history given in popular books is often extremely dubious or even simply fanciful. For
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example, Nim, Tangrams, and Magic Squares are often traced back to China of about
2000 BC. The oldest known reference to Nim is in America in 1903. Tangrams appear in
China and Europe at essentially the same time, about 1800, though there are related puzzles in
18C Japan and in the Hellenistic world. Magic Squares seem to be genuinely a Chinese
invention, but go back to perhaps a few centuries BC and are not clearly described until about
80AD. Because of the lack of a history of the field, results are frequently rediscovered.
When I began this bibliography in 1982, I had the the idea of producing a book (or
books) of the original sources, translated into English, so people could read the original
material. This bibliography began as the table of contents of such a book. I thought that this
would be an easy project, but it has become increasingly apparent that the history of most
recreations is hardly known. I have recently realised that mathematical recreations are really
the folklore of mathematics and that the historical problems are similar to those of folklore.
One might even say that mathematical recreations are the urban myths or the jokes or the
campfire stories of mathematics. Consequently I decided that an annotated bibliography was
the first necessity to make the history clearer. This bibliography alone has grown into a book,
something like Dickson's History of the Theory of Numbers. Like that work, the present
work divides the subject into a number of topics and treats them chronologically.
I have printed six preliminary editions of this work, with slightly varying titles. The
first version of 4 Jul 1986 had 224 topics and was spaced out so entries would not be spread
over two pages and to give room for page numbers. This stretched the text from 110pp to
129pp and was printed for the Strens Memorial Conference at the Univ. of Calgary in Jul/Aug
1986. I no longer worry about page breaks. The following editions had: 250 topics on 152
pages; 290 topics on 192 pages; 307 topics on 223 pages; 357 topics on 311 pages and 392
topics on 456 pages. The seventh edition was never printed, but was a continually changing
computer file. It had about 419 topics (as of 20 Oct 95) and 587 pages, as of 20 Oct 1995. I
then carried out the conversion to proportional spacing and this reduced the total length from
587 to 488 pages, a reduction of 16.87% which is conveniently estimated as 1/6. This
reduction was fairly consistent throughout the conversion process.
This eighth edition is being prepared for the Gathering for Gardner 6 in March 2004.
The text is 818 pages as of 18 Mar 2004. There are about 457 topics as of 18 Mar 2004.
A fuller description of this project in 1984-1985 is given in my article Some early
sources in recreational mathematics, in: C. Hay et al., eds.; Mathematics from Manuscript
to Print; Oxford Univ. Press, 1988, pp. 195-208. A more recent description is in my article:
Recreational mathematics; in: Encyclopedia of the History and Philosophy of the
Mathematical Sciences; ed. by I. Grattan-Guinness; Routledge & Kegan Paul, 1993;
pp. 1568-1575.
Below I compare this work with Dickson and similar works and discuss the coverage of
this work.
SIMILAR WORKS
As already mentioned, the work which the present most resembles is Dickson's History
of the Theory of Numbers.
The history of science can be made entirely impartial, and perhaps that is what it
should be, by merely recording who did what, and leaving all "evaluations" to those
who like them. To my knowledge there is only one history of a scientific subject
(Dickson's, of the Theory of Numbers) which has been written in this coldblooded,
scientific way. The complete success of that unique example -- admitted by all who
ever have occasion to use such a history in their work -- seems to indicate that historians
who draw morals should have their own morals drawn.
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E. T. Bell. The Search for Truth. George Allen & Unwin, London, 1935,
p. 131.
Dickson attempted to be exhaustive and certainly is pretty much so. Since his time,
many older sources have been published, but their number-theoretic content is limited and
most of Dickson's topics do not go back that far, so it remains the authoritative work in its
field.
The best previous book covering the history of recreational mathematics is the second
edition of Wilhelm Ahrens's Mathematische Unterhaltungen und Spiele in two volumes.
Although it is a book on recreations, it includes extensive histories of most of the topics
covered, far more than in any other recreational book. He also gives a good index and a
bibliography of 762 items, often with some bibliographical notes. I will indicate the
appropriate pages at the beginning of any topic that Ahrens covers. This has been out of print
for many years but Teubner has some plans to reissue it.
Another similar book is the 4th edition of J. Tropfke's Geschichte der
Elementarmathematik, revised by Vogel, Reich and Gericke. This is quite exhaustive, but is
concerned with older problems and sources. It presents the material on a topic as a history
with references to the sources, but it doesn't detail what is in each of the sources. Sadly, only
one volume, on arithmetic and algebra, appeared before Vogel's death. A second volume, on
geometry, is being prepared. For any topic covered in Tropfke, it should be consulted for
further references to early material which I have not seen, particularly material not available in
any western language. I cite the appropriate pages of Tropfke at the beginning of any topic
covered by Tropfke.
Another book in the field is W. L. Schaaf's Bibliography of Recreational
Mathematics, in four volumes. This is a quite exhaustive bibliography of recent articles, but
it is not chronological, is without annotation and is somewhat less classified than the present
work. Nonetheless it is a valuable guide to recent material.
Collecting books on magic has been popular for many years and quite notable
collections and bibliographies have been made. Magic overlaps recreational mathematics,
particularly in older books, and I have now added references to items listed in the
bibliographies of Christopher, Clarke & Blind, Hall, Heyl, Toole Stott and Volkmann &
Tummers -- details of these works are given in the list of Common References below. There
is a notable collection of Harry Price at Senate House, University of London, and a catalogue
was printed in 1929 & 1935 -- see HPL in Common References.
Another related bibliography is Santi's Bibliografia della Enigmistica, which is
primarily about word puzzles, riddles, etc., but has some overlap with recreational
mathematics -- again see the entry in the list of Common References. I have not finished
working through this.
Other relevant bibliographies are listed in Section 3.B.
COVERAGE
In selecting topics, I tend to avoid classical number theory and classical geometry.
These are both pretty well known. Dickson's History of the Theory of Numbers and
Leveque's and Guy's Reviews in Number Theory cover number theory quite well. I also tend
to avoid simple exercises, e.g. in the rule of three, in 'aha' or 'heap' problems, in the
Pythagorean theorem (though I have now included 6.BF) or in two linear equations in two
unknowns, though these often have fanciful settings which are intended to make them
amusing and some of these are included -- see 7.R, 7.X, 7.AX. I also leave out most
divination (or 'think of a number') techniques (but a little is covered in 7.M.4.b) and most
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arithmetic fallacies. I also leave out Conway's approach to mathematical games -- this is
extensively covered by Winning Ways and Frankel's Bibliography.
The classification of topics is still ad-hoc and will eventually get rationalised -- but it is
hard to sort things until you know what they are! At present I have only grouped them under
the general headings: Biography, General, History & Bibliography, Games, Combinatorics,
Geometry, Arithmetic, Probability, Logic, Physics, Topology. Even the order of these should
be amended. The General section should be subsumed under the History & Bibliography.
Geometry and Arithmetic need to be subdivided.
I have recently realised that some general topics are spread over several sections in
different parts. E.g. fallacies are covered in 6.P, 6.R, 6.AD, 6.AW.1, 6.AY, 7.F, 7.Y, 7.Z,
7.AD, 7.AI, 7.AL, 7.AN, most of 8, 10.D, 10.E, 10.O. Perhaps I will produce an index to
such topics. I try to make appropriate cross-references.
Some topics are so extensive that I include introductory or classifactory material at the
beginning. I often give a notation for the problems being considered. I give brief
explanations of those problems which are not well known or are not described in the notation
or the early references. There may be a section index. I have started to include references to
comprehensive surveys of a given topic -- these are sometimes given at the beginning.
Recreational problems are repeated so often that it is impossible to include all their
occurrences. I try to be exhaustive with early material, but once a problem passes into
mathematical and general circulation, I only include references which show new aspects of the
problem or show how the problem is transmitted in time and/or space. However, the point at
which I start leaving out items may vary with time and generally slowly increases as I learn
more about a topic. I include numerous variants and developments on problems, especially
when the actual origin is obscure.
When I began, I made minimal annotations, often nothing at all. In rereading sections,
particularly when adding more material, I have often added annotations, but I have not done
this for all the early entries yet.
Recently added topics often may exist in standard sources that I have not reread
recently, so the references for such topics often have gaps -- I constantly discover that Loyd or
Dudeney or Ahrens or Lucas or Fibonacci has covered such a topic but I have forgotten this -e.g. looking through Dudeney recently, I added about 15 entries. New sections are often so
noted to indicate that they may not be as complete as other sections.
Some of the sources cited are lengthy and I originally added notes as to which parts
might be usable in a book of readings -- these notes have now been mostly deleted, but I may
have missed a few.
STATUS OF THE PROJECT
I would like to think that I am about 75% of the way through the relevant material.
However, I recently did a rough measurement of the material in my study -- there is about 8
feet of read but unprocessed material and about 35 feet of unread material, not counting
several boxes of unread Rubik Cube material and several feet of semi-read material on my
desk and table. I recently bought two bookshelves just to hold unread material. Perhaps half
of this material is relevant to this work.
In particular, the unread material includes several works of Folkerts and Sesiano on
medieval MSS, a substantial amount of photocopies from Schott, Schwenter and Dudeney
(400 columns), some 2000 pages of photocopies recently made at Keele, some 500 pages of
photocopies from Martin Gardner's files, as well as a number of letters. Marcel Gillen has
made extracts of all US, German and EURO patents and German registered designs on
puzzles -- 26 volumes, occupying about two feet on my shelves. I have recently acquired an
almost complete set of Scripta Mathematica (but I have previously read about half of it),
Schwenter-Harsdörffer's Deliciæ Physico-Mathematicae, Schott's Joco-Seriorum and
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Murray's History of Board Games Other Than Chess. I have recently acquired the early
issues of Eureka, but there are later issues that I have not yet read and they persist in not
sending the current copies I have paid for!
I have not yet seen some of the earlier 19C material which I have seen referred to and I
suspect there is much more to be found. I have examined some 18C & 19C arithmetic and
algebra books looking for problem sections -- these are often given the pleasant name of
Promiscuous Problems. There are so many of these that a reference to one of them probably
indicates that the problem appears in many other similar books that I have not examined. My
examination is primarily based on those books which I happen to have acquired. There are a
few 15-17C books which I have not yet examined, notably those included at the end of the last
paragraph.
In working on this material, it has become clear that there were two particularly
interesting and productive eras in the 19C. In the fifteen years from 1857, there appeared
about a dozen books in the US and the UK: The Magician's Own Book (1857); Parlour
Pastime, by "Uncle George" (1857); The Sociable (1858); The Boy's Own Toymaker, by
Landells (1858); The Book of 500 Curious Puzzles (1859); The Secret Out (1859);
Indoor and Outdoor Games for Boys and Girls (c1859); The Boy's Own Conjuring
Book (1860); The Illustrated Boy's Own Treasury (1860, but see below); The Parlor
Magician (1863); The Art of Amusing, by Bellew (1866); Parlour Pastimes (1868);
Hanky Panky (1872); Within Doors, by Elliott (1872); Magic No Mystery (1876), just to
name those that I know. Most of these are of uncertain authorship and went through several
editions and versions. The Magician's Own Book, The Book of 500 Curious Puzzles, The
Secret Out, The Sociable, The Parlor Magician, Hanky Panky, and Magic No Mystery
seem to be by the same author(s). I have recently had a chance to look at a number of
previously unseen versions at Sotheby's and at Edward Hordern's and I find that sometimes
two editions of the same title are essentially completely different! This is particularly true for
US and UK editions. Many of the later UK editions say 'By the author of Magician's Own
Book etc., translated and edited by W. H. Cremer Jr.' From the TPs, it appears that they were
written by Wiljalba Frikell (1818-1903) and then translated into English. However, BMC and
NUC generally attribute the earlier US editions to George Arnold (1834-1865), and some
catalogue entries explicitly say the Frikell versions are later editions, so it may be that Frikell
produced later editions in some other language (French or German ??) and these were
translated by Cremer. On the other hand, the UK ed of The Secret Out says it is based on Le
Magicien des Salons. This is probably Le Magicien des Salons ou le Diable Couleur de
Rose, for which I have several references, with different authors! -- J. M. Gassier, 1814; M.
[Louis Apollinarie Christien Emmanuel] Comte, 1829; Richard (pseud. of A. O. Delarue),
1857 and earlier. There was a German translation of this. Some of these are at HPL but
??NYS. Items with similar names are: Le Magicien de Société, Delarue, Paris, c1860? and
Le Manuel des Sorciers (various Paris editions from 178?-1825, cf in Common References).
It seems that this era was inspired by these earlier French books. To add to the confusion, an
advertisement for the UK ed. of Magician's Own Book (1871?) says it is translated from Le
Magicien des Salons which has long been a standard in France and Germany. Toole Stott
opines that Frikell had nothing to do with these books -- as a celebrated conjuror of the times,
his name was simply attached to the books. Toole Stott also doubts whether Le Magicien des
Salons exists -- but it now seems pretty clear that it does, though it may not have been the
direct source for any of these works, but see below.
Christopher 242 cites the following article on this series.
Charles L. Rulfs. Origins of some conjuring works. Magicol 24 (May 1971) 3-5. He
discusses the various books, saying that Cremer essentially pirated the Dick & Fitzgerald
productions. He says The Magician's Own Book draws on Wyman's Handbook (1850,
??NYS), Endless Amusement, Parlour Magic (by W. Clarke?, 1830s, ??NYS), Brewster's
Natural Magic (??NYS). He says The Secret Out is largely taken, illustrations and all, from
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Blismon de Douai's Manuel du Magicien (1849, ??NYS) and Richard & Delion's Magicien
des salons ou le diable couleur de rose (1857 and earlier, ??NYS).
Christopher 622 says Harold Adrian Smith [Dick and Fitzgerald Publishers; Books at
Brown 34 (1987) 108-114] has studied this series and concludes that Williams was the author
of Magician's Own Book, assisted by Wyman. Actually Smith simply asserts: "The book
was undoubtedly [sic] written by H. L. Williams, a "hack writer" of the period, assisted by
John Wyman in the technical details." He gives no explanation for his assertion. He later
says he doubts whether Cremer ever wrote anything. He suggests The Secret Out book is
taken from DeLion. He states that The Boy's Own Conjuring Book is a London pirate
edition.
Several of the other items are anonymous and there was a tremendous amount of
copying going on -- problems are often reproduced verbatim with the same diagram or
sometimes with minor changes. In some cases, the same error is repeated in five different
books! I have just discovered some earlier appearances of the same material in The Family
Friend, a periodical which ran in six series from 1849 to 1921 and which I have not yet
tracked down further. However, vol. 1-3 of 1849-1850 and the volume for Jul-Dec 1859
contain a number of the problems which appear repeatedly and identically in the above cited
books. Toole Stott 407 is an edition of The Illustrated Boy's Own Treasury of c1847 but
the BM copy was destroyed in the war and the other two copies cited are in the US. If this
date is correct, then this book is a forerunner of all the others and a major connection between
Boy's Own Book and Magician's Own Book. I would be most grateful to anyone who can
help sort out this material -- e.g. with photocopies of these or similar books or magazines.
The other interesting era was about 1900. In English, this was largely created or
inspired by Sam Loyd and Henry Dudeney. Much of this material first appeared in magazines
and newspapers. I have seen much less than half of Loyd's and Dudeney's work and very little
of similar earlier material (but see below). Consequently problems due to Loyd or Dudeney
may seem to first appear in the works of Ball (1892, et seq.), Hoffmann (1893) and Pearson
(1907). Further examination of Loyd's and Dudeney's material will be needed to clarify the
origin and development of many problems. Though both started puzzle columns about 1896,
they must have been producing material for a decade or more previously which does not seem
to be known. I have just obtained photocopies of 401 columns by Dudeney in the Weekly
Dispatch of 1897-1903, but have not had time to study them. Will Shortz and Angela Newing
have been studying Loyd and Dudeney respectively and turning up their material.
The works of Lucas (1882-1895), Schubert (1890s) and Ahrens (1900-1918) were the
main items on the Continent and they interacted with the English language writers. Ahrens
was the most historical of these and his book is one of the foundations of the present work.
All of these also wrote in newspapers and magazines and I have not seen all their material.
I would be happy to hear from anyone with ideas or suggestions for this bibliography. I
would be delighted to hear from anyone who can locate missing information or who can
provide copies of awkward material. I am particularly short of information about recreations
in the Arabic period. I prepared a separate file, 'Queries and Problems in the History of
Recreational Mathematics', which is about 23 pages, and has recently been updated. I have
also prepared three smaller letters of queries about Middle Eastern, Oriental and Russian
sources and these are generally more up-to-date.
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TECHNICAL NOTES
I have prepared a CD containing this and much else of my material. I divided Sources
into four files when I used floppy discs as it was too big to fit on one disc, and I have not yet
changed this. The files are: 1: Introductory material and list of abbreviations/references;
2: Sections 1 - 6; 3: Section 7; 4: Sections 8 - 11. It is convenient to have the first file
separate from the main material, but I might combine the other three files. (I have tried to
send it by email in the past, but this document is very large (currently c4.1MB and the Word
version will be longer) and most people who requested it by email found that it overflowed
their mailbox and created chaos in their system -- this situation has changed a bit with larger
memories and improved transmission speeds.)
This file started on a DEC-10, then was transferred to a VAX. It is now on my PC
using Script Professional, the development of LocoScript on the Amstrad. Even in its earliest
forms, this provided an easy and comprehensive set of diacritical marks, which are still not all
available nor easy to use in WordPerfect or Word (except perhaps by using macros and/or
overstriking??). It also provides multiple cut and paste buffers and easy formatting, though I
have learned how to overcome these deficiencies in Word.
Script provides an ASCII output, but this uses IBM extended ASCII which has 8-bit
codes. Not all computers will accept or print such characters and sometimes they are
converted into printer control codes causing considerable confusion. I have a program that
converts these codes to 7-bits -- e.g. accents and umlauts are removed. However, ASCII loses
a great deal of the information, such as sub- and superscripts, so this is not a terribly useful
format.
Script also provides WordStar and "Revisable-Form-Text DCA" output, but neither of
these seems to be very successful (DCA is better than WordStar). Script later added a
WordPerfect exporting facility. This works well, though some (fairly rare) characters and
diacritical marks are lost and the output requires some reformatting. (Nob Yoshigahara
reports that Japanese WordPerfect turns all the extended ASCII characters into Kanji
characters!)
Reading the WordPerfect output in Word (you may need to install this facility) gives a
good approximation to my text, but in Courier 10pt. Selecting All and changing to Times
New Roman 12pt gives an better approximation. (Some files use a smaller font of 10pt and I
may have done some into 9pt.) You have to change this in the Header separately, using View
Header and Footer. The page layout is awkward as my page numbering header gets put into
the text, leaving a large gap at the top. I go into Page Setup and set the Paper Size to A4
and the Top, Bottom and Header Margins to 15mm and the Left and Right Margins to
25mm. (It has taken me some time to work this out and some earlier files may have other
settings.) However, I find that lines are a bit too close together and underlines and some
diacritical marks are lost, so one needs to also go into Format Paragraph Spacing -- Line
Spacing and choose At least and 12pt (or 10pt). I use hanging indentation in most of the
main material and this feature is not preserved in this conversion. By selecting a relevant
section and going into Format Paragraph Indentation -- Special and selecting Hanging, it
should automatically select 10.6mm which corresponds to my automatic spacing of five
characters in 12pt. Further, I use second level hanging indentation in quite a number of
places. You need to create a style which is the basic style with the left hand margin at
10.6mm (or 10 or 11 mm). When second level indenting is needed, select the desired section
and apply this style to it.
However, this still leaves some problems. I use em dashes a bit, i.e. –, which gets
converted into an underline, _. In Word, this is obtained by use of CTRL and the - sign on
the numeric keypad. One can use the find and replace feature, EXCEPT that a number of
other characters are also converted into underlines. In particular, Cyrillic characters are all
converted into underlines. This is not insuperable as I always(?) give a transliteration of
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Cyrillic (using the current Mathematical Reviews system) and one can reconstruct the original
Cyrillic from it. I notice that the Cyrillic characters are larger than roman characters and
hence may overlap. One can amend this by selecting the Cyrillic text and going into Format
Font Character Spacing Spacing and choosing Expanded By 2 pt (or thereabout). But a
number of characters with unusual diacritical marks are also converted to underlines or
converted to the unmarked character and not all of these are available in Word. E.g. ĭ, which
is the transliteration of й becomes just i. I am slowly forming a Word file containing the
Word versions of entries having the Cyrillic or other odd characters, and I will include this file
on my CD, named CYRILLIC.DOC. For diacritical marks not supported by Word, I use an
approximation and/or an explanation.
It is very tedious to convert the underlines back to em dashes, so I will convert every em
dash to a double hyphen --.
Finally, I have made a number of diagrams by simple typing without proportional
spacing and Word does not permit changing font spacing in mid-line and ignores spaces
before a right-alignment instruction. The latter problem can be overcome by using hard
spaces and the former problem is less of a problem, and I think it can be overcome.
Later versions of Script support Hewlett-Packard DeskJets and I am now on my second
generation of these, so the 7th and future editions will be better printed (if they ever are!).
However, this required considerable reformatting as the text looks best in proportional spacing
(PS) and I found I had to check every table and every mathematical formula and diagram.
Also, to set off letters used as mathematical symbols within text, I find PS requires two spaces
on each side of the letter -- i.e. I refer to x rather than to x. (I find this easier to do than to
convert to italics.) I also sometimes set off numbers with two spaces, though I wasn't
consistent in doing this at the beginning of my reformatting. The conversion to proportional
spacing reduced the total length from 587 to 488 pages, a reduction of 16.87% which is
conveniently estimated as 1/6. The percentage of reduction was fairly consistent throughout
the conversion process.
The printing of Greek characters went amiss in the second part of the 6th Preliminary
Edition, apparently due to the printer setting having been changed without my noticing -- this
happens if an odd character gets sent to the printer, usually in DOS when trying to use or print
a corrupted file, and there is no indication of it. I was never able to reproduce the effect!
The conversion to (Loco)Script provided many improved features compared to my
earlier DEC versions. I am using an A4 page (8¼ by 11⅔ inches) rather than an 8½ by 11
inch page, which gives 60 lines of text per page, four more or 7% more than when using the
DEC or VAX.
NEW SECTIONS IN THIS EDITION.
[SIXTH EDITION: 1: Fibonacci, 1: Montucla; 3.B; 4.A.1.a, 4.B.9, 4.B.10, 4.B.11, 4.B.12;
5.R.1.a, 5.W.1, 5.AA, 5.AB; 6.AS.1.b, 6.AS.2.a, 6.AS.5, 6.AW.4, 6.BP, 6.BQ, 6.BR; 7.I.1,
7.Y.2, 7.AY, 7.AZ; 7.BA; 8.I, 8.J; 9.E.2, 9.K; 10.A.4, 10.A.5, 10.U, 10.V, 10.W; 11.K.6,
11.K.7, 11.K.8.]
In the last edition, I had 8.K instead of 8.J in the list of New Sections and in the Contents.
1: Pacioli, Carroll, Perelman; 4.B.13, 4.B.14, 4.B.15; 5.B.2, 5.H.3 (the previous 5.H.3 has
been renumbered 5.H.4), 5.K.3, 5.R.1.b, 5.X.4, 5.AC, 5.AD, 5.AE, 5.AF, 5.AG.1, 5.AG.2;
6.AJ.4, 6.AJ.5, 6.AS.3.a, 6.AT.8, 6.AT.9, 6.AY.2, 6.BF.4, 6.BF.5, 6.BS, 6.BT, 6.BU, 6.BV,
6.BW; 7.H.6, 7.H.7 (formerly part of 7.H.5), 7.M.4.a, 7.M.4.b, 7.M.6, 7.R.4, 7.AC.3.a,
7.AC.7, 7.AH.1, 7.AJ.1, 7.BB, 7.BC; 8.K, 8.L; 10.A.6, 10.A.7, 10.A.8, 10.D has become
10.D.1, 10.D.2, 10.D.3, 10.E.4, 10.X, 10.Y, 10.Z, 10.AA, 10.AB, 10.AC, 10.AD, 10.AE;
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11.N, 11.O, 11.P, 11.Q, 11.R, 11.S. (65 new sections)
ACKNOWLEDGMENTS
I am immensely indebted to many mathematicians, historians, puzzlers, bookdealers
and others who have studied particular topics, as will be apparent.
I have had assistance from so many sources that I have probably forgotten some, but I
would like to give thanks here to the following, and beg forgiveness from anyone
inadvertently omitted -- if you remind me, I will make amendment. In some cases, I simply
haven't got to your letter yet! Also I have had letters from people whose only identification is
an undecipherable signature and phone messages from people whose name and phone number
are unintelligible.
Sadly, a few of these have died since I corresponded with them and I have indicated
those known to me with †.
André Allard, Eric J. Aiton†, Sue Andrew, Hugh Ap Simon, Gino Arrighi, Marcia Ascher,
Mohammad Bagheri, Banca Commerciale Italiana, Gerd Baron, Chris Base,
Rainier [Ray] Bathke, John Beasley, Michael Behrend, Jörg Bewersdorff, Norman L. Biggs,
C. [Chris] J. Bouwkamp, Jean Brette, John Brillhart, Paul J. Campbell,
Cassa di Risparmio di Firenze, Henry Cattan, Marianna Clark, Stewart Coffin,
Alan & Philippa Collins, John H. Conway, H. S. M. Coxeter, James Dalgety,
Ann E. L. Davis, Yvonne Dold, Underwood Dudley, Anthony W. F. Edwards,
John Ergatoudis, John Fauvel†, Sandro Ferace, Judith V. Field, Irving Finkel,
Graham Flegg, Menso Folkerts, David Fowler, Aviezri S. Fraenkel, Raffaella Franci,
Gregory N. Frederickson, Michael Freude, Walter W. Funkenbusch, Nora Gädeke,
Martin Gardner, Marcel Gillen, Leonard J. Gordon, Ron Gow, Ivor Grattan-Guinness,
Christine Insley Green, Jennifer Greenleaves (Manco), Tom Greeves,
H. [Rik] J. M. van Grol, Branko Grünbaum, Richard K. Guy, John Hadley, Peter Hajek,
Diana Hall, Joan Hammontree, Anton Hanegraaf†, Martin Hansen, Jacques Haubrich,
Cynthia Hay, Takao Hayashi, Robert L. Helmbold, Hanno Hentrich, Richard I. Hess,
Christopher Holtom, Edward Hordern†, Peter Hosek, Konrad Jacobs, Anatoli Kalinin,
Bill Kalush, Michael Keller, Edward S. Kennedy, Sarah Key (The Haunted Bookshop),
Eberhard Knobloch, Don Knuth, Bob Koeppel, Joseph D. E. Konhauser, David E. Kullman,
Mogens Esrom Larsen, Jim Lavis (Doxa (Oxford)), John Leech†, Elisabeth Lefevre,
C. Legel, Derrick [Dick] H. Lehmer†, Emma Lehmer, Leisure Dynamics,
Hendrik W. Lenstra, Alan L. Mackay, Andrzej Makowski, John Malkevitch,
Giovanni Manco, Tatiana Matveeva, Ann Maury, Max Maven, Jim McArdle,
Patricia McCulloch, Peter McMullen, Leroy F. Meyers†, D. P. Miles, Marvin Miller,
Nobuo Miura, William O. J. Moser, Barbara Moss, Angela Newing, Jennie Newman,
Tom and Greta O'Beirne††, Owen O'Shea, Parker Brothers, Alan Parr, Jean J. Pedersen,
Luigi Pepe, William Poundstone, Helen Powlesland, Oliver Pretzel, Walter Purkert,
Robert A. Rankin†, Eleanor Robson, David J. A. Ross, Lee Sallows, Christopher Sansbury,
Sol Saul, William L. Schaaf, Doris Schattschneider, Jaap Scherphuis, Heribert Schmitz,
Š. Schwabik, Eileen Scott†, Al Seckel, Jacques Sesiano, Claude E. Shannon†,
John Sheehan, A. Sherratt, Will Shortz, Kripa Shankar Shukla, George L. Sicherman,
Deborah Singmaster, Man-Kit Siu, Gerald [Jerry] K. Slocum, Cedric A. B. Smith† (and
Sue Povey & Jim Mallet at the Galton Laboratory for letting me have some of Cedric's books),
Jurgen Stigter, Arthur H. Stone, Mel Stover†, Michael Stueben, Shigeo Takagi†,
Michael Tanoff, Gary J. Tee, Andrew Topsfield, George Tyson†, Dario Uri,
Warren Van Egmond, Carlo Viola, Kurt Vogel†, Anthony Watkinson, Chris Weeks,
Maurice Wilkes, John Winterbottom, John Withers, Nob. Yoshigahara, Claudia Zaslavsky.
SOURCES - page 10
I would also like to thank the following libraries and museums which I have used:
University of Aberdeen; University of Bristol; Buckleys Shop Museum, Battle, East Sussex;
University of Calgary; University of Cambridge; Marsh's Library, Dublin;
FLORENCE:
Biblioteca Nazionale; Biblioteca Riccardiana;
University of Keele -- The Turner Collection(†) and its librarian Martin Phillips;
Karl-Marx-Universität, Leipzig: Universität Bibliothek and Sektion Mathematik Bibliothek,
especially Frau Letzel at the latter;
LONDON:
Birkbeck College; British Library (at Bloomsbury and then at St. Pancras; also at
Colindale); The London Library; School of Oriental and African Studies, especially
Miss Y. Yasumara, the Art Librarian; Senate House, particularly the Harry Price
Library; South Bank University; Southwark Public Library;
University College London, especially the Graves Collection and the Rare Book
Librarians Jill Furlong, Susan Stead and their staff; Warburg Institute;
MUNICH:
Deutsches Museum; Institut für Geschichte der Naturwissenschaften;
NEW YORK:
Brooklyn Public Library; City College of New York; Columbia University;
Newark Public Library, Newark, New Jersey;
University of Newcastle upon Tyne -- The Wallis Collection and its librarian Lesley Gordon;
OXFORD:
Ashmolean Museum; The Bodleian Library;
Museum of the History of Science, and its librarian Tony Simcock;
University of Reading; University of St. Andrews;
SIENA:
Biblioteca Comunale degli Intronati; Dipartimento di Matematica, Università di Siena;
University of Southampton; Mathematical Institute, Warsaw.
I would like especially to thank the following.
Interlibrary Loans (especially Brenda Spooner) at South Bank University and the British
Library Lending Division for obtaining many strange items for me.
Richard Guy, Bill Sands and the Strens bequest for a most useful week at the
Strens/Guy Collection at Calgary in early 1986 and for organizing the Strens Memorial
Meeting in summer 1986 and for printing the first preliminary edition of these Sources.
Gerd Lassner, Uwe Quasthoff and the Naturwissenschaftlich-Theoretisches Zentrum of
the Karl-Marx-Universität, for a very useful visit to Leipzig in 1988.
SOURCES - page 11
South Bank University Computer Centre for the computer resources for the early stages
of this project, and especially Ann Keen for finding this file when it was lost.
My School for printing these preliminary editions.
Martin Gardner for kindly allowing me to excavate through his library and files.
James Dalgety, Edward Hordern, Bill Kalush, Chris Lewin, Tom Rodgers and Will
Shortz for allowing me to rummage through their libraries.
John Beasley, Edward Hordern, Bill Kalush, Will Shortz and Jerry Slocum for
numerous photocopies and copies from their collections.
Menso Folkerts, Richard Lorch, Michael Segre and the Institut für Geschichte der
Naturwissenschaft, Munich, for a most useful visit in Sep 1994 and for producing a copy of
Catel.
Raffaella Franci and the Dipartimento di Matematica and the Centro Studi della
Matematica Medioevale at Università di Siena for a most useful visit in Sep 1994.
Takao Hayashi for much material from Japan and India.
My wife for organizing a joint trip to Newcastle in Sep 1997 where I made use of the
Wallis Collection.
Finally, I would like to thank a large number of publishers, distributors, bookdealers
and even authors who have provided copies of the books and documents upon which much of
this work is based. Bookdealers have often let me examine books in their shops. Their help is
greatly appreciated. There are too many of these to record here, but I would like to mention
Fred Whitehart (†1999), England's leading dealer in secondhand scientific books for many
years who had a real interest in mathematics.
SOURCES - page 12
CONTENTS
INTRODUCTION 1
Nature of This Work 1
Similar Works 2
Coverage 3
Status of the Project 4
Technical Notes 6
New Sections in This Edition
Acknowledgements 7
CONTENTS
7
10
ABBREVIATIONS 20
Diacritical Marks and Notation 20
Abbreviations of Journals and Series
Abbreviations of Publishers 21
Abbreviations of Months 21
Publishers' Locations 21
COMMON REFERENCES
21
22
SOME OTHER RECURRING REFERENCES
1.
79
BIOGRAPHICAL MATERIAL in Chronological Order
82
Alcuin, Fibonacci, Pacioli, Bachet, Leurechon/van Etten, Ozanam, Montucla, Carroll,
Hoffmann, Loyd & Loyd Jr, Lucas, Schubert, Ball, Dudeney, Ahrens, Perelman, Phillips.
2.
GENERAL PUZZLE COLLECTIONS AND SURVEYS
3.
GENERAL HISTORICAL AND BIBLIOGRAPHICAL MATERIAL
3.A.
3.B.
General Historical Material 91
Bibliographical Material 91
4.
MATHEMATICAL GAMES
4.A.
General Theory and Nim-like Games 97
4.A.1.
One Pile Game 97
4.A.1.a.
The 31 Game 100
4.A.2.
Symmetry Arguments 102
4.A.3.
Kayles 102
4.A.4.
Nim 103
4.A.5.
General Theory 105
Particular Games 106
4.B.1.
Tic-Tac-Toe = Noughts and Crosses
4.B.1.a.
In Higher Dimensions 114
4.B.2.
Hex 115
4.B.3.
Dots and Boxes 116
4.B.4.
Sprouts 117
4.B.
97
106
90
91
SOURCES - page 13
4.B.5.
4.B.6.
4.B.7.
4.B.8.
4.B.9.
4.B.10.
4.B.11.
4.B.12.
4.B.13.
4.B.14.
4.B.15.
Ovid's Game and Nine Men's Morris 118
Phutball 124
Bridg-It 124
Chomp 124
Snakes and Ladders 125
Mu Torere 127
Mastermind, etc. 127
Rithmomachia = The Philosophers' Game
Mancala Games 129
Dominoes, etc. 130
Svoyi Kosiri 130
5.
COMBINATORIAL RECREATIONS
5.A.
The 15 Puzzle, etc. 131
General 131
Early Alphabetic Versions 131
Loyd 132
The 15 Puzzle 132
5.A.1.
Non-square Pieces 139
5.A.2.
Three Dimensional Versions 140
5.A.3.
Rolling Piece Puzzles 141
5.A.4.
Panex Puzzle 142
Crossing Problems 142
5.B.1.
Lowering from Tower Problem 151
5.B.2.
Crossing a Bridge with a Torch 152
False Coins with a Balance 152
5.C.1.
Ranking Coins with a Balance 155
Measuring Problems 156
5.D.1.
Jugs & Bottles 156
5.D.2.
Ruler with Minimal Number of Marks 161
5.D.3.
False Coins with a Weighing Scale 162
5.D.4.
Timing with Hourglasses 162
5.D.5.
Measure Half a Barrel 162
Euler Circuits and Mazes 163
5.E.1.
Mazes 167
5.E.2.
Memory Wheels = Chain Codes 172
5.E.2.a
Pantactic Squares 173
Hamiltonian Circuits 174
5.F.1.
Knight's Tours and Paths 174
5.F.2.
Other Hamiltonian Circuits 181
5.F.3.
Knight's Tours in Higher Dimensions 182
5.F.4.
Other Circuits In and On a Cube 183
Connection Problems 183
5.G.1.
Gas, Water and Electricity 183
Coloured Squares and Cubes, etc. 184
5.H.1.
Instant Insanity = The Tantalizer 184
5.H.2.
MacMahon Pieces 185
5.H.3.
Path Forming Puzzles 187
5.H.4.
Other and General 187
Latin Squares and Euler Squares 190
5.I.1.
Eight Queens Problem 192
5.B.
5.C.
5.D.
5.E.
5.F.
5.G.
5.H.
5.I.
131
128
SOURCES - page 14
5.J.
5.K.
5.L.
5.M.
5.N.
5.O.
5.P.
5.Q.
5.R.
5.S.
5.T.
5.U.
5.V.
5.W
5.X
5.Y.
5.Z.
5.AA.
5.AB.
5.AC.
5.AD.
5.I.2.
Colouring Chessboard with No Repeats in a Line 195
Squared Squares, etc. 195
5.J.1.
Mrs Perkins's Quilt 197
5.J.2.
Cubing the Cube 198
5.J.3.
Tiling a Square of Side 70 with Squares of Sides 1, 2, ..., 24
Derangements 198
5.K.1
Deranged Boxes of A, B and A & B 199
5.K.2
Other Logic Puzzles Based on Derangements 199
5.K.3
Cayley's Mousetrap 200
Ménage Problem 200
Six People at a Party -- Ramsey Theory 201
Jeep or Explorer's Problem 201
Tait's Counter Puzzle: BBBBWWWW to WBWBWBWB 204
General Moving Piece Puzzles 207
5.P.1.
Shunting Puzzles 207
5.P.2.
Taquin 209
Number of Regions Determined by N Lines or Planes 209
5.Q.1.
Number of Intersections Determined by N Lines 210
Jumping Piece Games 210
5.R.1.
Peg Solitaire 210
5.R.1.a.
Triangular Version 213
5.R.1.b.
Other shapes 214
5.R.2.
Frogs and Toads: BBB_WWW to WWW_BBB 215
5.R.3.
Fore and Aft -- 3 by 3 Squares Meeting at a Corner 217
5.R.4.
Reversing Frogs and Toads: _12...n to _n...21 218
5.R.5.
Fox and Geese, etc. 219
5.R.6.
Octagram Puzzle 222
5.R.7.
Passing Over Counters 223
Chain Cutting and Rejoining 226
5.S.1.
Using Chain Links to Pay for a Room 227
Dividing a Cake Fairly 227
Pigeonhole Recreations 228
Think-A-Dot, etc. 229
Making Three Pieces of Toast 230
5.W.1.
Boiling Eggs 230
Counting Figures in a Pattern 231
5.X.1.
Counting Triangles 231
5.X.2.
Counting Rectangles or Squares 233
5.X.3.
Counting Hexagons 235
5.X.4.
Counting Circles 235
Number of Routes in a Lattice 235
Chessboard Placing Problems 238
5.Z.1.
Kings 239
5.Z.2.
Queens 239
5.Z.3.
Bishops 240
5.Z.4.
Knights 241
5.Z.5.
Rooks 241
5.Z.6.
Mixtures 241
Card Shuffling 242
Folding a Strip of Stamps 244
Properties of the Seven Bar Digital Display 244
Stacking a Deck to Produce a Special Effect 245
198
SOURCES - page 15
5.AE.
5.AF.
5.AG.
Reversing Cups 245
Spotting Dice 245
Rubik's Cube and Similar Puzzles 246
5.AG.1. Rubik's Cube 246
5.AG.2. Hungarian Rings, etc. 246
6.
GEOMETRIC RECREATIONS
6.A.
6.B.
6.C.
6.D.
6.E.
6.F.
Pi 248
Straight Line Linkages 249
Curves of Constant Width 250
Flexagons 251
Flexatube 253
Polyominoes, etc. 253
6.F.1.
Other Chessboard Dissections 262
6.F.2.
Covering Deleted Chessboard with Dominoes 264
6.F.3.
Dissecting a Cross into Zs and Ls 264
6.F.4.
Quadrisecting an L-Tromino, etc. 266
6.F.5.
Other Dissections into Polyominoes 268
Soma Cube 269
6.G.1.
Other Cube Dissections 270
6.G.2.
Dissection of 63 into 33, 43 and 53, etc. 271
6.G.3.
Dissection of a Die into Nine 1 x 1 x 3 271
6.G.4.
Use of Other Polyhedral Pieces 272
Pick's Theorem 272
Sylvester's Problem of Collinear Points 273
Four Bugs and Other Pursuit Problems 273
Dudeney's Square to Triangle Dissection 275
Crossed Ladders 275
6.L.1.
Ladder Over Box 277
Spider & Fly Problems 278
Dissection of a 1 x 1 x 2 Block to a Cube 279
Passing a Cube Through an Equal or Smaller Cube
-- Prince Rupert's Problem 279
Geometrical Vanishing 280
6.P.1.
Paradoxical Dissections of the Chessboard Based on
Fibonacci Numbers 280
6.P.2.
Other Types 282
Knotting a Strip to Make a Regular Pentagon 285
Geometric Fallacies 285
6.R.1.
Every Triangle is Isosceles 286
6.R.2.
A Right Angle is Obtuse 287
6.R.3.
Lines Approaching but not Meeting 287
6.R.4.
Others 287
Tangrams, et al. 287
General Histories 287
Specific Items 289
6.S.1.
Loculus of Archimedes 299
6.S.2.
Other Sets of Pieces 300
No Three in a Line Problem 301
Tiling 302
6.U.1.
Penrose Pieces 302
6.G.
6.H.
6.I.
6.J.
6.K.
6.L.
6.M.
6.N.
6.O.
6.P.
6.Q.
6.R.
6.S.
6.T.
6.U.
248
SOURCES - page 16
6.U.2.
Packing Bricks in Boxes 302
Silhouette and Viewing Puzzles 303
Burr Puzzles 306
6.W.1.
Three Piece Burr 306
6.W.2.
Six Piece Burr = Chinese Cross 307
6.W.3.
Three Piece Burr with Identical Pieces 309
6.W.4.
Diagonal Six Piece Burr = Trick Star 309
6.W.5.
Six Piece Burr with Identical Pieces 310
6.W.6.
Altekruse Puzzle 310
6.W.7.
Other Burrs 310
6.X.
Rotating Rings of Polyhedra 311
6.Y.
Rope Round the Earth 312
6.Z.
Langley's Adventitious Angles 314
6.AA. Nets of Polyhedra 314
6.AB. Self-Rising Polyhedra 316
6.AC. Conway's Life 316
6.AD. Isoperimetric Problems 316
6.AD.1. Largest Parcel One Can Post 318
6.AE. 6" Hole Through Sphere Leaves Constant Volume 319
6.AF. What Colour Was The Bear? 319
6.AG. Moving Around a Corner 322
6.AH. Tethered Goat 323
6.AI. Trick Joints 324
6.AJ. Geometric Illusions 325
6.AJ.1.
Two Pronged Trident 328
6.AJ.2.
Tribar and Impossible Staircase 329
6.AJ.3.
Café Wall Illusion 330
6.AJ.4.
Stereograms 331
6.AJ.5.
Impossible Crate 331
6.AK. Polygonal Path Covering N x N Lattice of Points, Queen's Tours, etc. 331
6.AL. Steiner-Lehmus Theorem 334
6.AM. Morley's Theorem 335
6.AN. Volume of the Intersection of Two Cylinders 335
6.AO. Configuration Problems 336
6.AO.1. Place Four Points Equidistantly = Make Four Triangles with Six
Matchsticks 343
6.AO.2. Place an Even Number in Each Line 345
6.AP. Dissections of a Tetrahedron 346
6.AP.1. Two Pieces 346
6.AP.2. Four Pieces 346
6.AQ. Dissections of a Cross, T or H 347
6.AR. Quadrisected Square Puzzle 348
6.AS. Dissection of Squares into a Square 349
6.AS.1. Twenty 1, 2, 5 Triangles Make a Square, i.e. Five Equal Squares to a
Square 349
6.AS.1.a.
Greek Cross to a Square 352
6.AS.1.b.
Other Greek Cross Dissections 353
6.AS.2. Two (Adjacent) Squares to a Square 353
6.AS.2.a.
Two Equal Squares to a Square 356
6.AS.3. Three Equal Squares to a Square 356
6.AS.3.a.
Three Equal 'Squares' to a Hexagon 356
6.AS.4. Eight Equal Squares to a Square 357
6.V.
6.W.
SOURCES - page 17
6.AS.5. Rectangle to a Square or Other Rectangle 357
Polyhedra and Tessellations 358
6.AT.1. Regular Polyhedra 358
6.AT.2. Star and Stellated Polyhedra 362
6.AT.3. Archimedean Polyhedra 364
6.AT.4. Uniform Polyhedra 369
6.AT.5. Regular-Faced Polyhedra 369
6.AT.6. Tessellations 369
6.AT.6.a.
Tessellating with Congruent Figures 369
6.AT.7. Plaiting of Polyhedra 371
6.AT.8. Dürer's Octahedron 371
6.AT.9. Other Polyhedra 371
6.AU. Three Rabbits, Dead Dogs and Trick Ponies 372
China 373
Other Asia 375
Paderborn 378
Medieval Europe 380
Modern Versions of the Three Rabbits Puzzle 388
Dead Dogs 389
Trick Mules
394
6.AV. Cutting Up in Fewest Cuts 394
6.AW. Division into Congruent Pieces 394
6.AW.1. Mitre Puzzle 394
6.AW.2. Rep-Tiles 395
6.AW.3. Dividing a Square into Congruent Parts 396
6.AW.4. Dividing an L-Tromino into Congruent Parts 397
6.AX. The Packer's Secret 397
6.AY. Dissect 3A x 2B to Make 2A x 3B, etc. 398
6.AY.1. O'Beirne's Steps 400
6.AY.2. Swiss Flag Puzzle 400
6.AZ. Ball Pyramid Puzzles 401
6.BA. Cutting a Card so One Can Pass Through It 402
6.BB. Doubling an Area Without Changing Its Height or Width 402
6.BC. Hoffmann's Cube 403
6.BD. Bridge a Moat with Planks 403
6.BE. Reverse a Triangular Array of Ten Circles 405
6.BF. Pythagorean Recreations 405
6.BF.1.
The Broken Bamboo 406
6.BF.2.
Sliding Spear = Leaning Reed 407
6.BF.3.
Well Between Two Towers 408
6.BF.4.
Rail Buckling 3411
6.BF.5.
Travelling on Sides of a Right Triangle 412
6.BG. Quadrisect a Paper Square with One Cut 412
6.BH. Moiré Patterns 412
6.BI.
Venn Diagrams for n Sets 413
6.BJ. 3D Dissection Puzzles 415
6.BK. Superellipse 415
6.BL. Tan-1 ⅓ + Tan-1 ½ = Tan-1 1, etc. 416
6.BM. Dissect Circle into Two Hollow Ovals 417
6.BN. Round Peg in Square Hole or Vice Versa 417
6.BO. Butterfly Problem 418
6.BP. Early Matchstick Puzzles 418
6.AT.
SOURCES - page 18
6.BQ.
6.BR.
6.BS.
6.BT.
6.BU.
6.BV.
6.BW.
Covering a Disc with Discs 419
What is a General Triangle? 420
Form Six Coins into a Hexagon 420
Placing Objects in Contact 421
Construction of n-gons 421
Geometric Constructions 423
Distances to Corners of a Square 424
7.
ARITHMETIC & NUMBER-THEORETIC RECREATIONS
7.A.
7.B.
7.C.
7.D.
7.E.
Fibonacci Numbers 426
Josephus or Survivor Problem 429
Egyptian Fractions 443
The First Digit Problem 443
Monkey and Coconuts Problems 444
7.E.1.
Versions with All Getting the Same 457
Illegal Operations Giving Correct Result 458
Inheritance Problems 459
7.G.1.
Half + Third + Ninth, etc. 459
7.G.2.
Posthumous Twins, etc. 464
Division and Sharing Problems -- Cistern Problems 467
7.H.1.
With Growth -- Newton's Cattle Problem 484
7.H.2.
Division of Casks 486
7.H.3.
Sharing Unequal Resources -- Problem of the Pandects 487
7.H.4.
Each Doubles Other's Money to Make All Equal, etc. 490
7.H.5.
Sharing Cost of Stairs, etc. 492
7.H.6.
Sharing a Grindstone 494
7.H.7.
Digging Part of a Well 494
Four Fours, etc. 496
7.I.1.
Largest Number Using Four Ones, etc. 503
Salary Puzzle 504
Congruences 505
7.K.1.
Casting Out Nines 506
Geometric Progressions 508
7.L.1.
1 + 7 + 49 + ... & St. Ives 510
7.L.2.
1 + 2 + 4 + .... 513
7.L.2.a.
Chessboard Problem 513
7.L.2.b.
Horseshoe Nails Problem 517
7.L.2.c.
Use of 1, 2, 4, ... as Weights, etc. 518
7.L.3.
1 + 3 + 9 + ... and Other Systems of Weights 519
Binary System and Binary Recreations 521
7.M.1.
Chinese Rings 523
7.M.2.
Tower of Hanoi 527
7.M.2.a.
Tower of Hanoi with More Pegs 530
7.M.3.
Gray Code 531
7.M.4.
Binary Divination 531
7.M.4.a.
Ternary Divination 533
7.M.4.b.
Other Divinations Using Binary or Ternary 533
7.M.5.
Loony Loop = Gordian Knot 537
7.M.6.
Binary Button Games 537
Magic Squares 540
Surveys 540
7.F.
7.G.
7.H.
7.I.
7.J.
7.K.
7.L.
7.M.
7.N.
426
SOURCES - page 19
7.O.
7.P.
7.Q.
7.R.
7.S.
7.T.
7.U.
7.V.
7.W.
7.X.
7.Y.
7.Z.
7.AA.
7.AB.
7.AC.
7.AD.
7.AE.
Possible Early References 541
7.N.1.
Magic Cubes 554
7.N.2.
Magic Triangles 556
7.N.3.
Anti-Magic Squares and Triangles 557
7.N.4.
Magic Knight's Tour 558
7.N.5.
Other Magic Shapes 559
Magic Hexagon 562
7.O.1
Other Magic Hexagons 563
Diophantine Recreations 565
7.P.1.
Hundred Fowls and Other Linear Problems 565
7.P.2.
Chinese Remainder Theorem 582
7.P.3.
Archimedes' Cattle Problem 588
7.P.4.
Present of Gems 589
7.P.5.
Selling Different Amounts 'At Same Prices' Yielding the Same 589
7.P.6.
Conjunction of Planets, etc. 594
7.P.7.
Robbing and Restoring 595
Blind Abbess and her Nuns -- Rearrangement Along Sides of a 3 x 3 Square
Conserving Side Totals 597
7.Q.1.
Rearrangement on a Cross 600
7.Q.2.
Rearrange a Cross of Six to Make Two Lines of Four 601
"If I Had One From You, I'd Have Twice You" 602
7.R.1.
Men Find a Purse and 'Bloom of Thymaridas' 608
7.R.2.
"If I Had 1/3 of Your Money, I Could Buy the Horse" 614
7.R.3.
Sisters and Brothers 623
7.R.4.
"If I Sold Your Eggs at my Price, I'd Get ...." 623
Dilution and Mixing Problems 624
7.S.1.
Dishonest Butler Drinking Some and Replacing with Water 624
7.S.2.
Water in Wine Versus Wine in Water 625
Four Number Game 626
Postage Stamp Problem 627
xy = yx and Iterated Exponentials 627
Card Piling over a Cliff 628
How Old is Ann? and Other Age Problems
629
Combining Amounts and Prices Incoherently 638
7.Y.1.
Reversal of Averages Paradox 640
7.Y.2.
Unfair Division 641
Missing Dollar and Other Erroneous Accounting 642
Negative Digits 643
7.AA.1. Negative Bases, etc. 644
Perfect Numbers, etc. 645
Cryptarithms, Alphametics and Skeleton Arithmetic 647
7.AC.1. Cryptarithms: SEND + MORE = MONEY, etc. 647
7.AC.2. Skeleton Arithmetic: Solitary Seven, etc. 650
7.AC.3. Pan-Digital Sums 652
7.AC.3.a Insertion of Signs to Make 100, etc. 653
7.AC.4. Pan-Digital Products 654
7.AC.5. Pan-Digital Fractions 656
7.AC.6. Other Pan-Digital and Similar Problems 657
7.AC.7. Self-descriptive Numbers, Pangrams, etc. 660
Selling, Buying and Selling Same Item 661
7.AD.1. Pawning Money 662
Use of Counterfeit Bill or Forged Cheque 662
SOURCES - page 20
7.AF.
Arithmetic Progressions 664
7.AF.1. Collecting Stones 664
7.AF.2. Clock Striking 666
7.AG. 2592 667
7.AH. Multiplying by Reversing 668
7.AH.1. Other Reversal Problems 669
7.AI. Impossible Exchange Rates 669
7.AJ. Multiplying by Shifting 669
7.AJ.1.
Multiplying by Appending Digits 671
7.AK. Lazy Worker 671
7.AL. If A is B, What is C? 674
7.AM. Crossnumber Puzzles 676
7.AN. Three Odds Make an Even, etc. 678
7.AO. Divination of a Permutation 680
7.AP. Knowing Sum vs Knowing Product 684
7.AQ. Numbers in Alphabetic Order 687
7.AR. 1089 687
7.AS. Cigarette Butts 690
7.AT. Bookworm's Distance 690
7.AU. Number of Cuts to Make n Pieces 691
7.AV. How Long to Strike Twelve? 692
7.AW. 28/7 = 13 692
7.AX. Sum = Product, etc. 692
7.AY. Sum of Powers of Digits 693
7.AZ. Divination of a Pair of Cards from its Rows 694
7.BA. Cycle of Numbers with Each Closer to Ten than the Previous
7.BB. Iterated Functions of Integers 696
7.BC. Unusual Difficulty Making Change 697
8.
PROBABILITY RECREATIONS
699
8.A.
8.B.
8.C.
8.D.
8.E.
8.F.
8.G.
8.H.
8.I.
8.J.
8.K.
8.L.
Buffon's Needle Problem 699
Birthday Problem 699
Probability that a Triangle is Acute 701
Attempts to Modify Boy-Girl Ratio 702
St. Petersburg Paradox 702
Problem of Points 703
Probability that Three Lengths Form a Triangle
Probability Paradoxes 705
8.H.1.
Bertrand's Box Paradox 705
8.H.2.
Bertrand's Chord Paradox 705
Taking the Next Train 706
Clock Patience or Solitaire 706
Sucker Bets 706
Nontransitive Games 707
9.
LOGICAL RECREATIONS
9.A.
9.B.
9.C.
9.D.
All Cretans are Liars, etc. 708
Smith -- Jones -- Robinson Problem
Forty Unfaithful Wives 712
Spots on Foreheads 712
708
712
704
696
SOURCES - page 21
9.E.
9.F.
9.G.
9.H.
9.I.
9.J.
9.K.
Strange Families 714
General Studies of Kinship Relations 714
Deceased Wife's Sister, etc. 715
General Family Riddles 716
9.E.1.
That Man's Father is My Father's Son, etc. 722
9.E.2.
Identical Siblings who are not Twins 726
The Unexpected Hanging 726
Truthtellers and Liars 726
Prisoner's Dilemma 729
Hempel's Raven Paradox 729
Use of a Fallen Signpost 729
Lewis Carroll's Barber Paradox 730
10.
PHYSICAL RECREATIONS
10.A.
Overtaking and Meeting Problems 731
10.A.1.
Circling an Army 743
10.A.2.
Number of Buses Met 745
10.A.3.
Times from Meeting to Finish Given 745
10.A.4.
The Early Commuter 746
10.A.5.
Head Start Problems 747
10.A.6.
Double Crossing Problems 748
10.A.7.
Trains Passing 748
10.A.8.
Too Slow, Too Fast 748
Fly Between Trains 748
Lewis Carroll's Monkey Problem 750
Mirror Problems 751
10.D.1.
Mirror Reversal Paradox 751
10.D.2.
Other Mirror Problems 753
10.D.3.
Magic Mirrors 753
Wheel Paradoxes 754
10.E.1.
Aristotle's Wheel Paradox 754
10.E.2.
One Wheel Rolling Around Another 754
10.E.3.
Hunter and Squirrel 755
10.E.4.
Railway Wheels Paradox 756
Floating Body Problems 756
Motion in a Current or Wind 758
Snail Climbing out of Well 759
Limited Means of Transport -- Two Men and a Bike, etc.
Resistor Networks 764
Problem of the Date Line 765
Falling Down a Hole Through the Earth 767
Celts = Rattlebacks 770
10.M.1. Tippee Tops 771
Ship's Ladder in Rising Tide 771
Erroneous Averaging of Velocities 772
False Balance 772
Push a Bicycle Pedal 773
Clock Hand Problems 774
Walking in the Rain 776
Centrifugal Puzzles 777
Shortest Route Via a Wall 777
10.B.
10.C.
10.D.
10.E.
10.F.
10.G.
10.H.
10.I.
10.J.
10.K.
10.L.
10.M.
10.N.
10.O.
10.P.
10.Q.
10.R.
10.S.
10.T.
10.U.
730
763
SOURCES - page 22
10.V.
10.W.
10.X.
10.Y.
10.Z.
10.AA.
10.AB.
10.AC.
10.AD.
10.AE.
Pick Up Puzzles = Pluck It 777
Puzzle Vessels 778
How Far Does a Phonograph Needle Travel?
Double Cone Rolls Uphill 784
The Wobbler 784
Non-Regular Dice 785
Bicycle Track Problems 788
Roberval's Balance 790
Pound of Feathers 790
Juggling over a Bridge 790
11.
TOPOLOGICAL RECREATIONS
11.A.
11.B.
11.C.
11.D.
11.E.
11.F.
11.G.
11.H.
Scissors on String 791
Two People Joined by Ropes at Wrists 792
Two Balls on String Through Leather Hole and Strap = Cherries Puzzle
Solomon's Seal 795
Loyd's Pencil Puzzle 797
The Imperial Scale 797
Trick Purses 798
Removing Waistcoat Without Removing Coat 799
11.H.1.
Removing Loop from Arm 799
Heart and Ball Puzzle and Other Loop Puzzles 799
Möbius Strip 802
Wire Puzzles 805
11.K.1.
Ring and Spring Puzzle 807
11.K.2.
String and Spring Puzzle 807
11.K.3.
Magic Chain = Tumble Rings 807
11.K.4.
Puzzle Rings 808
11.K.5.
Ring Mazes 808
11.K.6.
Interlocked Nails, Hooks, Horns, etc. 809
11.K.7.
Horseshoes Puzzle 809
11.K.8.
The Caught Heart 810
Jacob's Ladder and Other Hinging Devices 810
Puzzle Boxes 811
Three Knives Make a Support 813
Borromean Rings
815
The Lonely Monk
816
Turning an Inner Tube Inside Out 817
String Figures 817
Puzzle Knives 818
11.I.
11.J.
11.K.
11.L.
11.M.
11.N.
11.O.
11.P.
11.Q.
11.R
11.S.
784
791
793
SOURCES - page 23
ABBREVIATIONS
DIACRITICAL MARKS AND NOTATION
Before converting to LocoScript, I used various conventions, given below, to represent
diacritical marks. Each symbol (except ') occurred after the letter it referred to. I have now
converted these and all mathematical conventions into correct symbols, so far as possible, but
I may have missed some, so I am keeping this information for the present.
Common entries using such marks are given later in this section and only the
abbreviated or simplified form is used later -- e.g. I use Problemes for Bachet's work rather
than Problèmes. (Though this may change??)
Initially, I did not record all diacritical marks, so some may be missing though I have
checked almost all items. I may omit diacritical marks which are very peculiar.
Transliterations of Arabic, Sanskrit, Chinese, etc. are often given in very different
forms. See Smith, History, vol. 1, pp. xvii-xxii for a discussion of the problems. The use of
^ and ˉ seems interchangeable and I have used ^ when different versions use both ^ and ˉ
, except when quoting a title or passage when I use the author's form. [Smith, following Suter,
uses ^ for Arabic, but uses ˉ for Indian. Murray uses ˉ for both. Wieber uses ˉ for
Arabic. Van der Linde uses ´ for Arabic. Datta & Singh use ^ for Indian.]
There are two breathing marks in Arabic -- ayn ‘ and alif/hamzah ’ -- but originally I
didn't have two forms easily available, so both were represented by '. I have now converted
almost all of these to ‘ and ’. These don't seem to be as distinct in the printing as on my
screen.
French practice in accenting capitals is variable and titles are often in capitals, so
expected marks may be missing. Also, older printing may differ from modern usage -- e.g. I
have seen: Liège and Liége; Problèmes, Problêmes and Problémes. When available, I have
transcribed the material as printed without trying to insert marks, but many places insert the
marks according to modern French spelling.
Greek and Cyrillic titles are now given in the original with an English transliteration
(using the Amer. Math. Soc. transliteration for Cyrillic).
I usually ignore the older usage of v for u and i for j, so that I give mathematiqve
as mathematique and xiij as xiii.
I used a1, a2, ..., ai, etc. for subscripted variables, though I also sometimes used
a(1), a(2), ..., a(i), etc. Superscripts or exponents were indicated by use of ^, e.g. 2^3 is 8.
These have been converted to ordinary sub- and superscript usage, but ^ may be used when
the superscript is complicated -- e.g. for 2^ai or 9^(99).
Greek letters were generally spelled out in capitals or marked with square brackets, e.g.
PI, [pi], PHI, but these have probably all been converted.
My word processor does not produce binomial coefficients easily, so I use BC(n, k) for
n!/k!(n-k)!
Many problems have solutions which are sets of fractions with the same denominator
and I abbreviate a/z, b/z, c/z as (a, b, c)/z. Notations for particular problems are explained
at the beginning of the topic.
Rather than attempting to italicise letters used as symbols, I generally set them off by
double-spaces on each side -- see examples above. Other mathematical notations may be
improvised as necessary and should be obvious.
Recall that the symbols below occurred after the letter they referred to, except for ' .
"
denoted umlaut or diaeresis in general, e.g.: ä, ë, ï, ö, ü.
/
was used after a letter for accent acute, ́, after l for ł in Polish, and after o for ø in
Scandinavian.
\
denoted accent grave, ̀.
SOURCES - page 24
^
denoted the circumflex, ^, in Czech, etc.; the overbar (macron) ˉ or ^ for a long
vowel in Sanskrit, Hindu, etc.; and the overbar used to indicate omission in medieval MSS.
@
denoted the cedilla (French ç and Arabic ş) and the ogonek or Polish hook (Polish ą).
.
denoted the underdot in ḥ, ḳ, ṇ, ṛ, ṣ, ṭ, in Sanskrit, Hindu, Arabic. These are
sometimes written with a following h -- e.g. k may also be written kh and I may
sometimes have used this. (It is difficult to search for ḥ. , etc., so not all of these may be
converted.) This mark vanishes when converted to WordPerfect.
*
denoted the overdot for ġ, ṁ, ṅ, in Sanskrit, Hindu, Arabic. This vanishes over m
and n in WordPerfect.
~
denoted the Spanish tilde ~ and the caron or hachek ˇ, in ğ, š. The breve is a curved
version, ˘, of the same symbol and is essentially indistinguishable from the caron. It occurs
in Russian й, which is translitereated as ĭ.
_
denoted the underbar in ḏ , j, ṯ (I cannot find a j with an underbar in Arial). This mark
vanishes in WordPerfect.
'
denotes breathing marks in Arabic, etc. There are actually two forms of this -- ayn ’
and alif/hamzah ‘ -- but I didn't have two forms easily available and originally entered both
as apostrophe ' . These normally occur between letters and I placed the ' in the same space.
I have converted most of these.
Commonly occurring words with diacritical marks are: Académie, arithmétique,
bibliothèque, Birkhäuser, café, carré, école, Erdös, für, géomètre, géométrie, Göttingen,
Hanoï -- in French only, -ième, littéraire, mathématique, mémoire, ménage, misère, Möbius,
moiré, numérique, Pétersbourg, probabilités, problème (I have seen problêmes??), Rätsel,
récréation, Sändig, siècle, société, Thébault, théorie, über, umfüllung.
I have used ?? to indicate uncertainty and points where further work needs to be done.
The following symbols after ?? indicate the action to be done.
*
check for diacritical marks, etc.
NX
no Xerox or other copy
NYS
not yet seen
NYR not yet read
o/o
on order
SP
check spelling
Other comments may be given.
ABBREVIATIONS OF JOURNALS AND SERIES. See: AMM, CFF, CM, CMJ,
Family Friend, G&P, G&PJ, HM, JRM, MG, MiS, MM, MS, MTg, MTr, M500,
OPM, RMM, SA, SM, SSM in Common References below.
ABBREVIATIONS OF PUBLISHERS. See: AMS, C&W, CUP, Loeb Classical
Library, MA, MAA, NCTM, OUP in Common References below.
ABBREVIATIONS OF MONTHS. All months are given by their first three letters in
English: Jan, Feb, ....
PUBLISHERS' LOCATIONS. The following publisher's locations will not be cited
each time. Other examples may occur and can be found in the file PUBLOC.
AMS (American Mathematical Society), Providence, Rhode Island, USA.
Chelsea Publishing, NY, USA.
CUP (Cambridge University Press), Cambridge, UK.
SOURCES - page 25
Dover, NY, USA.
Freeman, San Francisco, then NY, USA.
Harvard University Press, Cambridge, Massachusetts, USA.
MA (Mathematical Association), Leicester, UK.
MAA (Mathematical Association of America), Washington, DC, USA.
NCTM (National Council of Teachers of Mathematics), Reston, Virginia, USA.
Nelson, London, UK.
OUP (Oxford University Press), Oxford, UK (and also NY, USA).
Penguin, Harmondsworth, UK.
Simon & Schuster, NY, USA.
COMMON REFERENCES.
NOTES. When referring to items below, I will usually include the earliest reasonable
date, even though the citation may be to a much later edition. For example, I would say
"Canterbury Puzzles, 1907", even though I am citing problem numbers or pages from the 1958
Dover reprint of the 1919 edition. Sometimes the earlier editions are hard to come by and I
have sometimes found that the earlier edition has different pagination -- in that case I will
(eventually) make the necessary changes.
Edition information in parentheses indicates items or editions that I have not seen,
though I don't always do this when the later version is a reprint or facsimile.
Abbaco.
See: Pseudo-dell'Abbaco.
Abbot Albert.
Abbot Albert von Stade. Annales Stadenses. c1240. Ed. by
J. M. Lappenberg. In: Monumenta Germaniae Historica, ed. G. H. Pertz, Scriptorum
t. XVI, Imp. Bibliopolii Aulici Hahniani, Hannover, 1859 (= Hiersemann, Leipzig,
1925), pp. 271-359. (There are 13 recreational problems on pp. 332-335.) [Vogel, on
p. 22 of his edition of the Columbia Algorism, dates this as 1179, but Tropfke gives
1240, which is more in line with Lappenberg's notes on variants of the text. The
material of interest, and several other miscellaneous sections, is inserted at the year
1152 of the Annales, so perhaps Vogel was misled by this.] I have prepared an
annotated translation of this: The problems of Abbot Albert (c1240). I have numbered
the problems and will cite this problem number.
Abraham.
R. M. Abraham. Diversions and Pastimes. Constable, London, 1933
= Dover, 1964 (slightly amended and with different pagination, later retitled: Tricks and
Amusements with Coins, Cards, String, Paper and Matches). I will cite the Constable
pages (and the Dover pages in parentheses).
Ackermann.
Alfred S. E. Ackermann. Scientific Paradoxes and Problems and Their
Solutions. The Old Westminster Press, London, 1925.
D. Adams. New Arithmetic. 1835.
Daniel Adams (1773-1864). ADAMS NEW ARITHMETIC.
Arithmetic, in which the principles of operating by numbers are analytically explained,
and synthetically applied; thus combining the advantages to be derived both from the
inductive and synthetic mode of instructing: The whole made familiar by a great variety
of useful and interesting examples, calculated at once to engage the pupil in the study,
and to give him a full knowledge of figures in their application to all the practical
purposes of life. Designed for the use of schools and academies in the United States. J.
Prentiss, Keene, New Hampshire, 1836, boarded. 1-262 pp + 2pp publisher's ads,
apparently inserted backward. [Halwas 1-6 lists 1st ed as 1835, then has 1837, 1838,
SOURCES - page 26
1839, 1842, c1850.] This is a reworking of The Scholar's Arithmetic of 1801.
D. Adams. Scholar's Arithmetic. 1801.
Daniel Adams (1773-1864). The Scholar's Arithmetic; or, Federal
Accountant: Containing. I. Common arithmetic, .... II. Examples and Answers with
Blank Spaces, .... III. To each Rule, a Supplement, comprehending, 1. Questions .... 2.
Exercises. IV. Federal Money, .... V. Interest cast in Federal Money, .... VI.
Demonstration by engravings .... VII. Forms of Notes, .... The Whole in a Form and
Method altogether New, for the Ease of the Master and the greater Progress of the
Scholar. Adams & Wilder, Leominster, Massachusetts, 1801; 2nd ed, 1802. 3rd ed ??.
4th ed, by Prentiss, 1807; 6th ed, 1810; 10th ed, 1816; Stereotype Edition, Revised and
Corrected, with Additions, 1819, 1820, 1824; John Prentiss, Keene, New Hampshire,
1825. [Halwas 8-14.] I have the 1825, whose Preface is for the 10th ed of 1816, so is
probably identical to that ed. The Preface says he has now made some revisions. The
only change of interest to us is that he has added answers to some problems. So I will
cite this as 1801 though I will be giving pages from the 1825 ed. The book was
thoroughly reworked as Adams New Arithmetic, 1835.
M. Adams. Indoor Games. 1912.
Morley Adams, ed. The Boy's Own Book of Indoor Games and
Recreations. "The Boy's Own Paper" Office, London, 1912; 2nd ptg, The Religious
Tract Society, London (same address), 1913. [This is a major revision of:
G. A. Hutchison, ed.; Indoor Games and Recreations; The Boy's Own Bookshelf;
New ed., Religious Tract Society, London, 1891 (possibly earlier) -- see 5.A.]
M. Adams. Puzzle Book. 1939.
Morley Adams. The Morley Adams Puzzle Book. Faber & Faber,
London, 1939.
M. Adams. Puzzles That Everyone Can Do. 1931.
Morley Adams. Puzzles that Everyone Can Do. Grant Richards,
London, 1931, boarded.
AGM.
Abhandlungen zur Geschichte der Mathematischen Wissenschaften mit
Einschluss ihrer Anwendungen. Begründet von Moritz Cantor. Teubner, Leipzig. The
first ten volumes were Supplements to Zeitschrift für Math. u. Physik, had a slightly
different title and are often bound in with the journal volume.
Ahrens, Wilhelm Ernst Martin Georg (1872-1927). See: A&N, MUS, 3.B, 7.N.
al-Karkhi.
Aboû Beqr Mohammed Ben Alhaçen Alkarkhî [= al-Karagi
= al-Karajī]. Untitled MS called Kitāb al-Fakhrī (or just Alfakhrî) (The Book
Dedicated to Fakhr al-Din). c1010. MS 952, Supp. Arabe de la Bibliothèque Impériale,
Paris. Edited into French by Franz Woepcke as: Extrait du Fakhrî. L'Imprimerie
Impériale, Paris, 1853; reprinted by Georg Olms Verlag, Hildesheim, 1982. My page
citations will be to Woepcke. Woepcke often refers to Diophantos, but his numbering
gets ahead of Heath's.
Alberti. 1747.
Giuseppe Antonio (or Giusepp-Antonio) Alberti (1715-1768). I Giochi
Numerici Fatti Arcani Palesati da Giuseppe Antonio Alberti. Bartolomeo Borghi,
Bologna, 1747, 1749. Venice, 1780, 1788(?). 4th ed., adornata di figure, Giuseppe
Orlandelli for Francesco di Niccolo' Pezzana, Venice, 1795 (reprinted: Arnaud,
Florence, 1979), 1813. Adornata di 16 figure, Michele Morelli, Naples, 1814. As: Li
Giuochi Numerici Manifestati, Edizione adorna di Figure in rame, Giuseppe Molinari,
Venice, 1815.
The editions have almost identical content, but different paginations. I have
compared several editions and seen little difference. The 1747 ed. has a dedication
which is dropped in the 2nd ed. which also omits the last paragraph of the Prefazione. I
only saw one other point where a few words were changed. I will give pages of 1747
(followed by 1795 in parenthesis). Much of Alberti, including almost all the material of
SOURCES - page 27
interest to us and many of the plates, is translated from vol. 4 of the 1723 ed. of
Ozanam.
(Serge Plantureux's 1993 catalogue describes a 1747-1749 ed. with Appendice al
Trattato de' Giochi Numerici (1749, 72 pp) & Osservazioni all'Appendice de' Giochi
Numerici (38 pp), ??NYS. The copy in the Honeyman Collection had the Appendice.
Christopher 3 has the Osservazioni. The Appendice is described by Riccardi as a severe
criticism of Alberti, attributed to Giovanni Antonio Andrea Castelvetri and published
by Lelio dall Volpe, Bologna, 1749. The Osservazioni are Alberti's response.)
Alcuin (c735-804).
Propositiones Alcuini doctoris Caroli Magni Imperatoris ad acuendos
juvenes. 9C.
IN: B. Flacci Albini seu Alcuini, Abbatis et Caroli Magni Imperatoris Magistri.
Opera Omnia: Operum pars octava: Opera dubia. Ed. D. Frobenius, Ratisbon, 1777,
Tomus secundus, volumen secundum, pp. 440-448. ??NYS. Revised and republished
by J.-P. Migne as: Patrologiae Cursus Completus: Patrologiae Latinae, Tomus 101,
Paris, 1863, columns 1143-1160.
A different version appears in: Venerabilis Bedae, Anglo-Saxonis Presbyteri.
Opera Omnia: Pars Prima, Sectio II -- Dubia et Spuria: De Arithmeticus
propositionibus. Tomus 1, Basel, 1563. (Rara, 131, says there were earlier editions:
Paris, 1521 (part), 1544-1545 (all), 1554, all ??NYS.) Revised and republished by J.-P.
Migne as: Patrologiae Cursus Completus: Patrologiae Latinae, Tomus 90, Paris, 1904,
columns 665-672. Incipiunt aliae propositiones ad acuendos juvenes is col. 667-672. A
version of this occurs in Ens' Thaumaturgus Mathematicus of 1636 -- cf under Etten.
The Alcuin has 53 numbered problems with answers. The Bede has 3 extra
problems, but the problems are not numbered, there are only 31 1/2 answers and there
are several transcription errors. The editor has used the Bede to rectify the Alcuin.
There is a recent critical edition of the text by Folkerts -- Die älteste
mathematische Aufgabensammlung in lateinischer Spräche: Die Alkuin
zugeschriebenen Propositiones ad Acuendos Iuvenes; Denkschriften der
Österreichischen Akademie der Wissenschaften, Mathematische-naturwissenschaftliche
Klasse 116:6 (1978) 13-80. (Also separately published by Springer, Vienna, 1978. The
critical part is somewhat revised as: Die Alkuin zugeschriebenen "Propositiones ad
Acuendos Iuvenes"; IN: Science in Western and Eastern Civilization in Carolingian
Times, ed. by P. L. Butzer & D. Lohrmann; Birkhäuser, Basel, 1993, pp. 273-281.) He
finds that the earliest text is late 9C and is quite close to the first edition cited above.
He uses the same numbers for the problems as above and numbers the extra Bede
problems as 11a, 11b, 33a. I use Folkerts for the numbering and the titles of problems.
John Hadley kindly translated Alcuin for me some years ago and made some
amendments when Folkerts' edition appeared. I annotated it and it appeared as:
Problems to Sharpen the Young, MG 76 (No. 475) (Mar 1992) 102-126. A slightly
corrected and updated edition, containing some material omitted from the MG version,
is available as Technical Report SBU-CISM-95-18, School of Computing, Information
Systems, and Mathematics, South Bank University, Oct 1995, 28pp.
Menso Folkerts and Helmuth Gericke have produced a German edition: Die
Alkuin zugeschriebenen Propositiones ad Acuendos Juvenes (Aufgabe zur Schärfung
des Geistes der Jugend); IN: Science in Western and Eastern Civilization in Carolingian
Times, ed. by P. L. Butzer & D. Lohrmann; Birkhäuser, Basel, 1993, pp. 283-362.
See also: David Singmaster. The history of some of Alcuin's Propositiones. IN:
Charlemagne and his Heritage 1200 Years of Civilization and Science in Europe: Vol.
2 Mathematical Arts; ed. by P. L. Butzer, H. Th. Jongen & W. Oberschelp; Brepols,
Turnhout, 1998, pp. 11-29.
SOURCES - page 28
AM. 1917.
H. E. Dudeney. Amusements in Mathematics. Nelson, 1917. (There
were reprintings in 1919, 1920, 1924, 1925, 1927, 1928, 1930, 1932, 1935, 1938, 1939,
1941, 1943, 1946, 1947, 1949, 1951, but it seems that the date wasn't given before
1941?) = Dover, 1958.
AMM.
American Mathematical Monthly.
AMS.
American Mathematical Society.
Les Amusemens. 1749.
Les Amusemens Mathématiques Precedés Des Elémens d'Arithmétique,
d'Algébre & de Géométrie nécessaires pour l'intelligence des Problêmes. André-Joseph
Panckoucke, Lille, 1749. Often listed with Panckoucke as author (e.g. by the NUC, the
BNC and Poggendorff), but the book gives no such indication. Sometimes spelled
Amusements. There were 1769 and 1799 editions.
Apianus. Kauffmanss Rechnung. 1527.
Petrus Apianus (= Peter Apian or Bienewitz or Bennewitz)
(1495-1552). Eyn Newe Unnd wolgegründte underweysung aller Kauffmanss
Rechnung in dreyen Büchern / mit schönen Regeln uň [NOTE: ň denotes an n with
an overbar.] fragstucken begriffen. Sunderlich was fortl unnd behendigkait in der
Welschē Practica uň Tolletn gebraucht wirdt / des gleychen fürmalss wider in
Teützscher noch in Welscher sprach nie gedrückt. durch Petrum Apianū von Leyssnick
/ d Astronomei zů Ingolstat Ordinariū / verfertiget. Georgius Apianus, Ingolstadt,
(1527), facsimile, with the TP of the 1544 ed. and 2pp of publication details added at
the end, Polygon-Verlag, Buxheim-Eichstätt, 1995, with 8pp commentary leaflet by
Wolfgang Kaunzner. (The TP of this has the first known printed version of Pascal's
Triangle.) Smith, Rara, pp. 155-157. (The d is an odd symbol, a bit like a δ or an 8,
which is used regularly for der both as a single word and as the ending of a word, e.g.
and for ander.) Smith notes that Apianus follows Rudolff (1526) very closely.
AR. c1450.
Frater Friedrich Gerhart (attrib.). Latin & German MSS, c1450, known
as Algorismus Ratisbonensis. Transcribed and edited from 6 MSS by Kurt Vogel as:
Die Practica des Algorismus Ratisbonensis; C. H. Beck'sche Verlagsbuchhandlung,
Munich, 1954. (Kindly sent by Prof. Vogel.) Vogel classifies the problems and gives
general comments on the mathematics on pp. 155-189. He gives detailed historical
notes on pp. 203-232. When appropriate, I will cite these pages before the specific
problems. He says (on p. 206) that almost all of Munich 14684 (see below) is included
in AR.
Arnold, George. See: Book of 500 Puzzles, Boy's Own Conjuring Book, Hanky Panky.
Arrighi, Gino. See: Benedetto da Firenze, Calandri, Pseudo-Dell'Abbaco, della Francesca,
Gherardi, Lucca 1754, P. M. Calandri.
Aryabhata.
Āryabhata (I)) [NOTE: ţ denotes a t with a dot under it and ş
denotes an s with a dot under it.] (476- ). Āryabhatīya. 499. Critically edited and
translated into English by Kripa Shankar Shukla, with K. V. Sarma. Indian National
Science Academy, New Delhi, 1976. (Volume 1 of a three volume series -- the other
two volumes are commentaries, of which Vol. 2 includes the commentary ĀryabhatīyaBhāşya, written by Bhaskara I in 629. Aryabhata rarely gives numerical examples, so
Bhaskara I provided them and these were later used by other Indian writers such as
Chaturveda, 860. The other commentaries are later and of less interest to us. Prof.
Shukla has sent a photocopy of an introductory booklet, which is an abbreviated version
of the introductory material of Vol. 1, with some extensions relating Aryabhata to other
writers.) The material is organized into verses. There is an older translation by Walter
Eugene Clark as: The Âryabhaţîya of Âryabhaţa; Univ. of Chicago Press, Chicago,
1930. (There was an Aryabhata II, c950, but he only occurs in 7.K.1.)
A&N.
Wilhelm Ahrens. Altes und Neues aus der Unterhaltungsmathematik.
SOURCES - page 29
Springer, Berlin, 1918.
Bachet, Claude-Gaspar (1581-1638). See: Problemes.
Bachet-Labosne. See: Problemes.
Badcock. Philosophical Recreations, or, Winter Amusements. [1820].
Philosophical Recreations, or, Winter Amusements. Thomas Hughes,
London, nd [1820]. [BCB 18-19; OCB, pp. 180 & 197. Heyl 22-23. Toole Stott 7577. Christopher 54-56. Wallis 34 BAD, 35 BAD. These give dates of 1820, 1822,
1828.] HPL [Badcock] RBC has three versions with slightly different imprints on the
title pages, possibly the three dates mentioned.
Wallis 34 BAD has this bound after the copy of: John Badcock; Domestic
Amusements, or Philosophical Recreations ...; T. Hughes, London, nd [1823], and it is
lacking its Frontispiece and TP -- cf in 6.BH. HPL [Badcock] has both books,
including the folding Frontispieces. The earlier does not give an author, but its Preface
is signed J. B. and the later book does give his name and calls itself a sequel to the
earlier. Toole Stott 75-80 clearly describes both works. Some of the material is used in
Endless Amusement II.
Baker. Well Spring of Sciences. 1562?
Humfrey Baker (fl. 1557-1587). The Well Sprynge of Sciences Which
teacheth the perfect worke and practise of Arithmeticke both in whole numbers and
fractions, with such easye and compendious instruction into the sayde arte, .... Rouland
Hall for James Rowbotham, London, 1562. [Smith, Rara, p. 327, says it was written in
1562 but wasn't actually printed until 1568, but a dealer says the 1st ed. was 1564 and
there was a 4th ed. in 1574, which I have examined.] Apparently much revised and
extended, (1580). Reprinted, with title: The Wel [sic] Spring of Sciences: Which
teacheth the perfect worke and practise of Arithmetike; Thomas Purfoote, London,
1591. I have seen Thomas Purfoot, London, 1612, which is essentially identical to
1591. I have also seen: Christopher Meredith, London, 1646; Christopher Meredith,
London, 1650; R. & W. L. for Andrew Kemb, London, 1655; which are all the same,
but differently paged than the 1591. I have also seen Baker's Arithmetick, ed. by Henry
Phillippes, Edward Thomas, London, 1670, which has different pagination and some
additional problems compared to the 1646/1655 ed. [Smith, Rara, 327-330 & 537, says
it was rewritten in 1580, but there is little difference between the 1580 and the many
later editions, so the 1591 ed. is probably close to the 1580 ed. The copy of the 1562 in
the Graves collection ends on f. 160r, but an owner has written a query as to whether
the book is complete. Neither Smith nor De Morgan seems to have seen a 1562 so they
don't give a number of pages for it. (STC records no copies of the 1562, 1564, 1576,
1584, 1607 editions, but there was a 1576 by [T. Purfoote], apparently the 5th ed., of
c500pp, in the Honeyman Collection.) Almost all the problems of interest occur on ff.
189r-198r of the 1591 ed. and hence are not in the Graves copy of the 1562 ed., but
H&S 61 refers to one of these problems as being in Baker, 1568. The 1574 ends at fol.
200 (misprinted as 19?, where the ? is an undecipherable blob) and Chapter 16, which is
headed: The 16 Chapter treateth of sportes and pastime, done by number, is on ff.
189r-200v, and contains just a few recreations, as in Recorde. So I will date the book as
1562?, but most of the later material as 1580?. The problems of 7.AF.1 and 10.A may
be in Graves copy of the 1562 ed. -- ??check. I will cite the 1580?, 1646 and 1670
editions, e.g. 1580?: ff. 192r 193r; 1646: pp. 302-304; 1670: pp. 344-345.] Bill Kalush
has recently sent a CD with 1574, 1580, 1591, 1598, 1602, 1607, 1612, 1617, 1650,
1655 on it -- ??NYR.
Bakhshali MS.
The Bakhshālī Manuscript, c7C. This MS was found in May 1881 near
the village of Bakhshālī, in the Yusufzāī district of the Peshawer division, then at the
northwestern frontier of India, but apparently now in Pakistan. This is discussed in
SOURCES - page 30
several places, such as the following, but a complete translation has only recently
appeared. David Pingree says it is 10C, but his student Hayashi opts for 7C which
seems pretty reasonable and I will adopt c7C.
1.
A. F. Rudolf Hoernle. Extract of his report in some journal of the
previous year. The Indian Antiquary 12 (Mar 1883) 89-90. A preliminary report,
saying it was found near Bakhshâlî in the Yusufzai District in the Panjâb.
2.
A. F. Rudolf Hoernle. On the Bakhshālī Manuscript. Berichte des VII.
Internationalen Orientalisten-Congresses, Wien, 1886. Alfred Hölder, Vienna, 1889.
Arische Section, p. 127-147 plus three folding plates. Cf next item. I will cite this as
Hoernle, 1886.
3.
A. F. Rudolf Hoernle. The Bakhshali manuscript. The Indian
Antiquary 17 (Feb 1888) 33-48 & Plate I opp. p. 46; 275-279 & Plates II & III opp.
pp. 276 & 277. This is essentially a reprint of the previous item, with a few changes or
corrections, but considerable additional material. He dates it c4C. I will cite this as
Hoernle, 1888.
4.
G. R. Kaye. The Bakhshālī Manuscript – A Study in Medieval
Mathematics. Archæeological Survey of India – New Imperial Series XLIII: I-III, with
parts I & II as one volume, (1927-1933). (Facsimile reprint in two volumes, Cosmo
Publications, New Delhi, 1981 – this is a rather poor facsimile, but all the text is
preserved. I have a letter detailing the changes between the original and this
'facsimile'.) I will only cite Part I – Introduction, which includes a discussion of the
text. Part II is a discussion of the script, transliteration of the text and pictures of the
entire MS. Part III apparently was intended to deal with the language used, but Kaye
died before completing this and the published Part III consists of only a rearranged
version of the MS with footnotes explaining the mathematics. Gupta, below, cites part
III, as Kaye III and I will reproduce these citations. He dates it c12C.
5.
B. Datta. The Bakhshâlî mathematics. Bull. Calcutta Math. Soc. 21
(1929) 1-60. This is largely devoted to dating of the MS and of its contents. He asserts
that the MS is a copy of a commentary on some lost work of 4C or 5C (?).
6.
R. C. Gupta. Some equalization problems from the Bakhshālī
manuscript. Indian Journal of the History of Science 21 (1986) 51-61. Notes that
Hoernle gave the MS to the Bodleian Library in 1902, where it remains, with shelf mark
MS. Sansk. d.14. He follows Datta in believing that this is a commentary on a early
work, though the MS is 9C, as stated by Hoernle. He gives many problems from Kaye
III, sometimes restoring them, and he discusses them in more detail than the previous
works.
7.
Takao Hayashi. The Bakhshālī Manuscript An ancient Indian
mathematical treatise. Egbert Forsten, Groningen, Netherlands, 1995. (Based on his
PhD Dissertation in History of Mathematics, Brown University, May 1985, 774pp.) A
complete edition and translation with extensive discussion of the context of the
problems. He dates it as 7C.
Ball, Walter William Rouse (1850-1925). See: Ball-FitzPatrick; MRE.
Ball-FitzPatrick.
French translation of MRE by J. Fitz-Patrick, published by Hermann,
Paris.
1st ed., Récréations et Problèmes Mathématiques des Temps Anciens &
Modernes. From the 3rd ed, 1896, of MRE, 'Revue et augmentée par l'auteur'. 1898.
The Note says 'M. Ball ... a bien voulu apporter à la troisième édition anglaise des
additions et des modifications importantes.' 352pp.
2nd ed., Récréations et Problèmes Mathématiques des Temps Anciens et
Modernes. From the 4th ed, 1905, of MRE, 'et enrichie de nombreuses additions'.
As three volumes, 1907-09. [I have vol. 1, 1907, which is 356pp. Pp. 327-355 is a
SOURCES - page 31
note by A. Hermann, Comptabilité d'une persone qui dépense plus que son revenu. I
have not yet seen the other volumes to compare with the 1926 reprint, but Strens's notes
in his copy indicate that they are identical.]
Reprinted in one vol., Gabay, Paris, 1992, 544pp.
Reprinted, 1926-1927. The only copies that I have seen are bound as one volume,
but with separate pagination. My copy has left out the title pages of vols. 2 & 3. The
copy in the Strens Collection has these title pages, but its vol. II is 1908. The 1926 vol.
1 says Nouvelle édition française, but the 1927 vol. 3 says Deuxième édition française.
[Vol. 1 is 326pp, omitting the note by Hermann. Vol. 2 is 363pp (pp. 322-355 is
a historical note on the cubic, based on Cossali (1797)). Vol. 3 is 363pp including:
Notes diverses de M. Aubry, pp. 137-206 (or 340? -- the Table des Matières and the
page set up do not make it clear if Aubry's Notes end on p. 206); Note de M.
Fitz-Patrick, La géométrie par le pliage et découpage du papier, pp. 341-360; A.
Margossian, De l'ordonnance des nombres dans les carrés magiques impairs, pp. 1-60
(pp. 61-64 is a Note on the same subject, presumably part of Margossian's material);
Capt. Reinhart, some geometric notes, pp. 130-136.]
Barnard. 50 Observer Brain-Twisters. 1962.
Douglas St. Paul Barnard. Fifty Observer Brain-Twisters A Book of
Mathematical and Reasoning Problems. Faber, 1962. US ed.: A Book of
Mathematical and Reasoning Problems: Fifty Brain Twisters; Van Nostrand, 1962.
The editions have identical pagination.
Bartl. c1920.
János Bartl. Preis-Verzeichnis von Bartl's Akademie für moderne
magische Kunst. Hamburg, c1920. Reprinted by Olms Verlag, Zürich, 1983, as:
Zauberkatalog Bartl. References are to the section: Vexier- und Geduldspiele,
pp. 305-312.
Bartoli. Memoriale. c1420.
Francesco Bartoli ( -1425). Memoriale (= Notebook) containing some
30 mathematical problems copied during 1400?-1425. Ms 1 F 54 of the Archives
départementales du Vaucluse, France. ??NYS -- described and quoted in: Jacques
Sesiano; Les problèmes mathématiques du Memoriale de F. Bartoli; Physis 26:1 (1984)
129-150.
BC.
Binomial Coefficient, i.e. BC(n, k) = n!/k!(n-k)!.
BCB. See: Hall, BCB.
BDM. See under DSB.
Bede, The Venerable (c672-735). (Now St. Bede.) See: Alcuin.
Benedetto da Firenze. c1465.
Benedetto da Firenze. Trattato d'Abacho. c1465. This was a popular
treatise and Van Egmond's Catalog 356 lists 18 copies under Benedetto. Six show B
as author, one has Benedetto, one has Benedetto da Firenze, one has Po Ma and one has
Filipo Chalandri, so it seems Benedetto is the most likely author. The MSS date from
c1465 to c1525 and contain 9 to 25 chapters.
The version in Cod. Acq. e doni 154, Biblioteca Medicea Laurenziana, Florence,
c1480. has been transcribed and edited by Gino Arrighi as: Pier Maria Calandri;
Tractato d'Abbacho; Domus Galilaeana, Pisa, 1974. The incipit names Po Ma as
author. Cf Van Egmond's Catalog 96. This version has 23 chapters.
Benson. 1904.
J. K. Benson. The Book of Indoor Games for Young People of All
Ages. C. Arthur Pearson, London, 1904. [This copies a lot from Hoffmann (or a
common ancestor?).]
Much of the material of Indoor Games is repeated in: J. K. Benson, ed.; The
Pearson Puzzle Book; C. Arthur Pearson, London, nd [1921 -- BMC]. This is not in
BMC or NUC under Benson -- but I have seen an ad listing this as by Mr. X and it is
listed under Mr. X in BMC. Puzzle Book pp. 1-96 = Indoor Games pp. 189-257;
SOURCES - page 32
Puzzle Book pp. 109-114 = Indoor Games pp. 258-262. The only different material in
Puzzle Book is pp. 97-108. Neither book refers to the other. Cf Mr. X in Section 4.A.1
Berkeley & Rowland. Card Tricks & Puzzles. 1892.
"Berkeley" [Peel, Walter H.] & Rowland, T. B. Card Tricks and
Puzzles. The Club Series, George Bell & Sons, London, 1892 -- according to BMC,
but my copy is 1897. Card Puzzles, etc., pp. 1-74 is by Berkeley; Arithmetical Puzzles,
pp. 75-120 is by Rowland.
Berlekamp, Elwyn R. (1940- ) See: Winning Ways.
Bestelmeier. 1801-1803.
G. H. [Georg Hieronimus] Bestelmeier. Magazin von verschiedenen
Kunst- und andern nützlichen Sachen .... [Toy catalogues.] Nuremberg, 1801-1803.
Eight issues and cumulative classified index reprinted by Olms, Zurich, 1979.
Issue VII is 1801; the others are 'neue verbesserte Auflage', 1803. This includes items
numbered 1 through 1111.
Selections, with English translations. Daniel S. Jacoby, ed. The Amazing
Catalogue of the Esteemed Firm of George Hieronimus Bestelmeier. Selected Excerpts
from Editions of 1793 and 1807. [A comment inside makes me wonder if 1793-1807 is
meant??] Merrimack Publishing Corp., NY, 1971, 82pp. The numeration is the same
as in the Olms edition, but the Jacoby continues to item 1321. Obviously these later
items come from the 1807 edition, but we cannot tell if they might date from 1805, say,
nor whether all the earlier items go back to 1793. Jerry Slocum uses Jacoby in his
Compendium and has kindly provided photocopies of Jacoby's pp. 70-82 containing all
the items after 1111 and some examples of the earlier items. Jacoby does not translate
the texts, but just provides English labels for each picture and these labels are
sometimes unconnected with the text.
Many of Bestelmeier's items are taken from Catel; Kunst-Cabinet; 1790.
Sometimes the figure is identical (often reversed) or is a poor copy. Texts are often
copied verbatim, or slightly modified, but often abbreviated. E.g. Catel often explains
the puzzle and this part is frequently omitted in Bestelmeier. Bestelmeier was the
successor to Catel, qv. The booklet by Slocum & Gebhardt (qv under Catel) gives
precise datings for the various parts of these catalogues, but I have not yet entered these
details.
Bhaskara I. 629.
Bhāskara I. Āryabhaţīya-Bhāşya. [NOTE: ţ denotes a t with a dot
under it and ş denotes an s with a dot under it.] 629. Critically edited, including an
English Appendix of the numerical examples used, by Kripa Shankar Shukla. Indian
National Science Academy, New Delhi, 1976. (Vol. 2 of a three volume series devoted
to the Āryabhaţīya (499) of Aryabhata (476- ), qv.) Bhaskara I repeats and exposits
Aryabhata verse by verse, but Aryabhata rarely gives numerical examples, so Bhaskara I
provided them and these were later used by other Indian writers such as Chaturveda,
860. His earlier Maha-Bhaskariya (Mahā-Bhāskarīya) of c629 is cited in 7.P.2.
Shukla's Appendix is sometimes brief, but sometimes very detailed, e.g. on the 26
examples of Chinese remainder problems.
Bhaskara II (1114-c1185).
Bhâskara II (1114-c1185, see Colebrooke).
Biggs, Norman L. See: BLW.
Bijaganita.
Bîjaganita of Bhaskara II, 1150 (see Colebrooke).
The Bile Beans Puzzle Book. 1933.
Bile Beans (C. E. Fulford, Ltd., Leeds, England). The Bile Beans
Puzzle Book. 1933.
Birtwistle. Math. Puzzles & Perplexities. 1971.
Claude Birtwistle. Mathematical Puzzles and Perplexities How to
SOURCES - page 33
Make the Most of Them. George Allen & Unwin, London, 1971.
Birtwistle. Calculator Puzzle Book. 1978.
Claude Birtwistle. The Calculator Puzzle Book. Paperfronts (Elliot
Right Way Books), Kingswood, Surrey, 1978. (There is a US ed. by Bell, NY, 1978.)
BL(LD).
British Library (Lending Division).
Blasius. 1513.
Johannis (or Joannes) Martinus Blasius (later denoted Sileceus or
Sciliceus). Liber Arithmetice Practice Astrologis Phisicis et Calculatioribus admodum
utilis. Thomas Kees for Joannis Parui & Joannis Lambert (in colophon; TP has
Jehanlambert), Paris, 1513. Facsimile by Heffer Scientific Reprint, Cambridge, 1960.
See Smith, Rara, pp. 95-97. The Glaisher article in 7.P.5 [Messenger of Mathematics
53 (1923-24) 1-131] discusses this book and says he only knows one example of it,
which he has in front of him, so I suspect this facsimile is from that copy. See Rara 9597. The Honeyman Collection had a copy, saying it was printed for J. Petit and J.
Lambert and that copy had Petit's device on the TP while the TP shown in Rara has
Lambert's device, which is as in this facsimile. There was a reprinting in 1514 and
extended editions in 1519 (ed. by Oronce Finé) and 1526 (ed. by T. Rhaetus)
[Honeyman Collection, nos. 350-352].
BLC.
British Library Catalogue, replacing BMC, in progress since 1970s.
BLC-Ø
Indicates that I could not find the item in the BLC.
BLW. 1976.
Norman L. Biggs, E. Keith Lloyd & Robin J. Wilson. Graph Theory
1736-1936. OUP, 1976.
Blyth. Match-Stick Magic. 1921.
Will Blyth. Match-Stick Magic. C. Arthur Pearson, London, 1921,
reprinted 1923, 1939.
BM(C).
British Museum (Catalogue (of books) to 1955. c1963).
BMC65.
Supplement to the above Catalogue for 1956-1965. c1968.
BN(C).
Bibliothèque National, Paris. (Catalogue, 1897-1981.)
Bodleian.
The Bodleian Library, University of Oxford, or its catalogue.
Bonnycastle. Algebra. 1782
John Bonnycastle (??-1821). An Introduction to Algebra, with Notes
and Observations; designed for the Use of Schools, and Other Places of Public
Education. 1782. The first nine editions appeared "without any material alterations".
In 1815, he produced a 10th ed., "an entire revision of the work" which "may be
considered as a concise abridgment" of his two volume Treatise on Algebra, 1813, (2nd
ed. in 1820). The 1815 ed. had an Appendix: On the application of Algebra to
Geometry. I have a copy of the 7th ed., 1805, printed for J. Johnson, London, and it is
identical to the 2nd ed. of 1788 except for a problem in the final section of
Miscellaneous Questions. However, the 9th ed. of 1812 has page numbers advanced by
10 except toward the end of the book. I also have the 13th ed. of 1824, printed for J.
Nunn and 11 other publishers, London, 1824. This version has an Addenda: A New
Method of resolving Numerical Equations, by his son Charles Bonnycastle (17971840), but is otherwise identical to the 10th ed. of 1815. The earlier text was expanded
by about 10% in 1815, so a number of problems only occur in later editions. I will cite
these later problems as 1815 and will cite the earlier problems as 1782. [Halwas 36-38
gives some US editions.]
Book of 500 Puzzles. 1859.
The Book of 500 Curious Puzzles: Containing a Large Collection of
Entertaining Paradoxes, Perplexing Deceptions in Numbers, and Amusing Tricks in
Geometry. By the author of "The Sociable," "The Secret Out," "The Magician's Own
Book," "Parlor Games," and " Parlor Theatricals," etc. Illustrated with a great Variety
of Engravings. Dick & Fitzgerald, NY, 1859. Compiled from The Sociable (qv) and
SOURCES - page 34
Magician's Own Book. Pp. 1-2 are the TP and its reverse. Pp. 3-36, are identical to
pp. 285-318 of The Sociable; pp. 37-54 are identical to pp. 199-216 of Magician's Own
Book and pp. 55-116 are identical to pp. 241-302 of Magician's Own Book. [Toole
Stott 103 lists it as anonymous. NUC, under Frikell, says to see title. NUC, under
Book, also has an 1882 ed, compiled by William B. Dick. Christopher 129. C&B lists
it under Cremer.]
The authorship of this and the other books cited -- The Sociable, The Secret Out,
The Magician's Own Book, Parlor Games, and Parlor Theatricals, etc. -- is confused.
BMC & NUC generally assign them to George Arnold (1834-1865) or Wiljalba (or
Gustave) Frikell (1818 (or 1816) - 1903), sometimes with Frikell as UK editor of
Arnold's US version -- but several UK versions say they are translated and edited by W.
H. Cremer Jr, and one even cites an earlier French book (though the given title may not
exist!, but cf Manuel des Sorciers, 1825) -- see the discussion under Status of The
Project, in the Introduction, above. The names of Frank Cahill, Henry Llewellyn
Williams and Gustave Frikell (Jr.) are sometimes associated with versions of these as
authors or coauthors. The Preface of The Sociable says that most of the Parlor
Theatricals are by Frank Cahill and George Arnold -- this may indicate they had little to
do with the parts that interest us. Toole Stott 640 opines that this reference led Harry
Price to ascribe these books to these authors.
A publisher's ad in the back says: "The above five books are compiled from the
"Sociable" and "Magician's Own."", referring to: The Parlor Magician [Toole Stott 543,
544]; Book of Riddles and Five Hundred Home Amusements [Toole Stott 107, 951];
Book of Fireside Games [possibly Toole Stott 300??]; Parlor Theatricals; The Book of
500 Curious Puzzles. However, [Toole Stott 951] is another version of The Book of
Riddles and Five Hundred Home Amusements "by the author of "Fireside Games"
[Toole Stott 300], "The Parlor Magic" [perhaps Toole Stott 543, 544], "Parlor Tricks
with Cards" [Toole Stott 1056 lists this as by Frikell, "abridged from The Secret Out"
(see also 547, 1142)], ..."; Dick & Fitzgerald, 1986 [sic, but must mean 1886??].
See Magician's Own Book for more about the authorship.
See also: Boy's Own Book, Boy's Own Conjuring Book, Illustrated Boy's Own
Treasury, Indoor and Outdoor, Landells: Boy's Own Toy-Maker, The Secret Out,
Hanky Panky, The Sociable.
Book of Merry Riddles. 1629?
The Book of Merry Riddles. London, 1629. [Santi 235.]
Several reprints. Also known as Prettie Riddles.
A Booke of Merry Riddles; Robert Bird, London, 1631. [Mark Bryant;
Dictionary of Riddles; Routledge, 1990, p. 100.]
Booke of Merry Riddles; John Stafford & W. G., London, 1660.
Reprint of the 1629 in: J. O. Halliwell; The literature of the sixteenth and
seventeenth centuries; London, 1851, pp. 67-102. [Santi 235.]
Reprint of the 1660 in: J. O. Halliwell; The Booke of Merry Riddles, together
with proper questions, and witty proverbs, to make pleasant pastime. Now first
reprinted from the unique edition printed at London in the year 1660. For the author,
London, 1866. This was a printing of 25 copies. There is a copy at UCL and a MS note
at the end says 15 copies were destroyed on 9 Apr 1866, signed: J. O. H., with Number
9 written below. [Santi 307.] I have seen this, but some of the riddles are quoted by
other authors and I will date all items as 1629? until I examine other material.
Reprint of the 1629 in: Alois Brandl; Shakespeares Book of Merry Riddles und
die anderen Räthselbücher seiner Zeit; Jahrbuch der deutschen ShakespeareGesellschaft 42 (1906) 1-64 (with the 1631 ed on pp. 53-63). ??NYR. [Santi 235 &
SOURCES - page 35
237.]
Borghi. Arithmetica. 1484.
Pietro Borghi = Piero Borgo or Borgi (?? - 1494). Qui comenza la
nobel opera de arithmethica ne la qual se tracta tute cosse amercantia pertinente facta &
compilata p Piero borgi da veniesia. Erhard Ratdolt, Venice, 1484. 2 + 116 numbered
ff. This is the second commercial arithmetic printed in Italy and was reprinted many
times. See Rara 16-22. This edition was reproduced in facsimile, with notes by Kurt
Elfering, as: Piero Borghi; Arithmetica Venedig 1484; Graphos, Munich, 1964; in:
Veröffentlichungen des Forschungsinstituts des Deutschen Museums für die Geschichte
der Naturwissenschaften und der Technik, Reihe C -- Quellentexte und Übersetzunge,
Nr. 2, 1965.
The 3rd ed of 1491 had a title: Libro dabacho. From the 4th ed of 1501, the title
was Libro de Abacho, so this is sometimes used as the title for the first editions also.
Rara indicates that the printing was revised to 100 numbered ff by the 4th ed. of 1491. I
have examined a 1509 ed. by Jacomo Pentio, Venice, ??NX. This has 100 numbered ff,
but the last three ff contain additional material, though Rara doesn't mention this until
the 11th ed of 1540. H&S discusses a problem and the folio in the 1540 ed is the same
as in the 1509 ed. The locations of interest in the 1509 ed. are c18ff before the
corresponding locations of the 1484. Van Egmond's Catalog 293-297 lists 13 Venetian
editions from 1484 to 1567.
It has been conjectured that this was a pseudonym of Luca Pacioli, but there is no
evidence for this [R. Emmett Taylor; No Royal Road Luca Pacioli and His Times;
Univ. of North Carolina Press, Chapel Hill, 1942, pp. 60 & 349].
See also: D. E. Smith; The first great commercial arithmetic; Isis 8 (1926) 41-49.
Bourdon. Algèbre. 7th ed., 1834.
Louis Pierre Marie Bourdon (1779-1854). Élémens d'Algèbre. 7th ed.,
Bachelier, Paris, 1834. (1st ed, 1817; 5th, 1828; 6th, 1831; 8th, 1837; 1840. Undated
preface in the 7th ed. describes many changes, so I will cite this as 1834, though much
of the material would have occurred earlier.)
Boy's Own Book. 1828.
William Clarke, ed. The Boy's Own Book. The bibliography of this
book is extremely complex -- by 1880, it was described as having gone through scores
of editions. My The Bibliography of Some Recreational Mathematics Books has 11
pages listing 76 English (40 UK, 37 US, 1 Paris) versions and a Danish version,
implying 88 English (50 UK, 37 US, 1 Paris) versions, and 10 (or 11) related versions,
and giving a detailed comparison of the versions that I have seen. Because of the
multiplicity of versions, I have cited it by title rather than by the original editor's name,
which is not in any of the books (except the modern facsimile) though this attribution
seems to be generally accepted. I have examined the following versions, sometimes in
partial photocopies or imperfect copies.
Vizetelly, Branston and Co., London, 1828, 448pp.; 2nd ed., 1828, 462pp.; 3rd
ed., 1829, 464pp (has an inserted advertisement sheet); 6th ed??, c1830, 462pp?? (my
copy lacks TP, pp. 417-418, 431-436, 461-462); 9th ed., 1834, 462pp. Longman,
Brown & Co., London, 24th ed., 1846, 462pp. [The latter five are identical, except for
a bit in the Prelude (and the extra sheet in 3rd ed), so I will just cite the first of these as
1828-2. It seems that all editions from the 2nd of 1828 through the 29th of 1848,
462pp. are actually identical except for a bit of the Prelude (and the advertisement sheet
in the 3rd ed.)]
First American Edition. Munroe & Francis, Boston & Charles S. Francis, NY,
1829, 316pp. Facsimile by Applewood Books, Bedford, Massachusetts, nd [1998?].
This is essentially an abridgement of the 2nd ed of 1828, copying the Prelude and
SOURCES - page 36
adding "So far the London Preface. The American publishers have omitted a few
articles, entirely useless on this side of the Atlantic, ...." The type is reset, giving some
reduction in pages. A number of the woodcuts have been omitted. The section title
pages are omitted. Singing Birds, Silkworms, White Mice, Bantams, Magnetism,
Aerostatics, Chess and Artificial Fireworks are omitted. Angling, Rabbits, Pigeons,
Optics are reduced. Rosamond's Bower is omitted from Paradoxes and Puzzles.
Surprisingly, The Riddler is increased in size. The 2pp Contents is omitted and an 8pp
Index is added.
Baudry's European Library & Stassin & Xavier, Paris, 1843, 448pp. [The
existence of a Paris edition was previously unknown to the vendor and myself, but it is
Heyl 354 and he cites Library of Congress. It is very different than the English and US
editions, listing J. L. Williams as author. Even when the topic is the same, the text, and
often the topic's name, are completely rewritten. See my The Bibliography of Some
Recreational Mathematics Books for details -- in it I have found it generally necessary
to treat this book separately from all other editions. I will cite it as 1843 (Paris). Much
of this, including almost all of the material of interest is copied exactly in Anon: Boy's
Treasury, 1844, qv, and in translated form in de Savigny, Livre des Écoliers, 1846, qv.
The problem of finding the number of permutations of the letters of the alphabet
assumes 24 letters, which makes me wonder if these books are based on some earlier
French work. Heyl 355 is probably the same book, with slight variations in the title, by
Dean and Munday, London, c1845.]
David Bogue, London, 1855, 611pp. [It seems that this version first appears in
1849 and continues through about 1859, when two sections were appended.]
[W. Kent (late D. Bogue), London, 1859, 624pp??. For almost all material of
interest, this is identical to the 1855 ed, so I will rarely (if ever?) cite it.]
[Lockwood & Co., London, 1861, 624pp. Identical to the 1859 ed., so I will not
cite it.]
Lockwood & Co., London, 1868, 696pp.
[Lockwood & Co., London, 1870, 716pp. Identical to 1868 with 20pp of
Appendices, so page numbers for material of interest are the same as in 1868, so I will
not cite it.]
[Crosby Lockwood & Co., London, 1880, 726pp. Identical to 1870, but having
the Appendices and 20 more pages incorporated into a new section. For almost all
material of interest, the page numbers are 30 ahead of the 1868 & 1870 page numbers,
so I will not cite it except when the page numbers are not as expected.]
[5th (US?) ed., Worthington, NY, 1881, 362pp. For almost all material of
interest, this is identical to the 1829 (US) ed., so I will rarely (if ever?) cite it.]
I will cite pages with edition dates and edition numbers or locations if needed (e.g.
1828-2: 410 or 1829 (US): 216). See also: Book of 500 Puzzles, Boy's Own
Conjuring Book, Illustrated Boy's Own Treasury.
Anonymous. The Riddler; A Collection of Puzzles, Charades, Rebusses,
Conundrums, Enigmas, Anagrams, &c. for the Amusement of Little Folks. S. Babcock,
New Haven, Connecticut, 1835. 22pp. My copy has leaf 11/12 half missing and leaf
17/18 missing; NUC & Toole Stott 1392 say it should be 24pp, so presumably leaf
23/24 is also missing here. [Toole Stott 1392 has The Riddler: or, Fire-Side
Recreations; a collection ..., 1838, also listed in NUC.] Paradoxes and Puzzles section
consists of the introduction and 11 puzzles copied almost exactly from the Paradoxes
and Puzzles section of Boy's Own Book, 2nd ed. of 1828 and this material is all in the
first American edition of 1829. Other material is charades, etc. and is all in both these
versions of Boy's Own Book. Shortz states that this is the first American book with
puzzles -- but there were at least five American versions of Boy's Own Book before this
and all the material in The Riddler, except some woodcuts, is taken from Boy's Own
SOURCES - page 37
Book, so this pamphlet seems to be a pirate version. NUC also lists a 1838 version.
Boy's Own Conjuring Book. 1860.
The Boy's Own Conjuring Book: Being a Complete Hand-book of
Parlour Magic; and Containing over One Thousand Optical, Chemical, Mechanical,
Magnetical, and Magical Experiments, Amusing Transmutations, Astonishing Sleights
and Subtleties, Celebrated Card Deceptions, Ingenious Tricks with Numbers, Curious
and Entertaining Puzzles, Charades, Enigmas, Rebuses, etc., etc., etc. Illustrated with
nearly two hundred engravings. Intended as a source of amusement for one thousand
and one evenings. Dick and Fitzgerald, NY, 1860. 384pp. [Toole Stott 115, corrected,
lists this as (1859), and under 114, describes it as an extended edition of The Magician's
Own Book -- indeed the running head of the book is The Magician's Own Book! -- but
see below. Toole Stott 481 cites a 1910 letter from Harris B. Dick, of the publishers
Dick & Fitzgerald. He describes The Boy's Own Conjuring Book as a reprint of
Magician's Own Book "evidently gotten up and printed in London, but singularly
enough it had printed in the book on the title-page -- New York, Dick & Fitzgerald."
Indeed, all the monetary terms are converted into British. Harold Adrian Smith [Dick
and Fitzgerald Publishers; Books at Brown 34 (1987) 108-114] states that this is a
London pirate edition. BMC has 384pp, c1860. NUC has a 384pp version, nd.
Christopher 145-149 are five versions from 1859 and 1860, though none has the blue
cover of my copy. Christopher 145 says the 1859 versions were printed by Milner &
Sowerby, Halifax, and describes it as an extraction from Magician's Own Book, but see
below. Christopher 148 cites Smith's article.] I also have a slightly different version
with identical contents except omitting the date and frontispiece, but with a quite
different binding, probably Christopher 149. [NUC lists 334pp, nd; 416pp, nd and
416pp, 1860. Toole Stott 114 is a 416pp version, 1861. Toole Stott 959 is a 534pp
version, 1861. C&B cite a New York, 1859 with 416pp, a New York, nd, 334pp and
London, c1850 (surely too early?).]
I have now compared this with The Magician's Own Book of 1857 and it is
essentially a minor reworking of that book. The Magician's Own Book has 17 chapters
and an answers chapter and a miscellaneous chapter of items which are almost all also
listed in the Contents under earlier sections. All together, there are some 635 items.
The Boy's Own Conjuring Book copies about 455 of these items essentially directly,
completely omitting the chapters on Electricity, Galvanism, Magnetism, Geometry, Art,
Secret Writing and Strength, and almost completely omitting the chapter on Acoustics.
Of the 488 items in the other chapters, 453 are copied into the Boy's Own Conjuring
Book, and this has in addition two of the acoustic problems, 125 new miscellaneous
problems and 38pp of charades, riddles, etc. (The later UK edition of Magician's Own
Book is very different from the US edition.) Many of the problems are identical to the
Boy's Own Book or the Illustrated Boy's Own Treasury. See also: Book of 500
Puzzles, Boy's Own Book, Illustrated Boy's Own Treasury, Landells: Boy's Own
Toy-Maker.
Boy's Treasury. 1844.
Anonymous. The Boy's Treasury of Sports, Pastimes, and Recreations.
With four hundred engravings. By Samuel Williams. [The phrasing on the TP could
be read as saying Williams is the author, but the NUC entry shows he was clearly listed
as the designer in later editions and his name appears on the Frontispiece.] D. Bogue,
London, 1844. Despite the similarity of title, this is quite different from Illustrated
Boy's Own Treasury and the similar books of c1860. [Toole Stott 116. Toole Stott 117
is another ed., 1847, 'considerably extended'. Toole Stott gives US editions: 959; 960;
118; 199 & 961-965 are 1st, 1847; 2nd, 1847; 3rd, 1848; 6 versions of the 4th, 1850,
SOURCES - page 38
1848, 1849, 1852, 1854, 1848. Hall, BCB 37 is a US ed. of 1850 = Toole Stott 119.
Christopher 151 is a US version of 1850? NUC lists 9 versions, all included in Toole
Stott. Toole Stott cites some BM copies, but I haven't found this in the BMC. A
section of this, with some additional material, was reissued as Games of Skill and
Conjuring: ..., in 1860, 1861, 1862, 1865, 1870 -- see Toole Stott 312-317.]
I have now found that much of this, including all the material of interest, is taken
directly from the 1843 Paris edition of Boy's Own Book, qv, by J. L. Williams,
including many of the illustrations - indeed they have the same Frontispiece, with S.
Williams' name on it.
BR. c1305.
Greek MS, c1305, Codex Par. Suppl. Gr. 387, fol. 118v-140v.
Transcribed, translated and annotated by Kurt Vogel as: Ein Byzantinisches
Rechenbuch des frühen 14.Jahrhunderts; Wiener Byzantinistische Studien, Band VI;
Hermann Böhlaus Nachf., Wien, 1968. I will cite problem numbers and pages from this
-- Vogel gives analysis of the methods on pp. 149-153 and historical comments on pp.
154-160, but I will not cite these.
Brahmagupta, c628. See: Brahma-sphuta-siddhanta; Colebrooke.
Brahma-sphuta-siddhanta.
Bráhma-sphuta-siddhânta of Brahmagupta, 628 (see Colebrooke). He
only states rules, which are sometimes obscure. It appears from Colebrooke, p. v, and
Datta (op. cit. under Bakhshali, p. 10), that almost all the illustrative examples and all
the solutions are due to Chaturveda Prthudakasvâmî in 860. Brahmagupta's rules are
sometimes so general that one would not recognise their relevance to these examples
and I have often not cited Brahmagupta. E.g. cistern problems are given as examples to
Brahmagupta's verse on how to add and subtract fractions. (See also Datta & Singh, I,
p. 248.) Some of these comments are taken from Bhaskara I in 629.
Brush.
Hubert Phillips. Brush Up Your Wits. Dent, London, 1936.
BSHM.
British Society for the History of Mathematics. The produce a useful
Newsletter.
Buteo. Logistica. 1559.
Johannes Buteo (= Jean Borrel, c1485-c1560 or c1492-1572). Ioan.
Buteonis Logistica, quæ & Arithmetica vulgò dicitur in libros quinque digesta: quorum
index summatim habetur in tergo. Gulielmus Rovillius, Lyons, 1559. Most of the
material is in books IV and V. H&S cites some problems in the 1560 ed with the same
pages as in the 1559 ed, so these editions are presumably identical. See Rara 292-294.
circa, e.g. c1300. Also c= means "approximately equal", though 
will be used in mathematical contexts.
C.
Century, e.g. 13C, -5C.
Calandri. Arimethrica. 1491.
Philippo Calandri. Untitled. Frontispiece is labelled "Pictagoras
arithmetrice introductor". Text begins: "Philippi Calandri ad nobilem et studiosus
Julianum Laurentii Medicē de arimethrica opusculū." Lorenzo de Morgiani & Giovanni
Thedesco da Maganza, Florence, 1491. Van Egmond's Catalog 298-299. The Graves
collection has two copies dated 1491, one with the folio number c iiii misprinted as
b iiii - cf Van Egmond for other differences in this unique variant. There was a reprint
by Bernardo Zucchetta, Florence, 1518 -- ??NYS but mentioned: in a handwritten note
in one of the Graves copies of the 1491 (giving Bernardo Zucchecta, 1517); in Smith,
Rara, p. 48 (giving Bernardo Zuchetta, 1518); in Riccardi [I, col. 208-209] (giving
Bernardo Zuchecta, 1515) and in Van Egmond's Catalog 299. "It is the first printed
Italian arithmetic with illustrations accompanying problems, ...." (Smith, Rara,
pp. 46-49). There are about 50 of these illustrations, which appear to be woodcuts, but
they are quite small, about 25mm (1") square, and the same picture is sometimes
c.
SOURCES - page 39
repeated for a related but inappropriate problem. Rara reproduces some of these,
slightly reduced. Riccardi [I, col. 208-209] says there may have been a 1490 ed. by
Bernardo Zuchecta, but Van Egmond did not find any example.
Calandri. Aritmetica. c1485.
Filippo Calandri. Aritmetica. c1485 [according to Van Egmond's
Catalog 158-159]. Italian MS in Codex 2669, Biblioteca Riccardiana di Firenze.
Edited by Gino Arrighi, Edizioni Cassa di Risparmio di Firenze, Florence, 1969. 2 vol.:
colour facsimile; transcription of the text. Copies of the facsimile were exhausted about
1980 and repeated requests to the Cassa di Risparmio have not produced a reprint,
though they usually send a copy of the text volume every time I write! I have now
(1996) acquired a example of the 2 vol. set and I find that copies of the text volume
which are not part of a set have 8 colour plates inserted, but these are not in the copy in
the set.
I cite folios from the facsimile volume and pages from the text volume. These
are in direct correspondence with the original except for those pages with full page
illustrations. The original begins with a blank side with a Frontispiece verso, then 9
sheets (18 pp.) of full page tables, then two blank sheets. The numbered folios then
begin and go through 110. Ff. 1r - 32r are pp. 3 - 65 of the text. F. 32v is a full page
calculation which is not in the text. Then ff. 33r - 110r are pp. 66 - 220 of the text.
F. 110v is a full page illustration omitted in the text. The first 80 folio numbers are in
elaborate Roman numerals centred at the head of the page. (These are sometimes
unusually written -- e.g. XXIIIIII.) The later folios were not originally numbered and
were later numbered in the top right corner using Hindu-Arabic numerals.
In Sep 1994, I examined the original MS, though it is on restricted access. The
original colours are rather more luminous than in the facsimile, but the facsimile is a
first class job. The history of this codex is obscure. It is said to have belonged to Piero
di Lorenzo dei Medici and it may be the book catalogued in the library of Francesco
Pandolfini, c1515, as 'uno libretto ... di Filippo Calandri in arithmetica'. The Riccardi
family collected continuously from their rise in the mid 15C until the library was
acquired by the city in 1813. A number of items from the Pandolfini catalogue can be
identified as being in the Riccardiana. Van Egmond's dating may be early as some
claim this was produced for Giuliano de' Medici, who was born in 1479.
Calandri. Raccolta. c1495.
Filippo Calandri. Una Raccolta di Ragioni. In: Cod. L.VI.45,
Biblioteca Comunale di Siena. Ed. by D. Santini. Quaderni del Centro Studi della
Matematica Medioevale, No. 4, Univ. di Siena, 1982. Van Egmond's Catalog 193
identifies this as ff. 75r-111v of the codex, titles it Ragone Varie and gives a date of
c1495.
Calandri. See also: Benedetto da Firenze, P. M. Calandri.
Cardan. Ars Magna. 1545.
Jerome Cardan = Girolamo Cardano = Hieronymus Cardanus
(1501-1576). Artis Magnae sive de Regulis Algebraicis Liber Unus. Joh. Petreium,
Nuremberg, 1545, ??NYS Included in Vol. IV of the Opera Omnia, Joannis Antonius
Huguetan & Marcus Antonius Ravaud, Lyon, 1663, and often reprinted, e.g. in 1967.
NEVER CITED??
Cardan. Practica Arithmetice. 1539.
Jerome Cardan = Girolamo Cardano = Hieronymus Cardanus
(1501-1576). Practica Arithmetice, & Mensurandi Singularis. (Or: Practica
Arithmeticae Generalis Omnium Copiosissima & Utilissima, in the 1663 ed.)
Bernardini Calusci, Milan, 1539. Included in Vol. IV of the Opera Omnia, 1663, see
above. Some of the section numbers are omitted in the Opera Omnia and have to be
intuited. I will give the folios from the 1539 ed. followed by the pages of the 1663 ed.,
SOURCES - page 40
e.g. ff. T.iiii.v-T.v.r (p. 113).
Cardan. De Rerum Varietate. 1557.
Jerome Cardan = Girolamo Cardano = Hieronymus Cardanus
(1501-1576). De Rerum Varietate. Henricus Petrus, Basel, 1557; 2nd ed., 1557; 5th
ed., 1581, ??NYS. Included in Vol. III of the Opera Omnia, 1663, see above.
Cardan. De Subtilitate. 1550.
Jerome Cardan = Girolamo Cardano = Hieronymus Cardanus
(1501-1576). De Subtilitate Libri XXI. J. Petreium, Nuremberg, 1550; Basel, 1553;
6th ed., 1560; and five other 16C editions, part ??NYS. Included in Vol. III of the
Opera Omnia, 1663, see above. French ed. by Richard Leblanc, Paris, 1556, 1584,
titled: Les Livres d'Hieronymus Cardanus: De la Subtilité et subtiles Inventions,
ensemble les causes occultes et les raisons d'icelles; 9th ed., 1611. I have seen a note
that the 1582 ed. by Henricus Petrus, Basel, was augmented by a riposte to attacks by
Scaliger with further illustrations.
Carlile. Collection. 1793.
Richard Carlile. A Collection of One Hundred and Twenty Useful and
Entertaining Arithmetical, Mathematical, Algebraical, and Paradoxical Questions: With
the Method of Working Each. Printed by T. Brice for the author, Exeter, 1793. Wallis
227 CAR, ??NX. Includes a number of straightforward problems covered here, but I
have only entered the more unusual examples.
Carroll-Collingwood. 1899.
The Lewis Carroll Picture Book. Stuart Dodgson Collingwood, ed.
T. Fisher Unwin, London, 1899. = Diversions and Digressions of Lewis Carroll, Dover,
1961. = The Unknown Lewis Carroll, Dover, 1961(?). Reprint, in reduced format,
Collins, c1910. The pagination of the main text is the same in the original and in both
Dover reprints, but is quite different than the Collins. I will indicate the Collins pages
separately. The later Dover has 42 additional photographs.
Carroll-Gardner. c1890? or 1996
Martin Gardner. The Universe in a Handkerchief. Lewis Carroll's
Mathematical Recreations, Games, Puzzles and Word Plays. Copernicus (Springer,
NY), 1996. As with Carroll-Wakeling, Carroll material will be dated as 1890?, but
there is much material by Gardner which is dated 1996.
Carroll-Wakeling. c1890?
Lewis Carroll's Games and Puzzles. Newly Compiled and Edited by
Edward Wakeling. Dover and the Lewis Carroll Birthplace Trust, 1992. This is mostly
assembled from various manuscript sheets of Carroll's containing problems which he
intended to assemble into a puzzle book. Wakeling has examined a great deal of such
material, including a mass of Carroll's notes to Bartholomew Price (1818-1898) who
was Sedleian Professor of Natural Philosophy at Oxford in 1853-1898. Price was at
Pembroke College, becoming the Master, adjacent to Carroll's Christ Church. He had
tutored Carroll (1833-1898) and they were close friends and in continual contact until
their deaths, both in 1898. However, few of the papers are dated and they are simply
loose sheets with no indication of being in order, so there is no way to date the undated
sheets and I have given a fairly arbitrary date of c1890? for these, though Carroll was
more active before then rather than after. Some items are taken from Carroll's youthful
magazines or his correspondence and hence are more precisely dated. The
correspondence is more fully given in Carroll-Collingwood.
In response to an inquiry, Wakeling wrote on 28 May 2003 and said that some of
the Carroll-Price notes were typewritten 'probably using Dodgson's Hammond
typewriter, purchased in 1888.' This gives a somewhat more precise dating than my
c1890? and I will give: 1888 to 1898 for such items, unless there is other evidence.
Carroll-Wakeling II. c1890?
SOURCES - page 41
Rediscovered Lewis Carroll Puzzles. Newly Compiled and Edited by
Edward Wakeling. Dover, 1995. See the notes to Carroll-Wakeling, above.
Cassell's. 1881.
Cassell's Book of In-Door Amusements, Card Games, and Fireside Fun.
Cassell, Peter, Gilpin & Co., London, 1881; Cassell, London, 1973. 217pp [probably +
1p + 6pp Index] (pp. 1-8 are preliminary matter). [There was a companion volume:
Cassell's Book of Sports and Pastimes. In 1887, the two were combined, with the spine
titled Cassell's Book of Outdoor Sports and Indoor Amusements. The front cover says
Out Door Sports, the back cover says Indoor Amusements, while the title page says
Cassell's Book of Sports and Pastimes. It contains all the main text of Book of In-Door
Amusements, ..., advanced by 744 pages. From at least 1896, Card Games and Parlour
Magic were completely revised and later there were a few other small changes. The
title varies slightly. Manson (qv) is a 1911 revision and extension to 340pp of main
text.]
Catel. Kunst-Cabinet. 1790.
Peter Friedrich Catel. Mathematisches und physikalisches KunstCabinet, dem Unterrichte und der Belustigung der Jugend gewidmet. Nebst einer
zweckmässigen Beschreibung der Stücke, und Anzeige der Preise, für welche sie beim
Verfassser dieses Werks P. F. Catel in Berlin zu bekommen sind. [I.e. this is a
catalogue of items for sale by post!] Lagarde und Friedrich, Berlin & Libau, 1790.
[MUS #113.] P. iv says he started his business in 1780.
There is a smaller Vol. 2, with the same title, except 'beim Verfasser dieses
Werkes P. F. Catel' is replaced by 'in der P. F. Catelschen Handlung', and the publisher
is F. L. Lagarde, Berlin, 1793.
My thanks to M. Folkerts for getting a copy of the example in the Deutsches
Museum made for me.
All citations are to vol. 1 unless specified.
Many of Bestelmeier's items are taken from Catel. Sometimes the figure is
identical (often reversed) or is a poor copy. Texts are often copied verbatim, or slightly
modified, but usually abbreviated. E.g. Catel often explains the puzzle and this part is
frequently omitted in Bestelmeier. Bestelmeier was the successor to Catel. Dieter
Gebhardt has searched for the various editions and associated price lists of the Catel and
Bestelmeier catalogues in German libraries and he and Jerry Slocum have published the
details in: Jerry Slocum & Dieter Gebhardt. Puzzles from Catel's Cabinet and
Bestelmeier's Magazine 1785 to 1823. English translations of excerpts from the
German Catel-Katalog and Bestelmeier-Katalog. Intro. by David Singmaster. History
of Puzzles Series. The Slocum Puzzle Foundation, PO Box 1635, Beverly Hills,
California, 90213, USA, 1997. I have not yet made detailed entries from this which
gives precise dates for the various parts of these catalogues.
CFF.
Cubism for Fun. This is the Newsletter of the Nederlandse Kubus Club
(NKC) (Dutch Cubists Club) which has been in English since the mid 1980s.
Chambers -- see: Fireside Amusements.
Charades, Enigmas, and Riddles. 1859.
Charades, Enigmas, and Riddles. Collected by A Cantab. [BLC gives
no author. "A Cantab." was a common pseudonym. One such author of about the right
time and nature was George Haslehurst.] (Cambridge, 1859).
3rd ed., J. Hall and Son, Cambridge, 1860, HB. Half-title, 6 + 96pp.
4th ed., Bell & Daldy, London, 1862. 8 preliminaries (i = half-title; FP facing iii
= TP; v-viii = Introduction; errata slip; two facing plates illustrating a charade for
Harrowgate [sic] Waters), 1-160, 32pp publisher's ads, dated Jan 1863; (my copy is
lacking pp. 63-64). The three plates are signed J.R.J. This is a substantial expansion of
the 3rd ed.
SOURCES - page 42
I also have photocopy of part of the 5th ed., Bell and Daldy, London, 1865, and
this shows it was even larger than the 4th ed, but most of the problems of interest have
the same or similar problem numbers in the three editions that I have seen. I will cite
them as in the following example. 1860: prob. 28, pp. 59 & 63; 1862: prob. 29, pp. 135
& 141; 1865: prob. 573, pp. 107 & 154.
Chaturveda.
Chaturveda Pŗthudakasvâmî [NOTE: ŗ denotes an r with an
underdot.]. Commentator on the Brahma-sphuta-siddhanta (qv), 860. Some of these
comments are taken from Bhaskara I in 629. Shukla calls him Pŗthūdaka, but
Colebrooke cites him as Ch.
Chessics.
Chessics. The Journal of Generalised Chess. Produced by G. P. Jelliss,
5 Biddulph Street, Leicester, LE2 1BH. No. 1 (Mar 1976) -- No. 29 & 30 (1987).
Succeeded by G&PJ.
Child. Girl's Own Book.
Mrs. L. Maria Child [= Mrs. Child = Lydia Maria Francis, later Child].
The Girl's Own Book. The bibliography of this book is confused. According to the
Opies [The Singing Game, p. 481], the first edition was Boston, 1831 and there was a
London 4th ed. of 1832, based on the 2nd US ed. However the earliest edition in the
BMC is a 6th ed. of 1833. I have examined and taken some notes from the 3rd ed.,
Thomas Tegg, London, 1832 -- unfortunately I didn't have time to go through the entire
book so I may have missed some items of interest. I have also examined the following.
Clark Austin & Co., NY, nd [back of original TP says it was copyrighted by
Carter, Hendee, & Babcock in Massachusetts in 1833]; facsimile by Applewood
Books, Bedford, Massachusetts, nd [new copy bought in 1998 indicates it is 4th ptg, so
c1990]. The facsimile is from a copy at Old Sturbridge Village. The back of the
modern TP says the book was first published in 1834 and the Cataloguing-inPublication data says it was originally published by Carter, Hendee and Babcock in
1834. However, the earliest version in the NUC is Clark, Austin, 1833. I am confused
but it seems likely that Carter, Hendee and Babcock was the original publisher in
Boston in 1831 and that that this facsimile is likely to be from 1833 or an 1834 reprint
of the same. The pagination is different than in the 1832 London edition I have seen.
The Tenth Edition, with Great Additions. By Mrs. Child. Embellished with 144
Wood Cuts. Thomas Tegg, London (& three other copublishers), 1839. 12 + 307 pp +
1p publisher's ad. Has Preface to the Second Edition but no other prefaces. This
Preface is identical to that in the 1833 NY ed, except that it omits the final P.S. of
season's greetings. The 1833 NY essentially has the same text, but they have different
settings and different illustrations with some consequent rearrangement of sections.
However the main difference is that the NY ed omits 41pp of stories. There are a
number of minor differences which lead to the NY ed having 9 extra pages of material.
The Eleventh Edition, with Great Additions. By Mrs. Child. Embellished with
124 Wood Cuts. Thomas Tegg, London (& three other copublishers), 1842. 12 + 363
pp + 1p publisher's ad. The Preface is identical to that in the 10th ed, but omits 'to the
Second Edition' after Preface. 90 pp of games and 40 pp of enigmas, charades, rebuses,
etc. have been added; 56 pp of stories have been dropped.
The Girl's Own Book of Amusements, Studies and Employments. New Edition.
Considerably enlarged and modernized by Mrs. L. Valentine, and others. William
Tegg, London, 1876. This differs considerably from the previous editions.
I will cite the above by the dates 1832, 1833, 1839, 1842, 1876.
Various sources list: 13th ed., 1844 [BMC, Toole Stott 831]; Clark Austin, NY,
1845 [NUC]; 16th ed., 1853 [BMC]; 17th ed. by Madame de Chatelain, 1856 [BMC,
NUC, Toole Stott 832]; 18th ed. by Madame de Chatelain, 1858 [BMC, Toole Stott
833]; 1858 [Osborne Collection (at Univ. of Toronto)]; rev. by Mrs. R. Valentine,
1861 [BMC, Osborne Collection]; rev. by Mrs. R. Valentine, 1862 [BMC, NUC]; rev.
SOURCES - page 43
by Mrs. R. Valentine, 1864 [BMC]; rev. by Mrs. R. Valentine, 1867 [BMC]; enlarged
by Mrs. L. Valentine, 1868 [NUC]; enlarged by Mrs. L. Valentine, 1869 [BMC];
enlarged by Mrs. L. Valentine, 1873 [NUC]; enlarged by Mrs. L. Valentine, 1875
[NUC]; enlarged by Mrs. L. Valentine, 1876 [BMC];
Heyl gives the following under the title The Little Girl's Own Book: Carter,
Hendee and Co., Boston, 1834; American Stationers Co, John B. Russell, Boston,
1837; Edward Kearney, NY, 1847; NY, 1849.
I think there were at least 33 editions. See my The Bibliography of Some
Recreational Mathematics Books for more details. Cf Fireside Amusements, below,
which is largely copied from Child.
Chiu Chang Suan Ching. c-150?
Chiu Chang Suan Ching (Nine Chapters on the Mathematical Art).
(Also called Chiu Chang Suan Shu and variously transliterated. The pinyin is Jiŭ Zhāng
Suàn Shù.) c-150? German translation by K. Vogel; Neun Bücher arithmetischer
Technik; Vieweg, Braunschweig, 1968. My citations will be to chapter and problem,
and to the pages in Vogel. (Needham said, in 1958, that Wang Ling was translating
this, but it doesn't seem to have happened.) Some of the material dates from the early
Han Dynasty or earlier, say c-200, but Chap. 4 & 9, the most original of all, have no
indication of so early a date. A text of c50 describes the contents of all the chapters and
Høyrup suggests that Chap. 4 & 9 and the final assembly of the book should be dated to
the [early] 1C.
Christopher. 1994.
Maurine Brooks Christopher & George P. Hansen. The Milbourne
Christopher Library. Magic, Mind Reading, Psychic Research, Spiritualism and the
Occult 1589-1900. Mike Coveney's Magic Words, Pasadena, 1994. 1118 entries.
References are to item numbers.
Christopher II. 1998.
Maurine Brooks Christopher & George P. Hansen. The Milbourne
Christopher Library -- II. Magic, Mind Reading, Psychic Research, Spiritualism and the
Occult 1589-1900. Mike Coveney's Magic Words, Pasadena, 1998. 3067 entries.
References are to item numbers. Recently received, ??NYR.
Chuquet. 1484.
Nicolas Chuquet. Problèmes numériques faisant suite et servant
d'application au Triparty en la science des nombres de Nicolas Chuquet Parisien. MS
No. 1346 du Fonds Français de la Bibliothèque Nationale, 1484, ff. 148r-210r.
Published in an abbreviated version as: Aristide Marre; Appendice au Triparty en la
science des nombres de Nicolas Chuquet Parisien; Bulletino di bibliografia e di storia
delle scienze matematiche e fisiche 14 (1881) 413-460. (The first part of the MS was
published by Marre; ibid. 13 (1880) 593-814; ??NYS) Marre generally transcribes the
text of the problem, but just gives the answer without any of the text of the solution. I
will cite problems by number. There are 166 problems. (Much of this was used in his
student's book: Estienne de la Roche; Larismethique novellement composee par maistre
Estienne de la roche dict Villefrāche; Lyons, 1520, ??NYS. (Rara 128-130).)
FHM
Graham Flegg, Cynthia Hay & Barbara Moss. Nicolas Chuquet,
Renaissance Mathematician. A study with extensive translation of Chuquet's
mathematical manuscript completed in 1484. Reidel, Dordrecht, 1985. This studies the
entire MS, of which the above Appendice is only the second quarter. It often gives a
full English translation of the text of the problem and the solution, but it may
summarize or skip when there are many similar problems. The problems in the first
part of the MS are not numbered in FHM. I will cite this as FHM xxx, where xxx is the
page number, with 'English in FHM xxx' when the problem is explicitly translated.
Clark. Mental Nuts. 1897, 1904, 1916.
A book of Old Time Catch or Trick Problems Regular old Puzzlers that kept your
SOURCES - page 44
Grandad up at night. Copyright, 1897, by S. E. Clark, Philadelphia. Flood &
Conklin Co. Makers of Fine Varnishes, Newark, N.J. 100 problems and answers.
32pp + covers.
A book of 100 Catch or Trick Problems Their simplicity invites attack, while their
cunningly contrived relations call forth our best thought and reasoning.
Copyright, 1897, by S. E. Clark, Philadelphia. Revised 1904 Edition. Waltham
Watches, Waltham, Massachusetts. This was an promotional item and jewellers
would have their address printed on the cover. My example has: With the
compliments of J. H. Allen Jeweler [sic] Shelbina, Mo. Thanks to Jerry Slocum
for this. In fact there are only 95 problems; numbers 68, 75, 76, 78, 84 are
skipped. 32pp + covers.
Revised Edition 1916, with no specific company mentioned. Enlarged PHOTOCOPY
from Robert L. Helmbold. 100 numbered problems, but some figures inserted
after no. 75 are the solutions to a problem in the other editions and I have counted
this as a problem (no. 75A), making 101 problems. 28pp + covers.
The editions are considerably different. Only 40 problems occur in all
three editions. There are 50 problems common to 1897 and 1904, 42 common to
1897 and 1916 and 71 common to 1904 and 1916, though this counting is a bit
confused by the fact that problems are sometimes combined or expanded or partly
omitted, etc. Solutions are brief. It includes a number of early examples or
distinct variants, which is remarkable for a promotional item. I have entered 36 of
the 1897 problems plus 13 of the 1904 problems not in 1897 and 7 of the 1916
problems not in 1897 or 1904. Many others are standard examples of topics
covered in this work, but are not sufficiently early to be worth entering.
I originally had the 1904 ed and cited the 1904 problems as 1897 on the
grounds that editions of this period do not change much, but having now seen the
1897 and 1916 eds, I realise that the editions are very different, so I will cite the
actual dates. Since only the 1897 version is paginated, I will just cite problem
numbers; the solutions are at the back.
Clarke, William. See: Boy's Own Book.
CM.
Crux Mathematicorum (originally titled Eureka until 4:3)
CMJ.
The College Mathematics Journal. Before the early 1980s, this was the
Two Year College Mathematics Journal.
Colebrooke. 1817.
Henry Thomas Colebrooke (1765-1837), trans. Algebra, with
Arithmetic and Mensuration from the Sanscrit of Brahmegupta and Bháscara. John
Murray, London, 1817. Contains Lîlâvatî and Bîjaganita of Bhâskara II (1150) and
Chapters XII (Arithmetic) and XIII (Algebra) of the Bráhma-sphuta-siddhânta of
Brahmagupta (628). There have been several reprints, including Sändig, Wiesbaden,
1973. (Edward Strachey produced a version: Bija Ganita: or the Algebra of the Hindus;
W. Glendinning, London, 1813; by translating a Persian translation of 1634/5.)
Collins. Book of Puzzles. 1927.
A. Frederick Collins. The Book of Puzzles. D. Appleton and Co., NY,
1927.
Collins. Fun with Figures. 1928.
A. Frederick Collins. Fun with Figures. D. Appleton and Co., NY,
1928.
Columbia Algorism. c1350.
Anonymous Italian MS, c1350 [according to Van Egmond's Catalog
253-254], Columbia X511 .A1 3. Transcribed and edited by K. Vogel; Ein italienisches
Rechenbuch aus dem 14.Jahrhundert; Veröffentlichungen des Forschungsinstituts des
Deutschen Museums für die Geschichte der Naturwissenschaften und der Technik,
SOURCES - page 45
Reihe C, Quellentexte und Übersetzungen, Nr. 33, Munich, 1977. My page references
will be to this edition. Van Egmond says it has a title in a later hand: Rascioni de
Algorismo.
The Algorism is discussed at length in Elizabeth B. Cowley; An Italian mathematical
manuscript; Vassar Medieval Studies, New Haven, 1923, pp. 379-405.
Conway, John Horton. (1937- ). See: Winning Ways.
Cowley, Elizabeth B. See: Columbia Algorism.
CP. 1907.
H. E. Dudeney. Canterbury Puzzles. (1907); 2nd ed. "with some fuller
solutions and additional notes", Nelson, 1919; 4th ed. = Dover, 1958. (I have found no
difference between the 2nd and 4th editions, except Dover has added an extra note on
British coins and stamps. I now have a 1st ed, which has different page numbers, but I
have not yet added them.)
CR
Comptes Rendus des Séances de l'Académie des Sciences, Paris.
Crambrook. 1843. W. H. M. Crambrook. Crambrook's Catalogue of Mathematical &
Mechanical Puzzles Deceptions and Magical Curiosities, contained in the Necromantic
Tent, Royal Adelaide Gallery, West Strand, London. ... To which is added, a Complete
Exposé [of] the Baneful Arts by which unwary Youth too often become the prey of
professed gamesters. And ... an extract from The Anatomy of Gambling. Second
Edition, Corrected & Enlarged. T. C. Savill, 107 St. Martin's Lane, 1843. 23pp.
Photocopy provided by Slocum. [According to: Edwin A. Dawes; The Great
Illusionists; Chartwell Books, Secaucus, New Jersey, 1979, p. 138, this is the first
known magical catalogue. It has a list of about 100 puzzles on pp. 3-5, with the rest
devoted to magic tricks. Unfortunately there are no pictures. Comparison with
Hoffmann helped identify some of the puzzles, but I can not identify many of them. I
have marked almost all these entries with ?? or check??, but the only way one can check
is if actual examples or an illustrated catalogue turn up. Some of the names are so
distinctive that it seems certain that the item does fit where I have cited it; others are
rather speculative. There are several names which may turn up with more investigation.
Toole Stott 190 says there should be 48pp, though the later pages may be the added
material on gambling.]
Cremer, William Henry, Jr. See under: Book of 500 Puzzles, Hanky Panky, Magician's
Own Book.
CUP.
Cambridge University Press.
Cyclopedia. 1914.
Sam Loyd's Cyclopedia of 5,000 Puzzles, Tricks and Conundrums (ed.
by Sam Loyd Jr). Lamb Publishing, 1914 = Pinnacle or Corwin, 1976. This is a
reprint of Loyd's "Our Puzzle Magazine", a quarterly which started in June 1907 and ran
till 1908. See OPM for details.
C&B. 1920.
Sidney W. Clarke & Adolphe Blind. The Bibliography of Conjuring
And Kindred Deceptions. George Johnson, London, 1920. Facsimile by Martino Fine
Books, Mansfield Centre, Connecticut, nd [obtained new in 1998].
C&W.
Chatto & Windus, London.
Datta & Singh.
Bibhutibhusan Datta & Avadhesh Narayan Singh. History of Hindu
Mathematics. Combined edition of Parts I (1935) and II (1938), Asia Publishing House,
Bombay, 1962. NOTE: This book makes some contentious assertions. Readers are
referred to the following reviews.
O. Neugebauer. Quellen und Studien zur Geschichte der Mathematik 3B (1936)
263-271.
S. Gandz. Isis 25 (1936) 478-488.
Datta, B. See: Bakhshali MS; Datta & Singh.
De Morgan (1806-1871). See: Rara.
SOURCES - page 46
De Viribus. See: Pacioli.
dell'Abbaco. See: Pseudo-dell'Abbaco.
Depew. Cokesbury Game Book.
Arthur M. Depew. The Cokesbury Game Book. Abingdon-Cokesbury
Press, NY & Nashville, 1939. [The back of the TP says it is copyright by Whitmore &
Smith -- ?? The Acknowledgements say material has been assembled from various
sources and colleagues who have been collecting and writing over the previous thirty
years.]
Dickson.
Leonard Eugene Dickson (1874-1954). History of the Theory of
Numbers, 3 vols. Carnegie Institution of Washington, Publication 256, 1919-1923;
facsimile reprint by Chelsea, 1952.
Dilworth. Schoolmaster's Assistant.
Thomas Dilworth. The Schoolmaster's Assistant: Being a
Compendium of Arithmetic, both Practical and Theoretical. (1743); 11th ed., Henry
Kent, London, 1762 (partly reproduced by Scott, Foresman, 1938.) 20th ed., Richard &
Henry Causton, London, 1780. De Morgan suggests the 1st ed. was 1744 or 1745, but
the testimonials are dated as early as Jan 1743, so I will assume 1743. Comparison of a
1762 ed. (Wallis 321 DIL) with my 1780 ed. shows the 1780 ed. is identical to the 1762
ed., except the section on exchange is much expanded, so the page numbers of all
material of interest are increased by 12pp. I will cite the pages of the 1762 ed., but give
the date as 1743. [Wallis also has: 14th ed., 1767; 15th ed., 1768; 1783; 22nd ed.,
1785; 1791; 24th ed., 1792; 1793; 33rd ed., 179-; 1799; 1800; 1804.] [Halwas
149-162 are some US editions.]
Diophantos. c250.
Diophantos. Arithmetica. c250. In: T. L. Heath; Diophantos of
Alexandria; 2nd ed., (OUP, 1910); Dover, 1964. Note: Bachet edited a Greek and Latin
version of Diophantos in 1620, which inserted 45 problems from the Greek Anthology
at the end of Book V. (It was in Fermat's copy of this work that Fermat wrote the
famous marginal note now called his Last Theorem; Fermat's son published an edition
with his father's annotations in 1670, but the original copy was lost in a fire.)
DNB.
Leslie Stephen, ed. The Dictionary of National Biography. Smith,
Elder and Co., London, 1885-1901 in 22 volumes. OUP took it over in 1917.
Decennial Supplements were added.
Compact Edition, with Supplement amalgamating the six decennial supplements
to 1960, OUP, 1975. The Compact Ed. shows the original volumes and pages so I will
cite them in ( ), followed by the pages in the Compact Ed.
Dodson. Math. Repository. (1747?); 1775.
James Dodson. The Mathematical Repository. Containing Analytical
Solutions of near Five Hundred Questions, mostly selected from Scarce and Valuable
Authors. Designed As Examples to Mac-Laurin's and other Elementary Books of
Algebra; And To conduct Beginners to the more difficult Properties of Numbers. 2nd
ed., J. Nourse, London, 1775, HB. (I have now acquired vols. II & III (1753 & 1755),
but these are largely concerned with annuities, etc., except the beginning of vol. II has a
section on indeterminate equations, entered in 7.P.1. From references in these volumes,
it seems that the 1775 ed. of volume I is pretty close to the first ed. of c1747, but has
been a little rearranged, so I have redated the entries as above.)
Doubleday -- n. 1969, etc.
Eric Doubleday. Test Your Wits, Vols. 1 - 5. Ace Publishing, NY,
1969; 1971; 1972; 1969[sic]; (1969), revised 1973. [Vols. 1 - 3 are good collections,
with a number of novel variations of standard problems. Vols. 4 & 5 are vol. 1 split
into two parts and much padded by putting each answer on a separate page! The books
refer to Doubleday as puzzle setter for a London newspaper and one of the best known
SOURCES - page 47
setters in the English speaking world. However, none of the older puzzle setters/editors
in England have ever heard of him and there is no book by him in the British Library
Catalogue. Surprisingly, there is also no book by him in the Library of Congress
Catalogue! I am beginning to think the author is a deception, but the first three books
are better than scissors and paste hack work.]
DSB.
Dictionary of Scientific Biography. Ed. by Charles C. Gillespie for the
American Council of Learned Societies. Scribner's, NY, 1970-1977, in 18 volumes. I
will give the volume and the pages.
The mathematical material has been reprinted in four volumes as: Biographical
Dictionary of Mathematicians Reference Biographies from the Dictionary of Scientific
Biography. Scribner's, NY, 1990? This has new pagination, continuous through the
four volumes. If I don't have the DSB details, I will cite this as BDM.
Dudeney, Henry Ernest (1857-1930). See: AM, CP, MP, PCP, 536. I also cite his columns
or contributions in The Captain, Cassell's Magazine, Daily Mail, London Magazine,
The Nineteenth Century, The Royal Magazine, Strand Magazine, Tit-Bits, The Tribune,
The Weekly Dispatch.
Eadon. Repository. 1794.
John Eadon. The Arithmetical and Mathematical Repository, Being a
New Improved System of Practical Arithmetic, in all its Branches; Designed for the Use
of Schools, Academies, Counting-Houses, and Also for the Benefit of private Persons
who have not the Assistance of a Teacher. In Four Volumes. Volume 1. In Three
Books. Printed for the author, and sold by G. G. and J. Robinson, Paternoster Row,
London, 1794.
EB
Encyclopædia Britannica. I tend to use my 1971 ed.
Endless Amusement I. c1818.
Anonymous. Endless Amusement; A Collection of Nearly 400
Entertaining Experiments In various Branches of Science; ..., All the Popular Tricks
and Changes of the Cards, .... 3rd ed.(?), Thomas Boys, London, nd [1825].
Frontispiece & TP are missing, but James Dalgety has inserted a photocopy of the TP of
the 3rd ed. [BMC lists 2nd ed., 1819?; 3rd ed., 1825? BMC65 lists 1st ed. by Thorp
& Burch, c1818; 2nd ed., c1820. Toole Scott 255-267 lists 3rd ed., c1820; 4th ed.,
1822; 5th ed., 1830; 6th ed., 1834; 7th ed., 1839. Hall, BCB 116-123 are: 1st ed.,
c1815; 2nd ed., c1820; 3rd ed., c1820; 3rd ed., Philadelphia, 1822; 4th ed., c1825;
5th ed., c1830; 6th ed., 1834; Philadelphia, 1847. Heyl 110-115, 121 are 1819; 2nd
& 3rd ed., M. Carey & Sons, Philadelphia, 1821 & 1822; 3rd ed, C. Tilt, London,
1825; Borradaile, NY, 1831; Henry Washburne & Thomas Tegg, London, 1839; Lea
& Blanchard, Philadelphia, 1847. Almost all of these are listed as 2 + 216 pp, so the
editions are probably all the same as the 1st ed., except that Hall notes that the 1st ed.
title is slightly different: Endless Amusement; A Collection of Upwards of 400
Entertaining and Astonishing Experiments. Among a Variety of other Subjects, are
Amusements in Arithmetic, Mechanics, Hydraulics .... All the Popular Tricks and
Changes of the Cards, ..., and Heyl gives a similar title for the 1825 ed. and the 1831
NY ed. has some variations. Christopher 330-338 are 2nd ed., Philadelphia, 1821; 3rd
ed., c1820; 3rd ed., Philadelphia, 1822; 4th ed., c1822; 4th ed., c1822 (slightly
different to preceding; 5th ed., c1830; 6th ed., 1834; 7th ed., 1839; Philadelphia,
1847. C&B list it under Thorp and Burch, the publishers, with no dates.] [There is a
Recreations in Science, ..., by the author of Endless Amusement, 1830.]
Endless Amusement II. 1826?
Anonymous. A Sequel to the Endless Amusement, Containing Nearly
Four Hundred Interesting Experiments, In various Branches of Science, ..., to Which are
SOURCES - page 48
Added, Recreations with cards, and a Collection of Ingenious Problems. Thomas Boys,
London, nd [1826?]. Pp. 203-216 are missing, but James Dalgety has inserted
photocopies. [BMC lists one ed., 1826? Hall, BCB 252 gives c1825. Heyl says this
refers to Thomas Boys ... and Thorp and Burch, London (1825). Toole Stott 623 gives
1825.]
= Anonymous. The Endless Amusement. New Series Containing
Nearly Four Hundred Interesting Experiments, ... (as above). Thomas Tegg & Sons,
London, 1837. Angela Newing has provided a photocopy of the interesting parts of this
and it is virtually identical to the 1826? ed., though it has been reset, resulting in an
extra word fitting on some lines, and it has rather poorer pictures. One problem has
been replaced by another. [Heyl 122.] 21 problems, including the replacement
problem, are copied in The New Sphinx.
= Anonymous. A Companion to the Endless Amusement. James
Gilbert, London, 1831. [Toole Stott 172 says this is a reprint of A Sequel ..., from the
same type, with new TP, and this is clear from examination of the example Wallis 187.5
COM. Heyl 66 dates it as c1820?]
Some of the material is taken from Badcock.
van Etten/Leurechon. 1624.
Recreation Mathematicque.
The bibliography of this book is very complicated. I have now made a separate
bibliography of this, augmented by many contributions from Voignier, which is now
(Aug 2001) 19pp, listing 50 French editions, 5 English editions, 4 Latin editions and 8
(or 9) Dutch editions -- a total of 67 (or 68) editions from 1624 to 1706, though at least
10 of the French editions may be 'ghosts'. This is part of my The Bibliography of Some
Recreational Mathematics Books.
This book has traditionally been attributed (since 1643) to Père Jean Leurechon,
SJ (c1591-1670), who was probably van Etten's university teacher, but the book
specifically names van Etten and there seems to be very little real evidence for
Leurechon's authorship. Trevor Hall's booklet and chapter are a substantial study of this
question and he concludes that there is no real reason to doubt van Etten's authorship,
though he may well have had help or inspiration from his teacher. Hall has also shown
that van Etten and his uncle, the book's dedicatee, were real people. (Toole Stott
429-431 dismisses Hall's work as a result of completely misunderstanding it!)
However, the book was amended, revised and translated many times, so that versions
may occur under the following names: Hendrik van Etten; Jean Leurechon;
D.H.P.E.M. = Denis (or Didier) Henrion, professeur en mathématique (or Professeur ès
Mathematiques), a pseudonym of Clément Cyriaque de Mangin, who also called
himself Pierre Hérigone; Claude Mydorge; Caspar (or Gaspar) Ens; Wynant van
Westen; William Oughtred; William Leake; not to mention Anonymous and versions
of the title -- I have found it under Recreations or Récréations and under
Vermakelijkheden. E.g. Lucas, RM1, 239-240, has 7 entries for this book under five
different authors and twice under Récréations.
Jacques Voignier; Who was the author of "Recreation Mathematique" (1624)?;
The Perennial Mystics #9 (1991) 5-48 (& 1-2 which are the cover and its reverse).
[This journal is edited and published by James Hagy, 2373 Arbeleda Lane, Northbrook,
Illinois, 60062, USA.] This is the second serious study of this book. He points out
evidence for Leurechon's connection with the book, which makes it seem more likely,
but definite evidence is still lacking, so I am suggesting that it may have been some kind
of joint production and I will change my references it to van Etten/Leurechon. The
work of Hall and Voignier form the basis of the following discussion, supplemented by
the standard catalogues and personal inspection of about a half of the French and
SOURCES - page 49
English editions -- generally after 1630.
Henrik van Etten. Recreation Mathematicque. Composee de Plusieurs
Problemes Plaisants et Facetieux. En faict d'Arithmeticque Geometrie, Mechanicque,
Opticque, & autres parties de ces belles sciences. Jean Appier Hanzelet,
Pont-a-Mousson, 1624 [taken from facsimile of the 1626 ed.]. 155pp., ??NYS.
2nd ed., 1626, ibid. = recent facsimile with no details, but with 'Pont à Mousson
13 - 10 - 54' written inside the back cover. [An apparently identical copy at the
Museum of the History of Science, Oxford, has a small insert saying it was reissued by
La Compagnie de Pont-à-Mousson, printed by l'Imprimerie Berger-Levrault, nd.]. 91
problems on xiv + 144 = 158pp. [The extra pages include questions V and VI of
problem 91 -- these questions occur in no other edition, except probably in the 1629
reissue in Pont-à-Mousson.]
After the two Hanzelet editions, there were three editions in Paris in 1626, by
Rolet Boutonné (2nd ed.), by Antoine Robinot (2nd ed.) and by Jean Moreau &
Guillaume Loyson (3rd ed.). Boutonné and Robinot were closely associated and their
output was interchangeable. Their 2nd eds. appear to be essentially the 1624 ed. The
Moreau & Loyson has Notes added to the problems and 8pp. of Additions. This was
the first to put the illustrations as woodcuts in the text rather than using copperplates for
five separate sheets of 8 figures. The Notes are signed D.A.L.G., but are due to Claude
Mydorge. (NUC indicates the Robinot had further comments signed D.H.P.E.M., later
identified as Denis (or Didier) Henrion Professeur En Mathématique (though Henrion is
a pseudonym of Clément Cyriaque de Mangin!) -- but this seems to be a confusion.) In
the next few years, editions appeared in Paris, Rouen and Lyon. In 1627, Boutonné
issued a '4th ed.' with "Nottes sur les recreations mathematiques ... Par D. H. P. E. M."
and the D.A.L.G. notes were omitted. In 1627, Claude Rigaud & Claude Obert, Lyon,
issued a version with 9pp of Additions as in the 1626 Moreau & Loyson.
In 1628, Charles Osmont, Rouen, issued a version in three parts: Récréations
mathématiques ... 1re et 2de partie. La 3e partie contient un recueil de plusieurs gentilles
et récréatives inventions de feux d'artifice .... Part 1 was van Etten's 91 problems, with
questions V & VI of prob. 91 omitted, omitting the D.A.L.G. notes and the Additions.
Part 2 had 45 new problems, often attributed to Mydorge and/or Henrion, but they had
no connection with this and the authorship of these problems is unknown, though
Voignier suggests the printer, Osmont. Part 3 is an independent treatise on fireworks
which Hall attributes to Hanzelet. This edition was reissued in Rouen by various
publishers in 1628, 1629, 1630, 1634, 1638 and in Lyon in 1642-1643, 1653, 1656,
1658, 1669, 1680.
In 1630, Boutonné and Robinot (their printing is indistinguishable and volumes
often have parts from both of them, indeed the Privilege is issued to them jointly) issued
an extended version in four parts, titled Examen du Livre des Recreations
Mathematiques, stated to be by Mydorge. Part 1 is van Etten's 91 problems, with parts
V & VI of prob. 91 omitted, with many problems being followed by an Examen signed
D.A.L.G. These are by Mydorge and are a revision of his material in the 1626 Moreau
& Loyson. Part 2 has its own TP and had 45 new problems, taken from the 1628 Rouen
ed. Part 3 has its own TP, but doesn't state the publisher, and is the independent treatise
on fireworks, also taken from the 1628 Rouen ed. Part 4 again has its own TP and is
Nottes [sic] sur les Recreation Mathematiques by D.H.P.E.M. and are additions to 27 of
van Etten's problems, taken or extended from the Notes in the 1627 4th ed. The book is
also described as 3 parts with the Nottes, but Parts 2 and 3 are consecutively paged,
leading to some descriptions of the book as being in 3 parts. The parts were probably
issued separately as they sometimes are catalogued separately and different copies of
SOURCES - page 50
the whole work often have a mixture of the Boutonné and Robinot printings. This most
extended form was reissued by various publishers in Paris: 1634(??), 1638, 1639, and
in Rouen: 1639 (two publishers), 1643 (two publishers ??), 1648?, 1649?
In 1659, Cardin Besonge, Paris, issued Les Récréations mathématiques, avec
l'examen de ses problèmes en arithmétique, géométrie, .... Premièrement reveu par
D. Henrion, depuis par M. Mydorge, et tout nouvellement corrigé et augmenté, 5e et
dernière édition. The Nottes are incorporated in the text (or perhaps omitted??). The
entire text is consecutively page-numbered. Reissued in Paris: 1660, 1661 and in
Rouen as the 6th ed.: 1660?, 1663?, 1664, 1669 (seven publishers!).
The 1630 Paris ed. and the 1626 ed. have the same problem numbers for the first
91 problems, as do almost all French editions. I will cite the problem number and the
pages of the 1626 ed. I will add reference to the 1630 Paris ed., when the latter has
additional information. Only one of the additional problems in part 2 (prob. 7) is of any
interest to us, but several of Henrion's Nottes give corrections, extensions, additional
references and even additional problems. I didn't find any of the D.A.L.G. notes of any
interest.
English editions.
Mathematicall Recreations. Or a Collection of sundrie [1653 has: many]
Problemes, extracted out of the Ancient and Moderne Philosophers, as secrets in nature,
and experiments in Arithmeticke, Geometrie, Cosmographie, Horologographie,
Astronomie, Navigation, Musicke, Opticks, Architecture, Staticke, Machanicks,
Chimestrie, Waterworkes, Fireworks, &c. Not vulgarly made manifest untill this time:
Fit for Schollers, Students, and Gentlemen, that desire to know the Philosophicall cause
of many admirable Conclusions. Usefull for others, to acuate and stirre them up to the
search of further knowledge; and serviceable to all for many excellent things, both for
pleasure and Recreation. Most of which were written first in Greeke and Latine, lately
compiled in French, by Henry Van Etten Gent. And now delivered in the English
tongue, with the Examinations, Corrections, and Augmentations. Printed by T. Cotes
for Richard Hawkins, London, 1633. 328pp. (This ed. is 'excessively rare'.)
Reissued by William Leake, London: 2nd ed., 1653; (1667(??)); 1674. 344pp.
[Hall, OCB, says the 2nd ed. is similar to the 1633 edition, but with an extra 16pp
description (of 1636) of some dials by Oughtred (which led to the book or the
translation often being attributed to Oughtred). Hall also states that the English editions
are based on the Rouen ed. of 1628. Sadly some interesting problems were omitted in
the English, leading to confusion in plate numbers. However, I have just noticed that
Prob. 63 is about two pages longer than the corresponding Prob. 70 of the French
editions.] The 1633, 1653 and 1674 editions are identical except for the additional
English material in the later editions. I will add citations to the English editions in
parentheses. I now have an imperfect copy of the 1674 ed, covers missing and lacking
the Frontispiece and pp. 273-282 and later material. Heyl 311 is a 1753 ed., which must
be an error for 1653.
W. Leybourn, qv, takes several sections directly from the English editions.
Latin editions.
In 1628(??), Caspar (or Gaspar) Ens made a Latin translation but added some
other material, e.g. 49 problems from Alcuin. I have only studied the 1636 ed.
carefully.
Thaumaturgus Mathematicus, Id est, Admirabilium Effectorum e
Mathematicarum Disciplinarum Fontibus Profluentium Sylloge. Casparo Ens L.
Collectore & Interprete. 1628. [Taken from 1636 TP. MUS #30 says this is only a
SOURCES - page 51
translation of van Etten. There is some doubt whether the 1628 edition exists!]
Reissued in 1636 and 1651. It has 89 of van Etten's problems (omitting 38 & 46)
and adding 25 new problems, with some numbering errors so the last is numbered 113.
This is followed by 55 problems of Alcuin, using the Bede version of 56 problems, but
omitting 18.
Thaumaturgus mathematicus Gasparo Ens lectore collectore, & interprete, Nunc
denuò Correctus, & Auctus. Apollonius Zambonus, Venice, 1706. 113 problems + 49
from Alcuin (check??). There are some differences between this and the 1636 ed.
[MUS #30 gives Köln, 1651, and further editions.]
Dutch editions.
In 1641, Wynant van Westen translated van Etten into Dutch. The title is: Het
eerste [- derde] deel van de Mathematische vermaecklyckheden. Te samen ghevoeght
van verscheyden ghenuchlijcke ende boertige werckstucken, soo uyt arithmetica,
geometria, astronomie, geographia, cosmographia, musica, physica, optica, catoptrica,
architectonica, sciotetica, als uyt andere ongehoorde mysterien meer. Ghetranslateert
uyt het fransch in nederduytsche tale: ende verrijckt, vermeerdert, ende verbetert met
verscheyden observatien ende annotatien, dienende tot onderrichtinge van eenige
duystere questien, ende mis-slaghen in den franschen druck. Door Wynant van Westen
.... op nieus oversien verbetert. Jacob van Biesen, Arnhem, 1641. 3 parts with separate
title pages and pagination, perhaps in 3 vols, but later in 1 vol.
This was reissued: Van Biesen, Arnhem, 1641, ??, 1644, 1662, 1671-72;
Lootsman and Jacobsz, Amsterdam, 1673. I haven't examined any of these.
Euler. Algebra. 1770.
Leonard Euler (1707-1783). Vollständig Anleitung zur Algebra. Royal
Academy of Sciences at Petersburg, 1770. [A Russian translation appeared in 1768.]
Translated into French by John III Bernoulli, with additions by Bernoulli and La Grange
(pp. 463-593 here), 1774. Translated from French into English as Element of Algebra,
with further notes, by Rev. John Hewlett, with a Memoir of Euler by Francis Horner
[Horner actually did the translation; Hewlett edited it.], (1797), 5th ed., Longman,
Orme, and Co., London, 1840. Reprinted, with Introduction by C. Truesdell (1972),
omitting 4 pp of Horner, Springer, NY, 1984 [hidden on back of title page]. I will cite
part, section, chapter, article and the pages from the Springer ed. (Part II has no
sections.) Unfortunately these numbers seem to have little connection with other
editions. [Though most of the recreational material in Euler is much older than Euler, I
have included it as a representative 18C text.] [Halwas 175-176 are some US editions - the 1818 edition was the first example of a translated algebra in the US.]
Family Friend.
The Family Friend. This was a magazine founded by Robert Kemp
Philp in 1849. The dating is awkward -- vol. 1 is dated 1850 on the cover, but the
Preface is dated 15 Nov 1849 and refers to the success of the past year, when it
appeared monthly. It also says the magazine will henceforth appear twice a month with
two volumes per year, due on the first of June and December. The Gardening section of
vol. 1 goes from Jan to Dec. The Preface of Vol. 2 is dated 10 Jun 1850 and its
gardening section covers Jan - Jun. The Preface of Vol. 3 is dated 15 Dec 1850 and its
Gardening section goes Jul - Dec. BMC shows Philp left in 1852 and the magazine
continued with two volumes per year through a fifth series, ending in 1867, then
restarted with one volume a year from 1870 until 1921. I have vols. 1 - 3 & the second
half of 1858, which is dated 1858-9, but appears to be Jul-Dec. None of the text is
signed. At the back of volumes are included answers to correspondents. The puzzles
are often identical to those in The Magician's Own Book or The Illustrated Boy's Own
SOURCES - page 52
Treasury, etc., but are considerably earlier.
FHM.
Graham Flegg, Cynthia Hay & Barbara Moss -- see under Chuquet.
Fibonacci.
Leonardo Pisano, called Fibonacci (c1170->1240). Liber Abbaci.
(1202); 2nd ed., 1228. In: Scritti di Leonardo Pisano; vol. I, ed. and pub. by
B. Boncompagni; Tipografia delle Scienze Matematiche e Fisiche, Rome, 1857. The
title pages give 'abbaci', but Boncompagni's text begins 'Incipit liber Abaci ... Anno
MCCII.', while the c1275 MS starts 'Incipit abbacus'. Both forms are used, sometimes
even in the same article -- e.g. Loria's biographical article, see in Section 1.
Richard E. Grimm was working on a critical edition of this and he kindly gave me
some details. There are 15 known MSS, all of the 1228 2nd ed. Six of these consist of
1½ to 3 chapters only; five of the others lack Chapter 10 and the second half of Chapter
9; one lacks Chapter 10 and one lacks much of Chapter 15, leaving two essentially
complete texts. The last four MSS mentioned are the most important: Siena L.IV.20,
c1275, lacking much of Chap. 15, "the oldest and best"; Siena L.IV.21, 1463 [Grimm
said c1465 -- there are dates up through 1464 in interest calculations, but the Incipit
specifically says 1463], which includes much other material from later writers, so it is at
least double the size of L.IV.20; Vatican Palatino #1343, end of 13C, lacking Chap. 10;
Florence Bibl. Naz. Conventi Soppressi C. 1. 2616, early 14C, "handsome but
frequently badly faded" so "that a later hand found it necessary to rewrite what he saw
there." When I examined it in Sep 1994, the black ink was indeed sometimes badly
faded but the numbers were in a clear red -- perhaps these are what was rewritten??
L.IV.20 has the beginning sentence ending "et correctus ab eodem a MCCXXVIII", but
Grimm says all the others are also of the 1228 ed even if they do not carry this addition
or the extra initial dedication. Sadly, I heard in Aug 1998 that Grimm had Alzheimer's
disease and was in a nursing home. Inquiry has revealed no trace of the photocopies of
all the Liber Abbaci MSS which he said he had obtained and in summer 2000 I heard he
had died.
Boncompagni used only one MS, then denoted Codex Magliabechiana, C. I,
2616, Badia Fiorentina, no. 73, now Conventi Soppressi, C. I. 2616, the badly faded
fourth MS described above.
In Sep 1994 and Mar 1998, I examined Siena L.IV.20 and 21 and Conv. Soppr.
C.1.2616. I have slides of the Incipit & Fibonacci numbers from all of these and some
other material.
The dates of 1202 and 1228 are based on the Pisan calendar.
Fibonacci-Sigler. Liber Abaci. Translated by Laurence E. Sigler as: Fibonacci's Liber
Abaci A Translation into Modern English of Leonardo Pisano's Book of Calculation.
Springer, New York, 2002. I have added page references to this, denoted S, after the
Boncompagni pages, e.g. pp. 397-398 (S: 543-544). I have given Sigler's English
wherever I previously had just quoted the Latin.
Fibonacci. Flos and Epistola.
Leonardo Pisano, called Fibonacci. MS of c1225 which begins "Incipit
flos Leonardi bigolli pisani ...", Biblioteca Ambrosiana, Milan, E. 75. In: Scritti di
Leonardo Pisano, vol. II, ed. and pub. by B. Boncompagni, Rome, 1862, pp. 227-252.
Part of the MS has a separate heading: "Epistola suprascripsit Leonardi ad
Magistrum Theodorum phylosophum domini Imperatoris" and is sometimes considered
a separate work. It occupies pp. 247-252 of the printed version. For an English
description, see: A. F. Horadam; Fibonacci's mathematical letter to Master Theodorus;
Fibonacci Quarterly 29 (1991) 103-107.
Italian translation (including the Epistola) and commentary: E. Picutti; Il 'Flos' di
Leonardo Pisano; Physis 25 (1983) 293-387.
Fireside Amusements. 1850.
Fireside Amusements. Chambers's Library for Young People. William
SOURCES - page 53
and Robert Chambers, Edinburgh, 1850, 188pp. The BMC has this under Fireside
Amusements and refers to Chambers for the Library, which was 19 vols, 1848-1851.
Pp. 187+ are missing in the copy I have seen, but it seems that just one page of solutions
is missing -- the NUC gives 188pp. The NUC lists a 1870 reprint.
[The BMC lists an 1880 ed with 159pp, part of Chambers's Juvenile Library,
NYS.]
Fireside Amusements A Book of Indoor Games. W. & R. Chambers, London
and Edinburgh, nd, 128pp. The BMC lists this as 1890[1889]. Though laid out entirely
differently, almost all the material is taken from the 1850 ed. I will cite both editions.
Much of the material of interest is taken from Child: Girl's Own Book.
Folkerts. Aufgabensammlungen. 13-15C.
Menso Folkerts. Mathematische Aufgabensammlungen aus dem
ausgehenden Mittelalter. Sudhoffs Archiv 55 (1971) 58-75. He examines 33
anonymous Latin manuscript problem collections from 13-15 C in Oxford, London,
Berlin, Munich, Vienna and Erfurt and catalogues the problems therein. Of these, only
Munich 14684 is published (cf below). He notes that many more such sources exist.
His catalogue covers 14 of my topics. I will not try to cite the individual MSS, since
many of the topics occur in over a dozen of them. I will simply say he has n sources,
though some of the sources have several examples.
Folkerts, Menso. See: Alcuin.
della Francesca. Trattato. c1480.
Piero della Francesca (1412-1492). Trattato d'Abaco. Italian MS in
Codex Ashburnhamiano 359* [291*] - 280 in the Biblioteca Mediceo-Laurenziana,
Florence. c1480 [according to Van Egmond's Catalog 84, based on watermarks in the
paper which date from 1470 to 1500, but Davis, below, p. 16, says c1450]. Transcribed
and annotated by Gino Arrighi, Testimonianze di Storia della Scienze 6, Domus
Galilæana, Pisa, 1970. Arrighi uses c. (for carta) instead of f. (for folio), but I will
use f. for consistency with other usage, followed by the pages in Arrighi in ( ). Arrighi
reproduces many of the diagrams, but he doesn't say anything about whether he has
included all of them. This MS appears to be that which was in the possession of Piero's
descendents until 1835 when it was reported as having disappeared. Guglielmo Libri,
the noted historian of mathematics, who was also a shady bookdealer, transcribed part
of this MS in vol. 3 of his Histoire de la Mathématique en Italie in 1840 as an
anonymous work, then sold it to Lord Ashburnham in 1847 (recorded in his collection
in 1881) whose collection was bought for the Laurentian Library in 1884. There are
three different catalogue numbers - I use the format used in Van Egmond's Catalog.
The MS had passed out of common knowledge until it was rediscovered in the
Laurentian Library in 1917 by Girolamo Mancini who recognised the handwriting as
Piero's.
This work and Piero's Libellus de Quinque Corporibus Regularibus are the
subject of a long standing plagiarism argument. Giorgio Vasari [Le Vite de' più
eccellenti pittori, scultori e architetti; 1550; The Essential Vasari, ed. by Betty
Burroughs from the 1850 translation of Mrs. Jonathan Foster, Unwin Books, London,
1962] states: "... Piero della Francesca, who was a master of perspective and
mathematics but who first went blind and then died before his books were known to the
public. Fra Luca di Borgo, who should have cherished the memory of his master and
teacher, Piero, did his best, on the contrary, to obliterate his name, taking to himself all
the honour by publishing as his own work that of that good old man. ... Maestro Luca
di Borgo caused the works of his master, Piero della Francesca, to be printed as his own
after Piero died." The mathematical works of Piero were unknown until they were
rediscovered in 1850/1880 and 1917. Examination shows that Pacioli certainly used
105 problems, many unusual, from Piero in the Summa. But he does praise Piero in the
SOURCES - page 54
Epistola (f. 2r) of the Summa, as "the monarch of painting of our times". It has been
suggested that Pacioli had a large hand in the writing of Piero's works and hence was
just reusing his own material and he frequently expands on it. However, there is no
evidence that Pacioli was ever a student of Piero. Entire books have been written on the
question, so I will not try to say any more. See: Margaret Daly Davis; Piero della
Francesca's Mathematical Treatises The "Trattato d'abaco" and "Libellus de quinque
corporibus regularibus"; Longo Editore, Ravenna, 1977, for detailed comparisons and
the work of R. E. Taylor in Section 1: Pacioli. Davis identifies 139 problems in the
Libellus, of which 85 (= 61%) are taken from the Trattato. Davis notes that Pacioli's
Summa, Part II, ff. 68v - 73v, prob. 1-56, are essentially identical to della Francesca's
Trattato, ff. 105r - 120r. See also section 6.AT.3 where the Libellus and the Pacioli &
da Vinci: De Divina Proportione are discussed.
The work is discussed and 42 problems are given in English in: S. A.
Jayawardene; The 'Trattato d'Abaco' of Piero della Francesca; IN: Cecil H. Clough,
ed.; Cultural Aspects of the Italian Renaissance Essays in Honour of Paul Oskar
Kristeller; Manchester Univ. Press, Manchester, nd [1976?]; pp. 229-243. I will note
'English in Jayawardene.' when relevant.
Frikell, Wiljalba (1818 (or 1816) - 1903). (The given name Gustave sometimes occurs -- I
thought Gustave might be a son of Wiljalba, but the son was named Adalbert ( -1889)
and his name was pirated by a clumsy imposter in England.)
See the discussion at: Book of 500 Puzzles, Boy's Own Conjuring
Book, Hanky Panky, Magician's Own Book, The Secret Out. Frikell was a noted
conjuror of the time and his name has been associated with the UK versions of these
books, but there is no evidence he had anything to do with them. The Art of Amusing,
by Frank Bellew, Hotten, London, 1866?, op. cit. in 5.E, has a note on the back of the
TP saying The Secret Out is a companion volume, just issued, by Hermann Frikell.
C&B, under Williams, Henry Llewellyn ("W. Frikell") lists: Hanky Panky;
Magician's Own Book, London & New York; (Magic No Mystery); The Secret Out
and says to also see Cremer.
Gamow & Stern. 1958.
George Gamow & Marvin Stern. Puzzle-Math. Macmillan, London,
1958.
Gardner.
Martin Gardner (1914- ). Many references are to both his SA column,
cited by (month & year), e.g. SA (Mar 1982), and to the appearance of the column as a
chapter in one of his books, abbreviated as shown below. In general, I will only give
the chapter reference as the various editions and translations are differently paginated.
Answers, comments and extensions appeared in succeeding issues of SA, usually in
Gardner's column, but sometimes in the Letters. All this material is collected in the
book chapter, sometimes by rewriting of the article, sometimes as notes or an
Addendum at the end of the chapter. Since many years usually passed before the book
version, the Addenda often contain material that never appeared in SA, as well as
references to work done as a result of the SA article. I have not tried to enter all of
Gardner's references here, so anyone interested in a topic that Gardner has considered
should consult the book version of Gardner's column. Currently some of the earlier
books are being reissued in new editions, with further extensions and updating. See
also the next entry.
For years from at least 1950, SA appeared in two volumes per year, each of six
issues. In year 1950 + n, vol. 182 + 2n covers Jan-Jun and vol. 183 + 2n covers
Jul-Dec.
1st Book
The Scientific American Book of Mathematical Puzzles and
SOURCES - page 55
Diversions. Simon & Schuster, 1959.
UK version: Mathematical Puzzles and Diversions from Scientific American. Bell,
London, 1961; Penguin (without the words 'from Scientific American'), 1965.
2nd Book
The Second Scientific American Book of Mathematical Puzzles and
Diversions. Simon & Schuster, 1961.
UK version: More Mathematical Puzzles and Diversions from Scientific American.
Bell, London, 1963. Penguin (without the words 'from Scientific American'), 1966.
(The UK versions omit Chapter 20: "The Mysterious Dr. Matrix". The dust wrapper of
the HB has a sentence referring to this chapter which has been blacked out. ??)
New MD
Martin Gardner's New Mathematical Diversions from
Scientific American. Simon & Schuster, 1966.
Unexpected
The Unexpected Hanging and Other Mathematical Diversions. Simon
& Schuster, 1969.
UK version: Further Mathematical Diversions. Allen & Unwin, London, 1970;
Penguin, 1977.
6th Book
Martin Gardner's Sixth Book of Mathematical Games from Scientific
American. Freeman, 1971.
Carnival
Mathematical Carnival. Knopf, NY, 1975; Penguin, 1978.
Magic Show
Mathematical Magic Show. Random House, NY, 1978.
Circus
Mathematical Circus. Knopf, NY, 1979.
Wheels
Wheels, Life and Other Mathematical Amusements. Freeman, 1983.
Knotted
Knotted Doughnuts and Other Mathematical Entertainments. Freeman,
1986.
Time Travel
Time Travel and Other Mathematical Bewilderments. Freeman, 1988.
Penrose Tiles
Penrose Tiles to Trapdoor Ciphers. Freeman, 1989.
Fractal
Fractal Music, Hypercards and More .... Freeman, 1992.
Last
The Last Recreations Hydras, Eggs, and Other Mathematical
Mystifications. Copernicus (Springer), NY, 1997. ??NYR.
Magic Numbers The Magic Numbers of Dr. Matrix. Prometheus, Buffalo, 1985.
Chaps. 1-18 previously appeared as: The Incredible Dr. Matrix; Scribner's, NY, 1976.
Chaps. 1-7 & 9 previously appeared as: The Numerology of Dr. Matrix; Simon &
Schuster, NY, 1967. In contrast to his other books above, the answers and comments
occur at the end of this book instead of following the original articles.
Workout
A Gardner's Workout Training the Mind and Entertaining the Spirit.
A. K. Peters, Natick, Massachusetts, 2001. This comprises 41 chapters of articles
written after his retirement from SA.
Gardner. MM&M. 1956.
Martin Gardner. Mathematics, Magic and Mystery. Dover, NY, 1956.
General Trattato. 1556.
Nicolo Tartaglia (c1499-1557). (La Prima Parte del) General Trattato
di Numeri et Misure. Curtio Troiano, Venice, 1556. (Modern Italian spells his given
name as Niccolò, but it appears as Nicolo on the title page.) Six parts actually appeared
in 1556-1560. All references are to Part 1. Unless otherwise specified, reference is to
Book 16 (of Part 1), but I also have references to Books 12 and 17. CAUTION -- the
running head in Book 17 says Libro Decimosesto for several pages before changing to
Libro Decimosettimo. Since it is hard to find the beginnings of books, this can cause
confusion. See Rara 275-279; Van Egmond's Catalog 345-346.
In 1578, Guillaume Gosselin produced an annotated translation of parts 1 & 2
into French as: L'Arithmetique de Nicolas Tartaglia -- cf Van Egmond's Catalog 347.
Ghaligai. Practica D'Arithmetica. 1521.
Francesco Ghaligai. Practica D'Arithmetica di Francesco Ghaligai
SOURCES - page 56
Fiorentino. Nuovamente Rivista, & con somma Diligenza Ristampata. I Giunti,
Florence, 1552. Smith, Rara, says that this is identical to the first (Latin?) edition by
Bernardo Zucchetta, Florence, 1521, except that edition was titled Summa De
Arithmetica, so I will date the entries as 1521. See Rara 132; Van Egmond's Catalog
316-317.
Gherardi. Libro di ragioni and Liber habaci. 1328 & c1310.
Paolo Gherardi. Two Italian MSS in Codici Magliabechiani Classe XI,
no. 87 & 88 in Bib. Naz. di Firenze. Van Egmond's Catalog 115-116. The first is dated
1327 (but see below). The second is undated, but clearly of a similar date which I
originally denoted 1327? - see below. Transcribed by Gino Arrighi; Collana di Storia
della Scienza e della Tecnica, No. 2; Maria Pacini Fazzi, Lucca, 1987. See also:
Warren Van Egmond; The earliest vernacular treatment of algebra: the Libro di ragioni
of Paolo Gerardi (1328); Physis 20 (1978) 155-189. Van Egmond notes that the date of
30 Jan 1327 is in our year 1328 and uses this in his Catalog. He doubts whether Liber
habaci is actually by Gherardi and his Catalog assigns no author to it, so I will put
Gherardi? as author. He dates it to c1310. His paper is concerned with the quadratic
and cubic equations and hence of little interest to us.
Good, Arthur. See: Tom Tit.
Gori. Libro di arimetricha. 1571.
Dionigi Gori. Libro di arimetricha. 1571. Italian MS in Biblioteca
Comunale di Siena, L. IV. 23. ??NYS. Extensively quoted and discussed in: R. Franci
& L. Toti Rigatelli; Introduzione all'Aritmetica Mercantile del Medioevo e del
Rinascimento; Istituto di Matematica dell'Università di Siena, nd [1980?]. (Later
published by Quattroventi, Urbino, 1981.) (I will quote Gori's folios and also give the
pages of this Introduzione.) Van Egmond's Catalog 191-192.
Graves.
The Graves Collection of early mathematical books at University
College London (UCL).
Guy, Richard Kenneth (1916- ). See: Winning Ways.
G4Gn
Gathering for Gardner n, held in Atlanta. 1: Jan 1993; 2: Jan 1996;
3: Jan 1998; 4: Feb 2000; 5: Apr 2002.
G&P.
Games & Puzzles. The first version ran from 1972 through 1981. The
second series started in Apr 1994 and finished with No. 16 in Jul 1995.
G&PJ.
Games and Puzzles Journal. Successor to Chessics. Ran through 12
issues, Sep 1987 -- Dec 1989, then restarted intermittently in May 1996.
Haldeman-Julius. 1937.
E. Haldeman-Julius. Problems, Puzzles and Brain-teasers. HaldemanJulius Publications, Girard, Kansas, 1937. Facsimile (I believe) presented by Bob
Koeppel at IPP13, 1993.
Hall. BCB. 1957.
Trevor H. Hall. A Bibliography of Books on Conjuring in English from
1580 to 1850. (Carl Waring Jones, Minneapolis, 1957); Palmyra Press, Lepton,
W. Yorks., 1957. 323 entries. I will cite item numbers. A Supplement is in Hall, OCB.
See Heyl for a list of items not in BCB.
Hall. OCB. 1972.
Trevor H. Hall. Old Conjuring Books. Duckworth, London, 1972.
This covers books in English up through 1850 and it includes a Supplement to his BCB
and should be checked for further information on items in BCB. This contains 39 new
items and additional notes to 36 previous items. New items are given interpolated item
numbers, e.g. 24.5. OCB also includes a slightly revised version of his booklet on van
Etten, see Section 1 below.
Halwas.
Robin Halwas, Ltd. List XV. American Mathematical Textbooks
SOURCES - page 57
1760-1850. Catalogue of 511 items being sold as a collection. London, 1997, 144pp.
Quite a number of English works and a few French works had US editions which are
detailed in this.
Hanky Panky. 1872.
Hanky Panky A Book of Easy and Difficult Conjuring Tricks Edited
by W. H. Cremer, Jun. (John Camden Hotten, London, 1872 [BMC & Toole Stott 193,
listed under Cremer, while C&B, under Cremer, give London, 1872]; Hotten was
succeeded by Chatto & Windus c1873 and they produced several editions [NUC has
1872, Toole Stott 1017 & Shortz have 1875].) My copy says: A new edition with 250
practical illustrations. John Grant, Edinburgh, nd [Toole Stott 1016 gives 1874; NUC
gives 1875? Christopher 235, under Cremer, is c1890. NUC says it is also attributed to
Henry Llewellyn Williams, but their entry under Williams says 'supposed author'. C&B
also list it under Williams. (This has been attributed to Frikell, but Toole Stott doubts
that Frikell had anything to do with this. I may put this under Cremer.)
HB.XI.22. 1488.
Stuttgart Landesbibliothek German MS HB.XI.22, 1488. Brief
description by E. Rath; Über einen deutschen Algorismus aus dem Jahr 1488; Bibl.
Math. (3) 14 (1913-14) 244-248.
Heath, Sir Thomas L. See: Diophantos; HGM.
Heyl. 1963.
Edgar Heyl (1911-1993). A Contribution to Conjuring Bibliography.
English Language 1580 to 1850. Edgar Heyl conjuring books, Baltimore, 1963.
Facsimile edition of 100 copies by Maurizio Martino Fine Books, PO Box 373,
Mansfield Center, Connecticut, 06250, nd [1998?]. 360 entries + appendix of 14 more,
almost all not in Hall, BCB.
HGM. 1921.
Sir Thomas L. Heath. A History of Greek Mathematics, 2 vols. (OUP,
1921); corrected reprint, Dover, 1981.
HM.
Historia Mathematica.
Hoernle, A. F. Rudolf. See: Bakhshali MS.
Hoffmann. 1893.
Professor Louis Hoffmann [pseudonym of Angelo John Lewis
(1839-1919)]. Puzzles Old and New. Warne, London, 1893. Reprinted with Foreword
by L. E. Hordern; Martin Breese, London, 1988.
In 1984, Hordern published a limited edition (15 copies) of "The Hordern
Collection of Hoffmann Puzzles 1850-1920", which gives colour photos of examples
from his collection and the appropriate text. I often cite these pictures as they often
differ from those in the following item, with the heading Hordern Collection.
Generally, the next item gives more specific dating and/or older examples.
In 1993, Hordern produced a corrected edition of all of Hoffmann as: Hoffmann's
Puzzles Old & New; published by himself. This has colour photos of all puzzles for
which known examples exist. I will cite this as Hoffmann-Hordern. The 1893 edition
gives solutions for each chapter in a following chapter, but both of Hordern's illustrated
versions give each solution immediately after the problem, with colour picture nearby.
A small section on Elementary Properties of Numbers is omitted from the 1993 edition.
See also: Tom Tit.
Honeyman Collection.
The Honeyman Collection of Scientific Books and Manuscripts. Sold
by Sotheby's [Sotheby Parke Bernet], 1978-1981. Seven volumes -- details given in
Section 3.B.
Hordern, L. Edward (1941-2000). See under Hoffmann and in 5.A.
HPL.
The Harry Price Library, Senate House, University of London OR its
catalogues.
Harry Price (1881-1948). Short-Title Catalogue and Supplementary
Catalogue of Works on Psychical Research, Spiritualism, Magic, Psychology,
SOURCES - page 58
Legerdemain and Other Methods of Deception, Charlatanism, Witchcraft, and technical
Works for the Scientific Investigation of Alleged Abnormal Phenomena from Circa
1450 A.D. to 1935 A.D. Compiled by Harry Price. (The first part was originally ... to
1929 A. D.; Proc. National Lab. of Psychical Research 1:2 (1929); National Laboratory
of Psychical Research, London, 1929. The second part was originally: Short-Title
Catalogue of the Research Library, for 1472 A.D. to the Present Day; Bull. Univ. of
London Council for Psychical Investigation 1 (1935); Univ. of London Council for
Psychical Investigation, 1935.) New Introduction by R. W. Rieber and Andy
Whitehead With an appendix entitled "The St. Louis Magnet" (which originally
appeared in 1845) by T. J. McNair and J. F. Slafter. Da Capo Press (Plenum), NY,
1982. NOTE: The works listed here are now in the Harry Price Library, though the
editors have added 36 items in their Introduction.
Hummerston. Fun, Mirth & Mystery. 1924.
R. A. Hummerston. The Book of Fun, Mirth & Mystery A feast of
delightful entertainment, including games, tricks, puzzles and solutions, "how to
makes," and various other means of amusement. Pearson, London, 1924.
Hunt. 1631 & 1651.
Nich. Hunt. Newe Recreations or The Mindes release and solacing.
Aug. Math. for Luke Fawne, 1631.
Nich. Hunt. New Recreations or A Rare and Exquisite Invention. J. M.
for Luke Fawn, London, 1651. This edition contains a few more pages and several
problems of interest and is differently paginated. I will give both page numbers for
problems in both editions. Bill Kalush has sent both texts on a CD.
Hutton. A Course of Mathematics. 1798?
Charles Hutton (1737-1823). A Course of Mathematics. Composed for
the Use of the Royal Military Academy. (In 2 vols, plus a third, 1798-1811.) A New
Edition, entirely Remodelled. By William Ramsay, B. A., Trinity College, Cambridge.
T. T. & J. Tegg, London, and Richard Griffin & Co., Glasgow, 1833 (in one volume).
8 + 822 pp.
Hutton-Rutherford. A Course of Mathematics. 1841?
Charles Hutton. A Course of Mathematics, Composed for the Use of
The Royal Military Academy. By Charles Hutton, LL.D., F.R.S., Late Professor of
Mathematics in that Institution. A new and carefully corrected Edition, Entirely Remodelled, and Adapted to the Course of Instruction Now Pursued in the Royal Military
Academy. By William Rutherford, F.R.A.S. Royal Military Academy. William Tegg,
London, 1857 [Preface dated Nov 1840, so probably identical or nearly identical to the
1841 ed]. 8 + 895 pp.
[Two volume versions: 1798/1801; 3rd, 1800/1801; 4th, 1803/1804; 5th,
[1810, NUC gives 1806- and 1807]; 6th, [1810-1811 -- NUC]. Three volume versions
-- apparently the early forms were just the earlier 2 volumes with an additional third vol:
6th, 1811; 1813; 7th, 1819-1820; 8th, 1824; 9th, 1827/1828. 10th ed by Olinthus
Gregory, in 3 vols., 1827-1831. New ed by William Ramsay in one vol., 1833; 1838.
11th ed by Gregory in 2 vols, 1836-1837. 12th ed, revised by Thomas Stephens Davies,
2 vols., 1841-1843. Ed by William Rutherford in one vol, 1841; 1843; 1846; 1849;
1851; 1853; 1857; 1860.
This is a pretty straightforward text, but it well illustrates the situation in early
19C England, outside Oxford and Cambridge. Almost all the material of interest is in
the first two sections: Arithmetic and Algebra and is identical in these two editions. I
imagine most of these problems appeared in the first edition, so I will date this as
1798?, citing pages as 1833 and 1857. However the 1857 has an additional three pages
on Practical Questions in Arithmetic which has 44 problems, some of which are
recreational, and another new problem. Assuming the 1857 is essentially the same as
SOURCES - page 59
the 1841, I will cite this as 1841?.]
See also: Ozanam-Hutton.
H&S. 1927.
Vera Sanford. The History and Significance of Certain Standard
Problems in Algebra. (Teachers College, Columbia University, NY, Contributions to
Education, No. 251, 1927) = AMS Press, NY, 1972.
Illustrated Boy's Own Treasury. c1847.
The Illustrated Boy's Own Treasury of I. - Science, II. - Drawing, III. Painting, IV. - Constructive Wonders, V. - Rural Affairs, VI. - Wild and Domesticated
Animals, Outdoor Sports & Indoor Pastimes forming a Complete Repository of Home
Amusements & Healthful Recreations embellished with five hundred descriptive
engravings. (John & Robert Maxwell, London, c1847 [Toole Stott 407]). Ward and
Lock, 1860 [Toole Stott 1091]. (3rd ed, for the Proprietors, 1865? [Toole Stott 408].)
[Toole Stott's descriptions make it seem that these editions are identical.] See also:
Boy's Own Book, Boy's Own Conjuring Book. [Many of the problems are the same as
in the other two books, but the illustrations here occasionally omit some labels, so these
must be errors in copying from some earlier source. If the c1847 date is correct, then
this considerably changes the chronology of these problems, with this book being the
major known intermediate between Boy's Own Book and Magician's Own Book. I will
hold off making these changes until I see the c1847 ed -- this may take some time as the
BM copy was lost in the war and the other two copies cited are in the US. Hall, BCB
187 is: The Illustrated Boys' Own Treasury of Indoor Pastimes; Robson, London,
c1845. This may be related to this book.]
Indoor & Outdoor. c1859.
Indoor and Outdoor Games for Boys and Girls: Comprising Parlour
Pastimes, Charades, Riddles, Fireside Games, Chess, Draughts, &c, &c. With a Great
Variety of Athletic Sports, Parlour Magic, Exercises for Ingenuity, and Much That is
Curious, Entertaining, and Instructive. James Blackwood, London, nd [c1859]. This is
a combination of two earlier books, comprising two separately paginated parts. The
earlier books are Parlour Pastime (1857 -- qv) and Games for All Seasons [Toole Stott
311 & BMC give 1858]. There is a later version of the first part -- Parlour Pastimes, qv,
which the BMC dates as 1868. Also there is another version of the combined ed "with
additions by Oliver Optic", as Sports and Pastimes for Indoors and Out, G. W. Cottrell,
Boston, 1863 [Toole Stott 1186, which identifies Optic as William Taylor Adams].
Both BMC and NUC say Indoor & Outdoor is by George Frederick Pardon. Hence the
problems in the first part will be cited as: Parlour Pastime, 1857 = Indoor & Outdoor,
c1859, Part 1 = Parlour Pastimes, 1868. Many of the problems are identical to Book of
500 Puzzles.
IPPn
n-th International Puzzle Party. 10 = London, 1989;
13 = Amsterdam, 1993; 16 = Luxembourg, 1996; 19 = London, 1999;
20 = Los Angeles, 2000; 22 = Antwerp, 2002. This are the ones I have attended, but
some material has appeared at other IPPs.
Jackson. Rational Amusement. 1821.
John Jackson. Rational Amusement for Winter Evenings; or, A
Collection of above 200 Curious and Interesting Puzzles and Paradoxes relating to
Arithmetic, Geometry, Geography, &c. With Their Solutions, and Four Plates.
Designed Chiefly for Young Persons. By John Jackson, Private Teacher of the
Mathematics. London: Sold by J. and A. Arch, Cornhill; and by Barry & Son,
High-Street; and P. Rose; Bristol. 1821. [Other copies, apparently otherwise identical,
say: London: Sold by Longman, Hurst, Rees, Orme, and Brown; G. and W. B.
Whittaker; and Harvey and Darton. And Barry and Son, High-Street, Bristol. 1821.
SOURCES - page 60
[Heyl 185. Toole Stott 413.] Will Shortz says this is the first English-language book
devoted to non-word puzzles.]
JRM.
Journal of Recreational Mathematics.
Kanchusen. Wakoku Chiekurabe. 1727.
Tagaya Kanchusen [pseud. of Fuwa Senkuro]. Wakoku Chiekurabe
[Japanese Wisdom Competition -- in Japanese]. 2 vols, 1727, 12 & 29 pp.
PHOTOCOPY from Shigeo Takagi's copy sent by Naoaki Takashima. Edited into
modern Japanese, with commentary on Kanchusen, by Shigeo Takagi, 1991, 42pp,
present from Takagi. Translated into English by Hiroko Dean, 1999, 15pp plus
annotations on the 42pp. Takagi and Takashima are working on a translation and
annotation into modern Japanese. We intend to produce an English version from Dean's
translation with commentary on the puzzles. I will cite pages from Takagi's edition.
(Partly reproduced in Akira Hirayama; Tôzai Sûgaku Monogatari [Mathematical Stories
from East and West]; (1973), 3rd ed., 1981, p. 208, ??NYS, from which it has been
reproduced in the exhibition Horizons Mathématiques at La Villette, Paris, and
elsewhere.)
Kaye, George R. See: Bakhshali MS.
King. Best 100. 1927
Tom King. The Best 100 Puzzles. W. Foulsham, London, nd [1927,
according to BMC -- my copy says 'Wartime reprint'.] A selection of these are
reproduced in a booklet: Foulsham's Games and Puzzles Book; W. Foulsham, London,
nd [c1930]. I will indicate this by = Foulsham's, no. & pp.
Knott, Cargill G. See under: Tom Tit.
Labosne. See under: Problemes.
Ladies' Diary. See under: T. Leybourn.
Landells. Boy's Own Toy-Maker. 1859.
E[benezer] Landells. The Boy's Own Toy-Maker: A Practical
Illustrated Guide to the Useful Employment of Leisure Hours. Griffith & Farran,
London, 1859(1858); Shepard, Clark & Brown, Boston, 1859; Griffith & Farran, 3rd
ed., 1860; D. Appleton, NY, 1860; Griffith & Farran, 6th ed., 1863 [Toole Stott
1286-1290]. [BMC has 1859(1858) and a longer 10th ed, 1881. NUC has the latter
four of the versions given by Toole Stott.] [The Preface to the Second Edition,
reproduced in the 3rd ed., says it appeared just two months after the first edition. Toole
Stott indicates that all the versions he cites are identical. I have 3rd ed., 1860. Shortz
has Appleton, 1860.] The date 1859(1858) indicates that the book appeared in late
1858 to catch the Christmas trade, but was postdated 1859 to seem current for the whole
of 1859, so I will date this as 1858. The 2nd ed. must be 1859. Comparison shows that
the section on Practical Puzzles is essentially an exact subset of the material in Boy's
Own Conjuring Book.
Leeming. 1946.
Joseph Leeming. Fun with Puzzles. (Lippincott, Philadelphia, 1946);
Comet Books (Pocket Books), NY, 1949.
Lemon. 1890.
"Don Lemon" [= "The Sphinx" = Eli Lemon Sheldon], selector.
Everybody's Illustrated Book of Puzzles. Saxon & Co., London, 1890 (with 1891 on
the back cover) and 1892. The 1892 ed. omits the text on the back cover and adds some
pages of publisher's advertisements, but is otherwise identical. 794 problems, about
100 being mathematical, on 125pp. This looks like a UK reprint of a US book, but the
NUC only lists London editions, so perhaps it is just selected from US publications.
Some of the problems are attributed to Golden Days, Good Housekeeping, St. Nicholas,
etc.
I also have an undated edition which says 'Selected by the Sphinx'. This has 744
SOURCES - page 61
problems on 122pp, about 45% of which come from the other edition. The NUC dates
this as 1895. I will refer to this edition as: Sphinx. 1895.
Leopold. At Ease! 1943.
Jules Leopold. At Ease! Ill. by Warren King. Whittlesey House
(McGraw-Hill), 1943. [This appears to be largely drawn from Yank, The Army
Weekly, over the previous few years.]
Leske. Illustriertes Spielbuch für Mädchen. 1864?
Marie Leske. Illustriertes Spielbuch für Mädchen Unterhaltende und
anregende Belustigungen, Spiele and Beschäftigungen für Körper und Geist, im
Zimmer sowie im Freien. (1864; 19th ed., 1904); 20th ed., Otto Spamer, Leipzig,
1907. There is no indication of any updating in the Foreword to the 19th ed. which is
included here, and it was common to describe new printings as new editions, so I will
date this as 1864? This book is jammed with material of all sorts, including lots of
rebuses, riddles and puzzles. It is a bit like Boy's Own Book. My copy is lacking pp.
159-160 and 211-212.
Leurechon, Jean (c1591-1670). See: van Etten.
T. Leybourn.
Thomas Leybourn, ed. The Mathematical Questions, proposed in the
Ladies' Diary, and Their Original Answers, Together with some New Solutions, from its
commencement in the year 1704 to 1816. 4 vols., J. Mawman, London, and two copublishers, 1817. I have only examined vols. I & II so far. The problems are proposed
each year with solutions in the following year. Leybourn puts the solutions just after the
problem and numbers almost all the problems consecutively, though I don't know if
these numbers are in the Ladies' Diary. Problems do not have any names and
sometimes have pseudonyms or vague names, e.g. Mr. Deare. I will give the names of
the proposer and solver(s), followed by Ladies' Diary and the two years involved, then
= T. Leybourn, his volume and pages and his question number. E.g. Chr. Mason,
proposer; Rob. Fearnside, solver. Ladies' Diary, 1732-33 = T. Leybourn, I: 223, quest.
168.
W. Leybourn. Pleasure with Profit. 1694.
William Leybourn. Pleasure with Profit: Consisting of Recreations of
Divers Kinds, viz. Numerical, Geometrical, Mechanical, Statical, Astronomical,
Horometrical, Cryptographical, Magnetical, Automatical, Chymical, and Historical.
Published to Recreate Ingenious Spirits; and to induce them to make farther scrutiny
into these (and the like) Sublime Sciences. And To divert them from following such
Vices, to which Youth (in this age) are so much Inclin'd. To this work is also Annext,
A Treatise of Algebra, ..., by R. Sault. Richard Baldwin and John Dunton, London,
1694. The text consists of several parts, labelled Tract. I, Tract. II, ..., which are
separately paginated. All material is from Tract. I unless otherwise specified. Several
sections are taken from the English editions of van Etten. [Santi 371.]
Li & Du. 1987.
Li Yan & Du Shiran. Chinese Mathematics: A Concise History. (In
Chinese: Commercial Press, Hong Kong, c1965.) English translation by John Crossley
& Anthony W.-C. Lun. OUP, 1987.
Libbrecht. 1973.
Ulrich Libbrecht. Chinese Mathematics in the Thirteenth Century.
MIT Press, Cambridge, Mass., 1973.
Lilavati. 1150.
Lîlâvatî of Bhaskara II, 1150 (see Colebrooke).
Lloyd, E. Keith. See: BLW.
Loeb Classical Library.
Published by Harvard Univ. Press, or Putnam's, NY, & Heinemann,
London.
Loyd, Sam (1841-1911) (& Sam Loyd Jr. (1873-1934). See: Cyclopedia, MPSL, OPM,
SLAHP.
SOURCES - page 62
Lucas, Édouard (1842-1891). See: RM and the following.
Lucas. L'Arithmétique Amusante. 1895.
Édouard Lucas. L'Arithmétique Amusante. Ed. by H. Delannoy,
C.-A. Laisant & E. Lemoine. (Gauthier-Villars, Paris, 1895.) = Blanchard, Paris, 1974.
Lucca 1754. c1330.
Scuola Lucchese. Libro d'abaco. c1390. Dal Codice 1754 (sec. XIV)
della Biblioteca Statale di Lucca. Edited by Gino Arrighi. Cassa di Risparmio di
Lucca, 1973. Arrighi gives folio numbers and I will cite these and the pages of his
edition. Arrighi has c1390, but Van Egmond's Catalog 163-164 gives c1330.
MA.
Mathematical Association (UK).
MAA.
Mathematical Association of America.
Magician's Own Book. 1857.
The Magician's Own Book, or The Whole Art of Conjuring. Being a
Complete Hand-Book of Parlor Magic, and Containing over One Thousand Optical,
Chemical, Mechanical, Magnetical, and Magical Experiments, Amusing
Transmutations, Astonishing Sleights and Subtleties, Celebrated Card Deceptions,
Ingenious Tricks with Numbers, Curious and Entertaining Puzzles, Together with All
the Most Noted Tricks of Modern Performers. The Whole Illustrated with over 500
Wood Cuts, and Intended as a Source of Amusement for One Thousand and One
Evenings. Dick & Fitzgerald, NY, ©1857. 12 + 362 pp. + 10 pp. publisher's ads. My
thanks to Jerry Slocum for providing a copy of this. [Toole Stott 481 lists this as
anonymous and entirely different from the UK ed. He cites a 1910 letter from Harris B.
Dick who says H. L. Williams may have edited it, but both Dick's father and John
Wyman may also have had a hand in it. Toole Stott 929, 930, 1378, 931 lists Dick &
Fitzgerald, 1862, 1866, 1868, 1870, all apparently identical to the 1857. 929-930 are
listed under Arnold and he there cites Cushing's Anonyms as saying the book is by
Arnold and Cahill. Christopher 622-625 are all Dick & Fitzgerald; 622-623 are 1st ed.,
624-625 are reprints of about the same time and my copy seems most likely to be 625.
C&B, under Cremer, say "It is believed that they were all written by H. L. Williams, a
prolific hack writer of the period." Christopher 622 says Harold Adrian Smith [Dick
and Fitzgerald Publishers; Books at Brown 34 (1987) 108-114] has studied this book
and concludes that Williams was the author, assisted by Wyman. Actually Smith
simply asserts: "The book was undoubedly [sic] written by H. L. Williams, a "hack
writer" of the period, assisted by John Wyman in the technical details." He gives no
explanation for his assertion, but it may be based on C&B. NUC lists this as by George
Arnold (1834-1865) and Frank Cahill, under both Arnold and Cahill. C&B list it under
Cremer, attributed to Arnold & Cahill, but they give a date of 1851, which must be a
transcription error. C&B also list it under Magician's, from New York, 1857, and under
Williams, but as London, 1857.] See the discussion under Status of the Project in the
Introduction for the sources of the material.
Boy's Own Conjuring Book, qv, appears to be a UK pirate edition largely drawn
from this. Book of 500 Puzzles copies about 80 pages of this. See the comments under
Book of 500 Puzzles. A fair number of the problems are identical to or similar to the
Boy's Own Book and a woodcut, a poem and the introduction to a section are taken
directly from Boy's Own Book. Otherwise I had thought that this book was the source
for the spate of puzzle books in the following 15 years, but I have found that some of
the identical puzzles appeared in The Family Friend c1850.
Magician's Own Book (UK version). 1871.
This is quite different than the previous book.
The Magician's Own Book. By the Author of "The Secret Out," "The
Modern Conjuror," &c. Edited by W. H. Cremer, Jun. Containing Ample Instructions
SOURCES - page 63
for Recreations in Chemistry, Acoustics, Pneumatics, Legerdemain, Prestidigitation,
Electricity (with and without apparatus). (In the middle of the page is an illustration of
a wizard in white on red.) Performances with Cups and Balls, Eggs, Hats, Flowers,
Coin, Books, Cards, Keys, Rings, Birds, Boxes, Bottles, Handkerchiefs, Glasses, Dice,
Knives, &c., &c. With 200 Practical Illustrations. John Camden Hotten, nd [1871].
This has a two page list of Very Important New Books at the beginning on pp. i-ii. This
lists Magician's Own Book as by the Author of "The Secret Out" and The Secret Out as
by the Author of the "Magician's Own Book". But a further note says "Under the title of
"Le Magicien des Salons" the first has long been a standard Magic Book with all French
and German Professors of the Art." -- see the discussion under Status of the Project in
the Introduction, above. This list is followed by a half-title, p. iii, whose reverse (p. iv)
has the printer's colophon, then a blank page v, backed by a Frontispiece, p. vi,
comprising Figures 105 & 110 from the text. The TP is p. vii,, backed by a blank p.
viii. The Preliminary on pp. ix-x has the address Piccadilly at the end and states this is
"an Entirely New Edition" and is by the same author as The Secret Out. It refers to
Cremer's display of Toys of the World at the recent International Exhibition (possibly
the 1862??) and to [Frank Bellew's] "The Art of Amusing" (of 1866 and published by
Hotten in 1870) and Clara Bellew's "The Merry Circle". Contents are given on pp.
xi-xii and then the text on pp. 13-326. [Toole Stott 194 lists this under Cremer and says
there are 30pp of publisher's catalogue at the end, dated 1872 -- I didn't record these
details. Christopher 239 lists this as "An entirely new edition" with 200 illustrations,
325 pp. + 30 pp. publisher's ads.]
I have also seen a John Grant, Edinburgh, ed. which omits pp. i-vi, and has a
simplified title page, saying it is A New Edition, and drops the address Piccadilly.
Otherwise the text appears to be identical. It has no date but Toole Stott 1015 gives the
date 1871. C&B, under Cremer, have London, 1871 with no indication of the New
York ed. C&B also list it under Williams.
I have a Chatto & Windus ed., which omits pp. i-vi, and whose TP has only slight
changes from the Hotten TP, saying it is A New Edition, but the text appears to be
identical, except for dropping the address Piccadilly from the end of the Preliminary.
It is dated 1890, with separately paginated publisher's catalogue of 32pp. dated Apr
1893.
Mahavira. 850.
Mahāvīrā(cārya). Gaņita-sāra-sangraha [NOTE: ņ denotes an n with
a dot under it and ń denotes an n with a dot over it.] (= Gaņita-sāra-samgraha [The m
should have a dot over it.] = Ganitasar Samgrha). 850. Translated by M. Rańgācārya.
Government Press, Madras, 1912. The sections in this are verses. I will refer to the
integral part of the first verse of the problem. E.g. where he uses 121½ - 123, I will
use v. 121. [This work is described by David Eugene Smith; The Ganita-SaraSangraha of Mahāvīrācārya; Bibliotheca Mathematica (3) (1908/09) 106-110. In: [G.
R. Kaye; A brief bibliography of Hindu mathematics; J. Asiatic Society of Bengal
(NS) 7:10 (Nov 1911) 679-686], this work is cited as 1908 with the note: "This is really
an advance copy of a work not yet actually published, kindly supplied to me by the
author." See the entry under Pearson, 1907, in 7.E.]
Mair. 1765?.
John Mair. Arithmetic, Rational and Practical. Wherein The
Properties of Numbers are clearly pointed out, the Theory of the science deduced from
first principles, the methods of Operation demonstratively explained, and the whole
reduced to Practice in a great variety of useful Rules. Consisting of Three Parts, viz.
I. Vulgar Arithmetic. II. Decimal Arithmetic. III. Practical Arithmetic. A. Kincaid & J.
Bell, Edinburgh, in three vols, 1765-1766 (Turner G1.14/1-3); 2nd ed., A. Kincaid &
W. Creech, and J. Bell, Edinburgh, 1772; 3rd ed, John Bell and William Creech,
Edinburgh, 1777. I have the 3rd ed and have seen the 2nd ed. All the material of
SOURCES - page 64
interest is in part 3, which first appeared as vol. 3 in 1765 and books of this era often
had little or no change between editions, so I will date entries as 1765?
Manson. Indoor Amusements. 1911.
J. A. Manson, compiler. Indoor Amusements. Cassell & Co., London,
1911. FP + 8pp + 340pp + 8pp Index (341-348). This is an extension of Cassell's Book
of In-Door Amusements ..., expanding the earlier 209pp of main text to 340pp. This is
partly due to using larger type, getting 47 lines per page instead of 54. The material
which was in Cassell's is generally unchanged.
Manuel des Sorciers. 1825.
Manuel des Sorciers ou Cours de Récréations Physiques,
Mathématiques, Tours de Cartes et de Gibecière, suive Des Petits Jeux de Société, et de
Leurs Pénitences. (Conort, Paris, 178?; 2nd ed, Metier & Levacher, Paris, 1802
[Christopher 642, C&B]; 4th ed, Ferra Jeune, Paris, 1815 [C&B]; 5th ed, Ferra Jeune,
1820 [C&B]); 6th ed, Augmentée d'une Notice sur la Magie noire, Ferra Jeune, Paris,
1825 [Christopher 643, C&B, HPL]. There are a great many French books with similar
titles from this era. They seem to be the predecessors of Magician's Own Book, etc. -cf the discussion under Status of the Project in the Introduction and under Book of 500
Puzzles and Magician's Own Book. This is the first that I have found and examined
carefully, at HPL. It is likely that most of the material dates back to the first ed of 178?,
but until I see some earlier editions, I'll date it as 1825, Gaidoz, in Section 7.B, cites the
2nd ed, but the material is on a different page than in the 1825.
Marinoni, Augusto. See: Pacioli. De Viribus. c1500.
McKay. At Home Tonight. 1940.
Herbert McKay. At Home Tonight. OUP, 1940. Section V: Puzzles
and problems, pp. 63-88.
McKay. Party Night. 1940.
Herbert McKay. Party Night. OUP, 1940. Sections on Dinner-Table
Tricks, pp. 134-171; Some Tricks in English, pp. 174-175; Arithmetical Catches and
Puzzles, pp. 176-184.
Metrodorus.
c510. In: The Greek Anthology, W. R. Paton, trans. Loeb Classical
Library, 1916-1918. Vol. 5, Book 14. This contains 44 mathematical problems, most
of which are attributed to Metrodorus, though he is clearly simply a compiler and some
may be much older. I have cited the pages of the English translation -- the Greek is on
the previous page. Paton gives English answers, but they are not in the Greek.
The Greek Anthology is the modern name for a combination of two anthologies
which were based on earlier compilations dating back to the time of Alexander (-4C),
e.g. the Garlands of Meleager (c-95) and Philippus of Thessalonika (c40) and the Cycle
of Agathias (c570). In the late 9C or early 10C, Konstantinos Kephalas assembled these
into one collection, but distributed them according to type and then added several other
collections -- this was somewhat revised c980. In 1301, Maximus Planudes re-edited
Kephalas' anthology, omitting much and adding some (Paton believes that Planudes'
source was missing a book). The Planudean version replaced Kephalas's version and
was printed in 1484. However a copy of Kephalas's version of c980 was discovered at
Heidelberg in the Palatine Library (hence the anthology is sometimes described as
Palatine) in 1606 and modern versions now use this version as the first 15 books and
put all of Planudes' additions as Book 16, the Planudean Appendix. The Anthology
comprises some 4000 poems. Modern scholars view Paton as obsolete, but I don't
know of any later versions of the Anthology which include the mathematical problems - e.g. they are not even mentioned in Peter Jay; The Greek Anthology; Allen Lane,
1973; Penguin, 1981.
See also: David Singmaster; Puzzles from the Greek Anthology; Math.
Spectrum 17:1 (1984/85) 11-15 for a survey of these problems.
SOURCES - page 65
Meyer. Big Fun Book. 1940.
Jerome S. Meyer. The Big Fun Book. Greenberg : Publisher, NY,
1940.
MG.
Mathematical Gazette.
Mikami. 1913.
Yoshio Mikami. The Development of Mathematics in China and
Japan. Teubner, Leipzig, 1913; reprinted, Chelsea, 1961? See also: Smith & Mikami.
Minguet. 1733.
Pablo Minguet (or Minguét) è (or é or e or y) Yról (or Irol) ( -1801?).
Engaños à Ojos Vistas, y Diversion de Trabajos Mundanos, Fundada en Licitos Juegos
de Manos, que contiene todas las diferencias de los Cubiletes, y otras habilidades muy
curiosas, demostradas con diferentes Láminas, para que los pueda hacer facilmente
qualquier entretenido. Pedro Joseph Alonso y Padilla, Madrid, nd [1733]. Frontispiece
+ 12 + 218 pp. Imprimaturs or licenses dated 3 Nov 1733, 10 Nov 1733 & 12 Dec
1733. [NUC. Christopher 672 for a 18 + 110 pp version. C&B gives versions with 18
+ 110 pp and with 12 + 218 pp. HPL has 4 versions -- the one I examined was 12 + 218
pp. The BM has a version, but it is not clear which.]
The early history of this book is confused. The first edition may have only had 18
+ 110 pp (or 105 pp ??), then was apparently frequently reprinted, without changing the
dates, sometimes with additions. Or it may be that both versions appeared in 1733.
However, my copy is identical to one in HPL which is catalogued as 1733 and Palau (a
list of Spanish book sales, c1955) lists six sales of the 12 + 218 pp version, dated 1733,
and only one sale of the 18 + 110 pp version, dated 1733. Christopher dates the 12 +
218 pp versions to c1760.
I now have discovered 26 editions of this work, and 2 and 9 editions of two
derivative works, but I have only seen a few versions. If anyone has access to a copy, I
would like a photocopy of the TP and other publishing details and of the Indice.
3rd ed, Domingo Fernandez de Arrojo, Madrid, 1755, 18 + 157 + 3 pp. [This
includes the same material as 1733, but it is reset with smaller type and much
rearranged and includes some new material. It seems to be the same as the 1766. Palau
gives this as 18 + 150 + 10 pp and says there was a cheap edition of 14 + 171 + 10 pp.
NUC gives 14 + 171 +11 pp, with publisher Domingo Fernandez. HPL has two
'entirely different' editions of 1755 -- the one I examined was 18 + 157 + 3 pp. BM has
a 1755, but it is not clear which.]
3rd ed, Dionisio Hernández, Madrid, 1755? [Palau, with nd.]
Antonio del Valle, Madrid, 1756. 171 + 20 (or 40??) pp. [Palau.]
Revised. Pedro J. Alfonso y Padilla, Madrid, c1760, 14 + 218 pp. [Christopher
673 & 674.]
Idem. Añadido en esta quarta impresion, 18 enigmas, 6 quisicosas muy curiosas.
4th ptg, D. Gabriel Ramirez, Madrid, 1766, 16 + 150 + 10 pp. [BM; Palau;
Christopher 675.]
Palau says he has seen a catalogue with a 1793 ed, but thinks this is a printing
error for either 1733 or 1893.
Palau lists an 1804 reprint of the 1733, 14 + 218 pp.
Sierra y Martí, Barcelona, 1820, 1 + 224 pp. [Identical to 1733, 12 + 218 pp,
except the text has been reset, spelling modernized, the front matter updated and the
text starts on p. 10, with everything the same as the 1733, except page numbers are
increased by 9, and the index is reduced in size. HPL; Palau; Christopher 676.]
Neuva Edicion corregida y aumentada por D. J. M. de L. Juan Francisco Piferrer,
Barcelona, 1822, 1 + 224 pp. [This is quite differently arranged than the 1733, 12 + 218
pp, and 1820 eds, and contains some extra material. Palau, with 1 + 240 pp; NUC;
Shortz; Christopher 677.].
Retitled: Juegos de Manos ó sea Arte de Hacer Diabluras, y Juegos de Prendas.
SOURCES - page 66
Que contiene varias demonstraciones de mágia, fantasmagoria, sombras y otros
entretenimientos de diversion para tertulias y sociedades caseras. ilustrado con láminas
Por D. Pablo Minguet, y aumentado considerablemente en esta nueva edicion con
infinidad de juegos nuevos, y con laminas intercaladas en el texto. D. Manuel Saurí,
Barcelona, 1847, 189 + 10 pp. [Palau; Christopher 678.]
Juegos de manos; ó sea, Arte de hacer diabluras ...ilustrado con 60 grabados....
New ed. Simon Blanquet, Mexico, nd [1856]. 7 + 498 pp. [NUC.]
Palau cites an 1857 reprint of the 1847, presumably the 2nd Saurí ed..
Title varied: Juegos de Manos ó sea Arte de Hacer Diabluras. Contiene: juegos
de prendas, de naipes, varias demonstraciones de majia, fantasmagoria, sombras y otros
entretenimientos de diversion, para tertulias y sociedades caseras. Por D. Pablo
Minguet. Tercera Edicion Aumentada con gran número de Juegos nuevos, y grabados
intercalados en el texto. Manuel Saurí, Barcelona, 1864. 1 + 213 pp. [From TP of
1993 facsimile. This omits one problem and some discussion that was in 1733 and adds
22 new problems, but I see some of these already appeared in 1755 and 1822. Palau,
noting that this is the 3rd ed from Saurí and mentioning a recent facsimile; HPL.]
Palau cites an 1875 Barcelona reprint as 185pp, but has no publisher's name,
probably the 4th Saurí ed.
Title varied: Juegos de manos; ó sea, El arte de hacer diabluras, contiene 150
clases de juegos, de prendas, de naipes, varias demonstraciones de mágia,
fantasmagoria, sombras y otros entretenimientos de diversion, para tertulias y
sociedades caseras. 5. ed., aumentada con gran numero de juegos nuevos y 70 grabados
intercalados en el texto. Manuel Saurí, Barcelona, 1876. 192pp. [NUC.]
Palau confusingly cites Sauri reprints of 192pp: 8th ed, 1885; 8th ed, 1888; 9th
ed, 1888. [Christopher 679 & 680 are the latter two. Perhaps there is an error in the
dates, e.g. the 1885 might really be the 7th ed.]
Title varied: Juegos de Manos o sea Arte de hacer Diabluras, contiene 150 clases
de juegos, de prendas de naipes, varias demonstraciones de magia, fantasmagorias,
sombras y otros entretenimientos de mucha diversion, para tertulias y sociedades
caseras. Décima edición aumentada con juegos nuevos, y 70 grabados intercalados en
el texto. Juan Tarroll y Cla., Barcelona, 1893. 192pp. [Palau.]
Palau lists 11th ed [from Sauri]. Sauri y Sabater, Barcelona, 1896. 192pp.
[NUC lists 2 copies of the 11th ed as Sauri y Sabater, 1897, 192pp & 189pp.]
12th ed [from Sauri]. Sauri, Barcelona, 1906. 190pp. [Christopher II 2102.
HPL with nd.]
Facsimile of the 1864 ed, with Presentación por Joan Brossa: De la brujería
blanca. Editorial Alta Fulla, Barcelona, 1981. 11pp new material + II-VIII + 9-213 pp
of facsimile (II is FP; III is TP; V-VIII is Al Lector; 9-12 is a poetic introductory
Relacion; 203-213 is Indice).
2nd ed (i.e. printing) of the 1981 facsimile of the 1864 ed, with a new cover,
1993. [DBS.]
Pp. 1-25 is a fairly direct translation of the 1723/1725 Ozanam, vol. IV,
pp. 393-406. A number of other pictures and texts also are taken from Ozanam. I will
give the date as 1733, though the expansion may not have occurred until c1755. I will
cite the 1755, 1822 and 1864 pages in parentheses, e.g. Pp. 158-159 (1755: 114-115;
1822: 175-176; 1864: 151).
MiS.
Mathematics in School.
Mittenzwey. 1880.
Louis Mittenzwey. Mathematische Kurzweil. Julius Klinkhardt,
Leipzig. 1880; 2nd ed., 1883; 3rd ed., 1895; 4th ed., 1904; 5th ed., 1907; 6th ed.,
1912; 7th ed., 1918. I will give the date as 1880 or 1895? I now have copies of the 1st,
4th, 5th and 7th eds. In working through the other editions, I have seen many more
SOURCES - page 67
items than I had previously recorded and I now think this is one of the most important
19C puzzle books.
[Ahrens, MUS #363 lists the first ed. being 1879, apparently taking the date of
the Foreword. He also has 3rd ed., 1903, but V&T (and another reference) cite 3rd ed.,
1895. I think this is a misinterpretation of the last Vorrede in the 4th ed., which is for
the 3rd and 4th ed. and dated 1903. Trey Kazee has obtained a copy of the 2nd ed. The
first two editions have the author's given name and have 300 problems; the 4th, 5th and
7th have 333. The Vorrede to the 2nd ed in the 2nd ed. says it has no major changes.
The Vorrede to the 3rd & 4th eds in the 4th ed says the 3rd ed was extended and the 4th
ed. has replaced some problems, so it seems that the 3rd probably had 333 problems.
Compared to the 1st ed, the 4th drops 9 problems and adds 42. The Vorrede to the 3rd,
4th and 5th eds in the 5th ed also says some problems have been replaced, but I have
not discovered any differences between the 4th and 5th eds except one minor
amendment, some resetting which changes the page breaks on pp. 1-10 and 36-37 and a
few line breaks. I suspect that the 4th and 5th eds are very similar to the 3rd. The 5th
and 7th eds. are very similar, but the 7th is reset with smaller type and occupies five
fewer pages. There are a few amendments and reorderings and four problems (36, 92,
122, 137) have been replaced, but a number of simple misprints persist through all
editions. I will give pages in 1st, 3rd?, and 7th eds, e.g. Prob. 193 & 194, pp. 36 & 89;
1895?: 218 & 219, pp. 41 & 91; 1917: 218 & 219, pp. 37 & 87.]
MM.
Mathematics Magazine.
Montucla, Jean Étienne (1725-1799). See: Ozanam; Ozanam-Montucla.
MP. 1926.
H. E. Dudeney. Modern Puzzles. C. Arthur Pearson, London, 1926;
new ed., nd [1936?]. (Almost all of this is in 536.)
MPSL1. 1959 & MPSL2. 1960.
Mathematical Puzzles of Sam Loyd, vol. 1 & 2, ed. by Martin Gardner,
Dover, 1959, 1960. (These contain about 2/3 of the mathematical problems in the
Cyclopedia, often with additional material by Gardner.)
MRE.
W. W. Rouse Ball (1850-1925). Mathematical Recreations and Essays.
(First three editions titled Mathematical Recreations and Problems of Past and Present
Times.) I have compiled an 8 page detailed comparison of the contents of all editions
as part of my The Bibliography of Some Recreational Mathematics Books.
1st ed., Feb 1892, 240pp.
2nd ed., May 1892 ('No material changes').
3rd ed., 1896, 276pp.
4th ed., 1905, 388pp. [In the 4th ed., it says 'First Edition, Feb. 1892. Reprinted,
May 1892. Second Edition, 1896. Reprinted, 1905.' However, it calls itself the 4th ed.
and the 3rd ed. calls itself 3rd and there are substantial changes in the 4th ed.]
5th ed., 1911, 492pp.
6th ed., 1914, 492pp.
7th ed., 1917, 492pp.
8th ed., 1919, 492pp.
9th ed., 1920, 492pp.
10th ed., 1922, 366pp.
11th ed., 1939, revised by H. S. M. Coxeter, 418pp.
Macmillan (for 1st to 11th ed.).
12th ed., 1974, revised by H. S. M. Coxeter, 428pp, U. of Toronto Press.
13th ed., 1987, revised by H. S. M. Coxeter, 428pp, Dover.
A few of the editions are actually reprintings of the previous edition: 2 is essentially the
same as 1, 6 as 5, 9 as 8, 13 as 12. Consequently I will rarely, if ever, cite
editions 2, 6, 9, 13. For each topic occurring in Ball, I have examined all the
editions, so the absence of a reference indicates the topic does not occur in that
SOURCES - page 68
edition -- unless it is buried in some highly unlikely place.
See also: Ball-FitzPatrick.
MS.
Mathematical Spectrum (Sheffield, UK).
MTg.
Mathematics Teaching (UK).
MTr.
Mathematics Teacher (US).
Munich 14684. 14C.
Munich Codex Lat. 14684. 14C. Ff. 30-33. Published by M. Curtze;
Mathematisch-historische Miscellan: 6 -- Arithmetische Scherzaufgaben aus dem 14
Jahrhundert; Bibliotheca Math. (2) 9 (1895) 77-88. 34 problems. Curtze gives brief
notes in German. Curtze says these problems also appear in Codex Amplonianus
Qu. 345, ff. 16-16', c1325, ??NYS. Munich 14684 comes from the same monastery (St.
Emmeran) as AR and AR incorporates much of it. In a later paper, Curtze says this is
13C -- ??NYR. Cf Folkerts, Aufgabensammlungen.
Murray. 1913.
Harold James Ruthven Murray. A History of Chess. (OUP, 1913);
reprinted by Benjamin Press, Northampton, Massachusetts, nd [c1986].
MUS. 1910 & 1918.
Wilhelm Ernst Martin Georg Ahrens (1872-1927). Mathematische
Unterhaltungen und Spiele. 2nd ed., 2 vols., 1910, 1918, Teubner, Leipzig. [The first
ed. was 1901 in one volume. There is a 3rd ed. of Vol 1, 1921, but it is a reprint of the
2nd ed. with just 2 pages of extra notes and the typographical corrections made.] I will
tend to cite this, as e.g. MUS 1 153-155. MUS #n denotes item n in the substantial
Literarischer Index, MUS 2 375-431.
[MUS II vii lists 22 items which he had been unable to see and which he
suspected might not exist. I have seen the following items from the list: 86 (= Les
Amusemens, above), 102 (Hooper, listed in Some Other Recurring References, below;
cf Section 4.A.1), 145 (Jackson, see above), 212 (author's name is Horatio Nelson
Robinson); item 32 exists as an English edition of van Etten, but the citation gives the
publisher as though he was the author; I have seen a copy of item 82 advertised for
sale. A number of items (135, 152, 164, 221, 223, 277, 297, 317) are cited by Wölffing
- op. cit. in Section 3.B.]
Muscarello. 1478.
Pietro Paolo Muscarello. Algorismus. MS of 1478. Published in 2
vols.: I -- facsimile; II -- transcription with notes and commentaries; Banca
Commerciale Italiana, Milan, 1972. I will cite the folios (given in vol. I) and the pages
of the transcribed version in vol. II. Van Egmond's Catalog 275-276.
M500.
This is the actual name of the journal of the M500 Society, the Open
University student mathematics society.
NCTM.
National Council of Teachers of Mathematics.
nd.
no date. Estimated dates may follow in [ ].
Needham. 1958.
Joseph Needham (1900-1995). Science and Civilization in China,
Vol. 3. CUP, 1958. (Occasional references may be made to other volumes:
Vol. 2, 1956; Vol. 5, Part IV, 1980.)
The New Sphinx. c1840.
Anonymous. The New Sphinx An elegant Collection of upwards of
500 Enigmas Charades Rebusses Logogriphes Anagrams Conundrums &c. &c. To
which are added, a Number of Ingenious Problems. T. Tegg & Son, London, nd, HB
with folding frontispiece. [Vendor suggests it is 1840s. Shortz has 4th ed, by Gye &
Baine and says it is c1840. He also has 'a new(?) edition', by T. Tegg, and says it is
c1843. He says the chapter of geometrical problems and brainteasers was new in the
4th ed. Heyl 238 is a 7th ed., London, 18??, referring to HPL, where I find it in the
Supplement.] The chapter of problems has 27 problems, of which 21 are copied from
SOURCES - page 69
Endless Amusement II, 1837 ed., 20 of which come from the 1826? ed.
E. P. Northrop. Riddles in Mathematics. 1944.
Eugene P. Northrop. Riddles in Mathematics. Van Nostrand, 1944;
English Universities Press, 1945; revised ed., Penguin, 1961. The Van Nostrand ed has
the main text on pp. 1-262. The EUP ed. has it on pp. 1-242. The Penguin ed. has it on
pp. 11-240. The revision seems to consist of only a few additional notes. I will cite the
dates and pages, e.g. 1944: 209-211 & 239; 1945: 195-197 & 222; 1961: 197-198 &
222.
H. D. Northrop. Popular Pastimes. 1901.
Henry Davenport Northrop. Popular Pastimes for Amusement and
Instruction being a Standard Work on Games, Plays, Magic and Natural Phenomena
Suitable for All Occasions containing Parlor Games; Charming Tableaux; Tricks of
Magic; Charades and Conundrums; Curious Puzzles; Phrenology and Mind Reading;
Palmistry, or How to Read the Hand; Humorous and Pathetic Recitations, Dialogues,
Etc., Etc. including The Delightful Art of Entertaining The Whole Forming a
Charming Treasury of Pastimes for the Home, Public Schools and Academies, Lodges,
Social Gatherings, Sunday Schools, Etc., Etc. Frank S. Brant, Philadelphia, 1901.
[Not in any of my bibliographies. Vendor says only two copies in NUC, none in BL.]
NUC.
National Union Catalogue Pre-1956 Imprints. Library of Congress,
USA. c1960. ??check details
Nuts to Crack.
Nuts to Crack, Part nn. Or, Enigmatical Repository; containing near
mmm Hieroglyphics, Enigmas, Conundrums, Curious Puzzles, and Other Ingenious
Devices. R. Macdonald, 30 Great Sutton Street, Clerkenwell, London. These are single
broadsheets. The publisher's details are often trimmed from the bottom of the sheet. At
least 25 annual parts appeared, from Part I of 1832, but the year is not always given.
Answer books -- The Nutcrackers -- also appeared and the publishers kept the old sheets
available for some years. This series is very rare -- Will Shortz and James Dalgety have
the only examples known to me. I have photocopy of almost all from Dalgety and
Shortz, ??NYR. mmm is either 250 or 200 and the problems are individually numbered
in each part. I will cite problems as, e.g. Nuts to Crack I (1832), no. 200.
NX.
No copy. Usually prefixed by ?? as a flag for further action.
NYR.
Not yet read -- i.e. I have a copy which I have not yet studied. Usually
prefixed by ?? as a flag for further action.
NYS.
Not yet seen. Usually prefixed by ?? as a flag for further action.
OCB. See: Hall, OCB.
OED.
Oxford English Dictionary. (As: New English Dictionary, OUP,
1884-1928), reprinted with supplements, OUP, 1933 and in various formats since.
o/o.
On order.
OPM. 1907-1908.
Our Puzzle Magazine. Produced by Sam Loyd. The pages were
unnumbered. The Magazine was reprinted as the Cyclopedia as follows, but some
pages of the Magazine were omitted and the answers to each magazine were normally
in the next one.
Vol. 1, No. 1 (Jun 1907) = Cyclopedia pp. 7-70.
Vol. 1, No. 2 (Oct 1907) = Cyclopedia pp. 71-121.
Vol. 1, No. 3 (Jan 1908) = Cyclopedia pp. 122-178.
Vol. 1, No. 4 (Apr 1908) = Cyclopedia pp. 179-234.
Since the Cyclopedia goes to p. 339, there appear to have been two further
issues which have not been seen by anyone??
(The above data were provided by Jerry Slocum.)
OUP.
Oxford University Press.
SOURCES - page 70
Ozanam. 1694.
The bibliography of this book is a little complicated. I have prepared a
more detailed 7 pp. version covering the 19 (or 20) French and 10 English editions,
from 1694 to 1854, as well as 15 related versions -- as part of my The Bibliography of
Some Recreational Mathematics Books.
Jacques Ozanam (1640-1717). Recreations Mathematiques et
Physiques, qui contiennent Plusieurs Problémes [sic] utiles & agreables,
d'Arithmetique, de Geometrie, d'Optique, de Gnomonique, de Cosmographie, de
Mecanique, de Pyrotechnie, & de Physique. Avec un Traité nouveau des Horloges
Elementaires. 2 vols., Jombert, Paris, 1694, ??NYS. [Title taken from my 1696 ed.]
[BNC. NUC -- but NUC lists a 1693 3rd ed. from Amsterdam, which appears to
be a misreading for 1698. MUS II 380 says 1st ed. was Récréations Mathématiques,
Paris, 1694, 2 vols. Serge Plantureux's 1993 catalogue describes a 1694 edition in
2 vols., by Jombert and notes that it is the original edition, that the privilege is dated
11 Jan 1692, but that it was not printed until 30 Apr 1694. The dating of the privilege
may account for some references to the first edition being 1692 -- e.g. the Preface to the
1778 Ozanam-Montucla ed. says the first ed. was 1692, but Hutton changes this to
1694. MRE, 1st ed, 1892, pp. 3-4, says the the 1st ed. was 2 volumes, Amsterdam,
1696, but this was amended in his 4th ed., 1905.
This first appeared in two volumes, but later versions were sometimes in one
volume. I have references to versions in Paris: 1694, 1696, 1697, 1698, possibly 1700?
and apparently 1720; and in Amsterdam: 1696, 1697, 1698, 1700. There is no
indication of any textual changes in these, except that the pages are numbered
consecutively in later versions. Plantureaux describes a 1696 edition as: Paris, Jombert
(mais Hollande), so there seems to have been some piracy going on. I have the 1696 ed.
I will assume that the 1696 is essentially identical in content to the 1694, though in the
second volume, the page numbers may be different and there is some confusion of plate
numbering.
The Traité des Horologes élémentaires, which appears in the 1694 ed., is a
translation of Domenico Martinelli's Horologi elementari. NUC says this was
separately paginated in 1694, but it occupies pp. 473-583 of the 1696 ed and pp. 301482 of vol. 3 of the 1725 ed.]
About 1723, the work was revised into 4 vols., sometimes described as 3 vols.
and a supplement. MUS #52 gives 1720, 1723, 1724, 1725 and says the dates vary in
the literature. The 1725 has privilege dated 1720, but I haven't found any catalogue
entry for a 1720 ed. of this revision, so it may be a spurious date based on the privilege.
Nouv. ed.
Recreations Mathematiques et Physiques, qui contiennent Plusieurs Problêmes
[sic] d'Arithmétique, de Géométrie, de Musique, d'Optique, de Gnomonique, de
Cosmographie, de Mécanique, de Pyrotechnie, & de Physique. Avec un Traité des
Horloges Elementaires. Par feu [misprinted Parfeu in vol. 1] M. Ozanam, de
l'Académie Royale des Sciences, & Professeur en Mathematique. Nouvelle edition,
Revûë, corrigée & augmentée.
Vol. 4 has different title page.
Recreations Mathematiques et Physiques, ou l'on traite Des Phosphores Naturels
& Artificiels, & des Lampes Perpetuelles. Dissertation Physique & Chimique. Avec
l'Explication des Tours de Gibeciere, de Gobelets, & autres récréatifs & divertissans.
Nouvelle edition, Revûë, corrigée & augmentée.
Claude Jombert, Paris, 1723. [Taken from my 1725 ed.]
[Ball and Glaisher [op. cit. in 7.P.5, p. 119] both cite a 1723 ed. as though they
SOURCES - page 71
had seen it, but there is no BMC entry for this date -- perhaps there is a copy at
Cambridge??. I have seen one volume in an exhibition which was 1723. MUS #52
says it was edited by Grandin. NUC -- "The editor is said to be one Grandin." I have a
brief 1899 reference to this ed.
I have 1725, which is apparently a reprint of the 1723. The privilege/approbation
is dated 16 May 1722 in Vol. 3 and Vol. 4 and also 28 Apr and 15 May 1720 in Vol. 3.
NUC says this is 1723 with new title pages. BNC has: Nouvelle édition ... augmentée
[par Grandin], 4 vols, Paris, 1725. It was reprinted in 1735, 1737?, 1741, 1750/1749,
1770.
The text and plates of the 1725 and 1735 eds. seem identical, though some of the
accessory material -- lists of corrections and of plates -- has been omitted and other has
been rearranged. I have seen two versions of the 1735 -- one has the plates inserted in
the text, the other has them at the end as ordinary pages, while my 1725 has them at the
end on folding pages. Most of the 1725 plates are identical to the 1696 plates, but there
were a number of additions and reorderings. The 1725 plates have their 1696 plate
numbers and 1725 page references at the top with new, more sequential, plate numbers
at the bottom. The 1725 text sidenotes refer to the plate numbers at the top, while the
1735 and later sidenotes refer to the bottom numbers. (However some of the new
illustrations in vol. 4 are not described in the text and this makes me wonder if there
was an earlier version with these new plates??) I will give the 1725 top plate numbers,
followed by the bottom numbers in ( ) -- e.g. plate 12 (14). The 1741 and the
1750/1749 eds. are essentially identical to the 1735 ed.
Ball, MRE, and MUS #52 say the 1750 and/or the 1770 ed. were revised by
Montucla, but all other sources say his revision was 1778. Indeed Montucla was only
25 in 1750. Inspection of 1750 copies in the Turner Collection and at the Institute für
Geschichte der Naturwissenschaft shows the 1750 is identical to my 1725 ed. except for
some accents and a new publisher.]
English versions
Recreations Mathematical and Physical; Laying down, and Solving Many
Profitable and Delightful Problems of Arithmetick, Geometry, Opticks, Gnomonicks,
Cosmography, Mechanicks, Physicks, and Pyrotechny. By Monsieur Ozanam,
Professor of the Mathematicks at Paris. Done into English, and illustrated with very
Many cuts. R. Bonwick, et al., London, 1708.
[Pp. 130-191 are omitted, but there is no gap in the text and the Contents also
shows these pages are lacking. Ball, MRE. BMC. NUC. Hall, OCB, p. 165. Hall,
BCB 216. UCL. Toole Stott 520, noting the gap. Bodleian. This is a pretty direct
translation of the 1696 French ed. or an early simple revision. Prob. 18-20 of
Cosmographie have been omitted. C&B list this and say there were three later editions,
though they then list the 1756 and 1790 editions.]
2nd ed.
Recreations for gentlemen and ladies: or, Ingenious Amusements. Being
Curious and diverting sports and pastimes, natural and artificial. With Many
Inventions, pleasant Tricks on the Cards and Dice, Experiments, artificial Fireworks,
and other Curiosities, affording variety of entertainments. James Hoey, Dublin, 1756.
[Taken from Toole Stott entry.]
[NUC. Hall, BCB 212. Hall, OCB, p. 165, but giving the 1790 title. Toole Stott
518, but he has Hoez, which seems to be either a misreading or a miswriting??]
3rd ed.
Recreations for Gentlemen and Ladies; being Ingenious Sports and Pastimes.
Containing Many curious Inventions, pleasant Tricks on Cards and Dice; Arithmetical
Sports; new Games; Rules for Assuredly winning at all Games, whether of Cards or
Dice; Recreative Fire-works; Tricks to promote Diversion in Company, and other
SOURCES - page 72
Curiosities.... James Hoey, Dublin, 1759. [Taken from Hall, BCB 213.]
[Ball, MRE. Hall, BCB 213. Hall, OCB, p. 165. Bodleian.]
4th ed.
Recreations for gentlemen and ladies; being ingenious sports and pastimes:
containing Many curious Inventions, pleasant Tricks on Cards and Dice; Arithmetical
Sports; new Games; Rules for Assuredly winning at all Games, whether of Cards or
Dice; Recreative Fire-works; Tricks to promote Diversion in Company, and other
Curiosities.... The fourth edition. Peter Hoey, Dublin, 1790. [Taken from Toole Stott
entry.]
[BMC calls it the 4th ed. [abridged]. NUC. Hall, BCB 214. Hall, OCB, p. 165.
Toole Stott 519. Bodleian.]
I will cite these and the following editions by date, though the varying problem
numbers and volume numbers will make this a bit unwieldy. All references to the 4
volume versions are to vol. I unless specified otherwise. See the entry in 4.A.1 as an
example. Note that I give the problem number first because this is usually the same in
the 1790, 1803 and 1814 editions, and often in the 1840. Figure numbers will also been
given with the problem number, although the 1840 has the figures in the text with
different numbers. Additions will be entered at the relevant point.
Ozanam-Hutton. 1803.
Recreations in Mathematics and Natural Philosophy: ... first composed
by M. Ozanam, of the Royal Academy of Sciences, &c. Lately recomposed, and greatly
enlarged, in a new Edition, by the celebrated M. Montucla. And now translated into
English, and improved with many Additions and Observations, by Charles Hutton, ....
4 vols., T. Davison for G. Kearsley, London, 1803.
[This is a pretty direct translation of the 1790 Ozanam-Montucla ed. with a few
changes, and some notes and extra material, generally in sections which do not interest
us. Only one or two plates have been changed. Erroneous problem numbers have been
retained.
There was an 1814 ed. by Longman, Hurst, Rees, Orme and Brown, London. The
texts are basically identical, but the 1814 has been reset to occupy about 15% fewer
pages, the problem numbers have been corrected, a few corrections/additions have been
made and the plates do not fold out.]
Ozanam-Montucla. 1778.
J. E. Montucla (1725-1799)'s revision of Ozanam.
Récréations Mathématiques et Physiques, Qui contiennent les Problêmes & les
Questions les plus remarquables, & les plus propres à piquer la curiosité, tant des
Mathématiques que de la Physique; le tout traité d'une maniere à la portée des Lecteurs
qui ont seulement quelques connoissances légeres de ces Sciences. Par feu M. Ozanam,
de l'Académie royale des Sciences, &c. Nouvelle Edition, totalement refondue &
considérablement augmentée par M. de C. G. F. Claude Antoine Jombert, fils aîné,
Paris, 1778, 4 vols. Approbation & privilege dated 5 Aug 1775 & 4 Sep 1775.
[BMC says this is "par M. de C. G. F. [i.e. M. de Chanla, géomètre forézien,
pseudonym of J. E. Montucla.]" BMC, under Montucla, says M. de Chanla is a
pseudonym of Montucla. BNC, under Montucla, describes Montucla as Éd. Lucas,
RM1, p. 242 lists this under Chaula "attribué à Montucla". MUS #52 has Chaula. NUC
has Chanla. Montucla's connection with the book was so little known that the 1778
version was sent to him in his role as Mathematical Censor and he made some additions
to it before approving it. Hutton says the 'last edition' (presumably 1790) bears
Montucla's initials. 'Forézien' means from Feurs or the Forez region. Reprinted in
1785-1786 and 1790 (see below).
This is a considerable reworking of the earlier versions. In particular, the
SOURCES - page 73
interesting material on conjuring and mechanical puzzles in Vol. IV has been omitted.
There are occasional misnumberings of problems. I recall the plates are folding at the
end of each volume, but I didn't note this specifically.]
Nouv. ed.
"Nouvelle édition, totalement refondue et considérablement augmentée par M. de
M***" [BMC adds: [i.e. Jean Étienne Montucla]]. Firmin Didot, Paris, 1790.
[NUC lists this as a reissue of 1778 with new TPs. I have this ed.]
Ozanam-Riddle. 1840.
(Edward Riddle (1788-1854)'s revision of Ozanam-Hutton.)
Recreations in mathematics and natural philosophy: translated from Montucla's
edition of Ozanam, by Charles Hutton, LL.D. F.R.S. &c. A new and revised edition,
with numerous additions, and illustrated with upwards of four hundred woodcuts, By
Edward Riddle, Master of the Mathematical School, Royal Hospital, Greenwich.
Thomas Tegg, London, 1840. [Taken from my copy. MUS #130 asserts this is by a C.
Biddle, but this must be due to be a misreading or misprint.]
Another ed.
Recreations in science and natural philosophy: Dr. Hutton's translation of
Montucla's edition of Ozanam. The present new edition of this celebrated work is
revised By Edward Riddle, Master of the Mathematical School, Royal Hospital,
Greenwich, who has corrected it to the present era, and made numerous additions. This
Edition is also Illustrated by upwards of Four Hundred Woodcuts. Thomas Tegg,
London, 1844.
Another ed.
Recreations in Science and Natural Philosophy. Dr. Hutton's translation of
Montucla's edition of Ozanam. New Edition, revised and corrected, with numerous
additions, by Edward Riddle, Master of the Mathematical School, Royal Hospital,
Greenwich. Illustrated by upwards of Four Hundred Woodcuts. William Tegg,
London, 1851.
[Reprinted by William Tegg, 1854.]
All the Riddle printings seem to be from the same plates -- the date of the
Prefatory Note and the Erratum given on p. xiv are the same in 1840 and 1851. Marcia
Ascher cites an 1844 edition from Nuttall & Hodgson, but this is the printer.
These have the figures in the text, but otherwise seem to be little different than
Ozanam-Hutton. I will generally cite it just as 1840.
P. M. Calandri. See: Benedetto da Firenze.
Pacioli. De Viribus. c1500.
Luca Pacioli (or Paciuolo) (c1445-1517). De Viribus Quantitatis.
c1500. Italian MS in Codex 250, Biblioteca Universitaria di Bologna. Santi 3 dates it
as 1498 and describes the later parts which deal with riddles, etc., but include some
magic, etc. However, Pacioli petitioned for a privilege to print this in 1508 and Part 2,
Chap. CXXIX, ff 228r-228v, has a date of 1509, so he may have been working on the
MS for many years. Van Egmond's Catalog 55-56 is not as helpful as usual.
Part 1: Delle forze numerali cioe di Arithmetica is described in: A. Agostini; Il
"De viribus quantitatis" di Luca Pacioli; Periodico di Matematiche (4) 4 (1924) 165-192
(also separately published with pp. 1-28). Agostini's descriptions are sometimes quite
brief -- unless one knows the problem already, it is often difficult to figure out what is
intended. Further, he sometimes gives only one case from Pacioli, while Pacioli does
the general situation and all the cases. All references are to the problem numbers in this
part, unless specified otherwise. I will use problem numbers and names as in the MS at
the problem -- these often differ considerably from the numbers and names given in the
SOURCES - page 74
index at the beginning of the MS. There are 81 problems in part 1, but the Index lists
120 -- in a few cases, the Index name clearly indicates a problem similar to an actual
problem and I will mention this. There are microfilms at the Warburg Institute
(currently misplaced) and at Munich and Siena. I printed Part 1 and some other relevant
material from the Warburg microfilm, some 125pp. When I read this, I saw that the
material near the last pages I had copied would be of interest, but when I went back to
copy this material, the microfilm had been misplaced.
Dario Uri has photographed the entire MS and enhanced the images and put them
all on a CD. This has 614 images, including the insides of the covers. This is often
more legible than the microfilm, but the folio numbers are often faint, sometimes
illegible. It was not until the transcription (below) became available that I could read
the material just after this point and see that there were more interesting problems, but I
found it difficult to read the Italian (many words are run together and/or archaic) and the
diagrams referred to are lacking. Dario was able to carry on and found the Chinese
Rings and about a dozen other interesting items. He has put some material up on his
website: http://digilander.libero.it/maior2000/. This includes the indexes and a number
of the most interesting items, with his comments and diagrams of later examples of the
puzzles. I have now gone through all of the text and found a number of problems of
interest for this bibliography. Nonetheless, quite a number of problems, some clearly of
interest, remain obscure.
Transcription by Maria Garlaschi Peirani, with Preface and editing by Augusto
Marinoni. Ente Raccolta Vinciana, Milano, 1997. (The publisher did not reply to a
letter, but Bill Kalush kindly obtained a copy for me. Dario Uri says it can be bought
from: Libreria Pecorini, 48 foro Buonaparte, Milano; tel: 02 8646 0660;
fax: 02 7200 1462; web: www.pecorini.com.) I will cite the text as Peirani and any
references to Marinoni's work as Marinoni. The transcription is not exactly literal in
that Peirani has expanded abbreviations and inserted punctuation, etc. Also, Peirani
seems to have worked from the microfilm or a poor copy as she sometimes says the
manuscript has an incorrect form which she corrects, but Dario Uri's version clearly
shows the MS has the correct form. Peirani uses the problem numbers and names in the
MS (see comment above about these differing from those in the Index), but with some
amendments. I will probably give problem names as in the MS, with some of Peirani's
amendments. I will give translations of the names, but some of them are pretty
uncertain and some have defeated me completely. Marinoni, pp. VIII-IX indicates the
MS was written in about 1496-1509.
The title is a bit cryptic, but I think the best English version is: On the Powers of
Numbers, but Pacioli [f. Ir] has 'forze numerali' and R. E. Taylor [op. cit. in Section 1,
pp. 307 & 339] follows Agostini and uses: On the Forces of Quantity.
Pacioli. Summa. 1494.
Luca Pacioli (or Paciuolo or Paccioli) (??-c1509). Sūma de
Arithmetica Geometria Proportioni & Proportionalita. Paganino de Paganini, Venice,
1494 -- cf Van Egmond's Catalog 325-326; facsimile printed by Istituto Poligrafico e
Zecca dello Stato, Rome, for Fondazione Piero della Francesca, Comune di
Sansepolcro, 1994, with descriptive booklet edited by Enrico Giusti. There was a
second ed., Paganino de Paganinis, Toscolano, 1523, but the main text seems identical,
except for corrections (and errors) and somewhat different usage of initial letters and
colour. For extensive studies of this book, see the works by Narducci, Taylor, Davis
and Rankin given in Section 1. Davis identifies material taken from Piero della
Francesca's works. Taylor says 99 copies of the 1494 and 36 copies of the 1523 are
known. The text is in two parts -- the second part is geometry and is separately paged.
All page references will be to the first part unless specified as Part II. Problems are
numbered at the right hand edge of the last line of the previous problem. See Rara 54-
SOURCES - page 75
59.
Davis notes that Pacioli's Summa, Part II, ff. 68v - 73v, prob. 1-56, are essentially
identical to della Francesca's Trattato, ff. 105r - 120r.
Panckoucke, André Joseph (1700-1753). See: Les Amusemens.
Pardon, George Frederick (1824-1884). See: Indoor & Outdoor; Parlour Pastime; Parlour
Pastimes.
Parlour Pastime. 1857.
Parlour Pastime for the Young: Consisting of Pantomime and Dialogue
Charades, Fire-side Games, Riddles, Enigmas, Charades, Conundrums, Arithmetical
and Mechanical Puzzles, Parlour Magic, etc. etc. Edited by Uncle George [NUC says
this is George Frederick Pardon]. James Blackwood, London, 1857 [Toole Stott 545;
Christopher 724]. This was combined with Games for All Seasons [Toole Stott 311;
Christopher 723] into Indoor & Outdoor, c1859, qv. There is a later edition, Parlour
Pastimes, 1868, qv. Hence the problems will be cited as: Parlour Pastime, 1857 =
Indoor & Outdoor, c1859, Part 1 = Parlour Pastimes, 1868. Many of the problems are
identical to Book of 500 Puzzles.
Parlour Pastimes. 1868?
Parlour Pastimes: A Repertoire of Acting Charades, Fire-side Games
Enigmas, Riddles, Charades, Conundrums, Arithmetical and Mechanical Puzzles,
Parlour Magic, etc., etc. James Blackwood, London, nd. [BMC, NUC and Toole Stott
1136 date this 1868 and say it is by George Frederick Pardon. Toole Stott 1136
indicates that By G. F. P. is on the TP, but it is not in my example. Toole Stott 1137 is
1870, a slightly smaller ed.] It is an expanded version of Parlour Pastime, with the
material of interest to us being directly copied, though the page layout varies slightly.
The running head of this is actually Parlour Pastime. Hence the problems will be cited
as: Parlour Pastime, 1857 = Indoor & Outdoor, c1859, Part 1 = Parlour Pastimes,
1868. Many of the problems are identical to Book of 500 Puzzles.
PCP. 1932.
H. E. Dudeney. Puzzles and Curious Problems. Nelson, 1932; revised
ed., nd [1936?]. (Almost all of this is in 536.) There are almost no changes in the
revised ed., except that problem 175 and its solution have been corrected -- it is a cross
number puzzle and the text was for a different diagram. See: 7.AM.
Peano. Giochi. 1924.
Giuseppe Peano (1858-1932). Giochi di Aritmetica e Problemi
Interessanti. G. B. Paravia, Torino, nd [1924 and later reprints]. (Thanks to Luigi Pepe
for a photocopy of this.)
Pearson. 1907.
A. Cyril Pearson. The Twentieth Century Standard Puzzle Book.
Routledge, London, nd [1907]. Three parts in one volume, separately paginated. The
parts were also published separately. Each part has several numbered sequences of
problems.
Peck & Snyder. 1886.
Price List of Out & Indoor Sports & Pastimes. Peck & Snyder,
126-130 Nassau Street, N. Y., 1886. Reprinted, with some explanatory material, in the
American Historical Catalogue Collection, Pyne Press, Princeton, 1971. Unpaginated -I have numbered the pages starting with 1 as the original cover.
Peirani, Maria Garlaschi. See: Pacioli. De Viribus. c1500.
Perelman. FFF. 1934.
Yakov Isidorovich Perelman [ Я . И . П е р е л м а н ] (1882-1942).
Figures for Fun. Ж и в а я М а т е м а т и к а [Zhivaya Matematika], Н а у к а [Nauka],
Moscow. The books give no indication of the original dates, but Tatiana Matveeva has
kindly searched the Russian State Library and found it was originally published by
Г о с . т е х н . - т е о р . и з д а т ., Leningrad-Moscow, 1934. Schaaf I 9 cites
Recreational Arithmetic, 6th ed., Leningrad, 1935 and Sphinx 5 (1935) 96 reviews the
SOURCES - page 76
5th ed. of L'Arithmétique Récréative, Leningrad, 1934 -- both presumably the same
book ??
Translated by G. Ivanov-Mumjiev. Foreign Languages Publishing House,
Moscow, 1957, 120 sections.
(2nd ed., 1973 -- used for MCBF, below, apparently the same as the 3rd ed.)
Translated by G. Ivanov-Mumjiev. 3rd ed., MIR, 1979, 123 sections. The 3rd
ed. drops 3 sections and adds 6 sections and has some amended English.
Perelman. FMP. 1984.
Yakov Isidorovich Perelman [Я . И . П е р е л м а н ]. Fun with Maths and
Physics. MIR, Moscow, 1984. [This is a translation of З а н и м а т е л ь н ы и З а д а ч и
и О ы т ы [Zanimatel'nye Zadachi i Oryty], Д е т с к а я Л и т е р а т у р ы [Detskaya
Literatura], Moscow.) (There was a З а н и м а т е л ь н ы и З а д а ч и , with 4th ed. in
1935 – no earlier version in Russian State Library. This title originally published by
Д е т т и з , 1959.) Compiled by I. I. Pruskov. Translated by Alexander Repyev. This is
a compilation from several of his books from 1913 to c1942 (when he died). I have not
yet seen the earlier books (??NYS), but if this is mainly based on the earlier book of the
similar title, this would date the material to c1935? and I will use this date.
Perelman. MCBF. c1980?
Yakov Isidorovich Perelman [Я . И . П е р е л м а н ]. Mathematics Can
Be Fun. 3rd ed., MIR, 1985. This consists of the following, originally separate, works,
but with the second part having its page and problem numbers continued from the first
part. Both these works exist in many other editions and translations.
Figures for Fun, translated from Живая Математика [Zhivaya Matematika],
Наука [Nauka], Moscow, translated 1973 -- with 123 sections. Translator not specified,
but presumably G. Ivanov-Mumjiev, as in FFF above.
Algebra Can be Fun, translated from Занимательная А л г е б р а
[Zanimatel'naya Algebra] (3rd ed. was published by О Н Т И , Leningrad-Moscow,
1937 -- The Russian State Library apparently has no earlier edition), edited and
supplemented by V. Boltyansky, Н а у к а [Nauka], Moscow, 1976, translated by G.
Yankovsky, 1976.
References to this will be to material not in FFF, so will be dated 1937.
Phillips, Hubert (1891-1964). See: Brush; Week-End.
Pike. Arithmetic. 1788.
Nicolas Pike (1743-1819). A New and Complete System of
Arithmetic, composed for the Use of the Citizens of the United States. John Mycall,
Newbury-Port, Massachusetts, 1788. (I have a 2nd ed., 1797, [Halwas 318], ??NYR.
This went through at least 5 editions and then at least six variants, often abridged for
schools [Halwas 318-326].)
Poggendorff.
J. C. Poggendorff. Biographisch-Literarisches Handwörterbuch zur
Geschichte der Exacten Wissenschaften enthaltend Nachweisungen über
Lebensverhältnisse und Leistungen von Mathematikern, Astronomen, Physikern,
Chemikern, Mineralogen, Geologen usw aller Völker und Zeiten. Johann Ambrosius
Barth, Leipzig. Facsimile by Maurizio Martino, Storrs-Mansfield (later Mansfield
Center), Connecticut.
Vols. I (A - L) and II (M - Z). (1863), nd [bought in 1996].
Vol. III (1858-1883), edited by B. W. Feddersen & A. J. von Oettingen;
Parts I (A - L) and II (M - Z). (1898), nd [bought in 1998].
Vol. IV (1883-1904), edited by Arthur von Oettingen;
Parts I (A - L) and II (M - Z). (1904), nd [bought in 1998].
[Vol. V covers 1904-1922. Vol. VI covers 1922-1949. One can get I-VI on
microfiche. Vol. VIIa covers 1932-1953 and apparently comprises 5 volumes. There is
also a VIIa Supplement which gives material supplementary to vols. I-VI.]
SOURCES - page 77
Prévost. Clever and Pleasant Inventions. (1584), 1998.
J. Prévost. (La Première Partie des Subtiles et Plaisantes Inventions,
Contenant Plusieurs Jeux de Récréation. Antoine Bastide, Lyons, 1584. ??NYS.)
Translated by Sharon King as: Clever and Pleasant Inventions Part One Containing
Numerous Games of Recreations and Feats of Agility, by Which One May Discover the
Trickery of Jugglers and Charlatans. Hermetic Press, Seattle, 1998. [No Second Part
ever appeared. Hall, OCB, pp. 43, 100 & 113.] This is apparently the first book
primarily devoted to conjuring. Only five copies of the original are known. There was
a facsimile in 1987. My thanks to Bill Kalush for bringing this work to my attention.
Price, Harry (1881-1948). See: HPL.
Problemes. 1612.
Claude-Gaspar Bachet (c1587-1638). Problèmes plaisans &
délectables qui se font par les nombres. (1st ed., 1612); 2nd ed., 1624, P. Rigaud, Lyon
(for 1 & 2 ed.); revised by A. Labosne, (3rd ed., 1874; 4th ed., 1879); 5th ed., 1884,
Gauthier-Villars, Paris (for 3, 4, 5 ed.).) 5th ed. reprinted by Blanchard, Paris, 1959 et
al., with a Frontispiece portrait and an introduction by J. Itard, based on the article by
Collet and Itard cited in 1 below.
I have now obtained a photocopy of the 2nd ed. and have examined a 1st ed. I
had believed that Bachet added 10 problems in the 2nd ed., but the additional section of
10 problems, beginning "S'Ensuivent quelques autres ..." is already in the 1612 1st ed.
In the 1612, there are two problems V, but in 1624, these are made into two parts of
prob. V. However, he does extend the initial section of 22 problems to 25 problems,
inserting the new material as problems 3, 16 and 21. Prob. 16 (1612) = 18 (1624) has
additional material. Also, Bachet greatly expands his preliminary material on the
properties of numbers from 14 to 52 pages, but Labosne drops this. Otherwise, the
material seems identical and the main text seems pretty much identical with the fifth
edition except that orthography is modernised -- e.g. plaisans becomes plaisants, mesme
becomes même, luy becomes lui, etc. I have now compared the 3rd ed with the 5th ed
and I could find no differences between them -- though I didn't check every word.
Labosne adds a Supplement of 15 problems, four Notes and a table of contents.
Labosne's Préface given in the 5th ed. is for the 3rd ed. I will cite problem numbers and
pages from the 1st ed., 1612; 2nd ed., 1624 and the 5th ed., 1884 (1959 reprint), e.g.
Prob. XIX, 1612, 99-103. Prob. XXII, 1624: 170-173; 1884: 115-117. I will generally
not give problem titles as they usually run to several lines. I will denote Labosne's
supplementary problems as Bachet-Labosne, 1874.
I have seen a 4th ed. by Gauthier-Villars, 1905, no editor named, containing only
37 of the 50 problems in the 5th ed. A contemporary review by E. Lampe (Fortschritte
der Math. 36 (1905) 300-301) was also mystified by this edition. C&B list this ed.
Pŗthudakasvâmî or Pŗthūdaka. See: Chaturveda.
Pseudo-dell'Abbaco. c1440.
This is attributed to Paolo dell'Abbaco (sometimes called Dagomari)
(c1281-1367). Trattato d'Aritmetica. (c1370, according to Arrighi, but see below).
Codex Magliabechiano XI, 86 at Biblioteca Nazionale di Firenze. Edited by Gino
Arrighi, Domus Galilaeana, Pisa, 1964. Arrighi gives some black & white
reproductions of illustrations. I examined this MS in Sep 1994 and found the
illustrations are often lightly coloured and that Arrighi's illustrations were probably
made from poorish photocopies -- the writing on the opposite side shows through much
more in several of his illustrations than it does in the originals. I have colour slides of
11 pages.
Warren Van Egmond [New light on Paolo dell'Abbaco; Annali dell'Istituto e
Museo di Storia della Scienza di Firenze 2:2 (1977) 3-21 and Van Egmond's Catalog
114-115] asserts this MS is a c1440 compilation, based on watermark evidence, and
SOURCES - page 78
doubts that it is due to dell'Abbaco, giving the author as pseudo-dell'Abbaco.
Smith, Rara, 435-440 describes a different MS at Columbia, headed 'Trattato
d'Abbaco, d'Astronomia e di segreti naturali e medicinali', which he dates c1339. Van
Egmond, above, gives the title of this as 'Trattato di tutta l'arte dell'abacho', but Van
Egmond's Catalog 254-255 describes it as Plimpton 167, a codex containing two works.
The first is the dell'Abbaco: Trattato di tutta l'arte dell'abacho; the second is Rinaldo da
Villanova: Medichamento Generale, which has the title Trattato d'Abbaco,
d'Astronomia e di segreti naturali e medicinali added in a later hand. The first includes
the Regoluzze which is sometimes cited separately. This is quite a different book than
the c1440 Trattato. There is a c1513 version at Bologna, MS B 2433, which is dated
1339 -- Dario Uri has sent a CD of images of it. See the entry for dell'Abbaco in 7.E.
Putnam. Puzzle Fun. 1978.
Graham R. Putnam, ed. Puzzle Fun. Fun Incorporated, np [Chicago?],
1978.
Rara. 1970.
David Eugene Smith. Rara Arithmetica. (1908; with some addenda,
1910; Addenda, 1939, published both separately and with the 1910 ed.); 4th ed.,
combining the original with both Addenda and with De Morgan's Arithmetical Books of
1847 and a new combined index, Chelsea, 1970. References are to the main entry of
this. Check the index for references to the Addenda and to De Morgan.
Rational Recreations. 1824.
Rational Recreations. Midsummer MDCCCXXIV. Knight and Lacey,
London. This is a six part work, but is bound together -- perhaps the parts were issued
monthly. The parts are consecutively paginated. [Toole Stott 590. Toole Stott 591 is
2nd ed, 1825 and 592 is 3rd ed, 1825, copublished in Dublin. Hall BCB 235, 236 are
1824 and 1825. C&B. HPL. Not in Christopher. I have examined the BL copy.]
Recorde. First Part. 1543.
Recorde. Second Part. 1552.
Recorde-Mellis. Third Part. 1582.
Recorde (or Record), Robert (1510?-1558). The Grounde of Artes
Teaching the worke and practice of Arithmetike. .... The dating of this book is
uncertain. Smith, Rara, p. 526 records a 1540 edition. An edition by Reynold Wolff,
London, at the Bodleian (Douce R.301) has generally been dated as 1542 and there is a
facsimile by Theatrum Orbis Terrarum, Amsterdam & Da Capo Press, NY, 1969,
with the date 1542. There were reprints in 1543 and 1549. However, the DSB entry for
Recorde ignores the Smith 1540 edition (presumably because it has not been confirmed)
and says the 1542 is now dated as 1550?, making the 1543 the first edition. This
edition only contained material on whole numbers.
In 1552, Recorde added a Second Part dealing with fractions, so the earlier
material will be called the First Part.
At some stage, John Dee augmented it, but it appears he simply made some
revisions and additions to the existing text without adding new topics. The Dee
material was added in 1590 (Smith) or 1573 (De Morgan).
In 1582, John Mellis added a Third Part, mostly on rules of calculation, published
by J. Harison & H. Bynneman, London.
By 1640, the title was changed to: Record's Arithmetick, or, The Ground of Arts;
Teaching The perfect Work and Practice of ARITHMETICK, both in whole Numbers
and Fractions, after a more easie and exact form then in former time hath been set forth.
Afterwards augmented by Mr. JOHN DEE. And since enlarged with a third part of
RULES of PRACTICE, abridged into a briefer method then hitherto ..., by JOHN
MELLIS.
By 1648, more material was added by Robert Hartwell. I have a 1668 edition
SOURCES - page 79
which has a little more material by Thomas Willsford, but these latter two extensions
are of no interest to us. It is clear that the text was increased by accretion, with only
minor revisions of Recorde's text, which is generally preserved in gothic (= black-letter)
type, and this is indicated by Smith. So the presence of a problem in Part One or Part
Two or Part Three of the 1668 ed almost certainly indicates its presence in the first
version of these parts. This is certainly true for Part One, as I have the facsimile to
compare, and it is confirmed by brief examination of a 1582 ed, though at the time, I
was looking at Part Three and did not know of the material in Part Two. I will cite the
pages from my 1662 ed and the side notes which are titles of the problems, and pages of
any earlier editions that I have seen.
Riccardi.
Pietro Riccardi. Biblioteca Matematica Italiana dalla Origine della
Stampa ai Primi Anni del Secolo XIX. G. G. Görlich, Milan, 1952, 2 vols. This work
appeared in several parts and supplements in the late 19C and early 20C, mostly
published by the Società Tipografica Modense, Modena, 1878-1893. For details, see in
Section 3.B.
Riddle, Edward (1788-1854). See: Ozanam-Riddle.
The Riddler. See under Boy's Own Book.
Riese. Coss. 1524.
Adam Riese (c1489-1559). Die Coss. German MS of 1524 found at
Marienberg in 1855. Described and abstracted in Programm der Progymnasial- und
Realschulanstalt zu Annaberg 1860. Reprinted in 1892. My reference to this comes
from Johannes Lehmann; Rechnen und Raten; Volk und Wissen, Berlin (DDR), 1987,
pp. 7-14, esp. p. 13. I have since seen the Glaisher paper, op. cit. in 7.G.1 under
Widman, esp. p. 37. Glaisher and Lehmann cite: Bruno Berlet; Adam Riese, sein Leben
und seine Art zu rechnen; Die Coss von Adam Riese; Leipzig & Frankfurt, 1892.
Glaisher notes that this was a pamphlet. BLLD provided a copy from Biblioth. Regia
Berolinen. G., but it was lacking a title page. It seems to have the title: Zur Feier des
vierhundertsten Geburtsjahres von Adam Riese. It was printed by Königl.
Universitätsdruckerei von H. Stürtz in Würzburg. The Vorwort is dated 1892, but only
signed 'Der Verfasser' and his name does not appear anywhere except on the spine of
the library's cover. The booklet has two parts.
Adam Riese, sein Leben, seine Rechenbücher und seine Art zu rechnen (from the
Programm for 1855), pp. 1-26. This is a discussion of Riese's Rechnung, but it also
mentions some material from his 'grosse Rechenbuch' titled Rechenung nach der lenge,
auf den Linihen und Feder, written in 1525 but not published until 1550. Glaisher, loc.
cit., p. 43, says he sees no authority for the date of 1525 and assumes it was written
c1550. (I have recently obtained a 1976 reprint of this work, ??NYR)
Die Coss von Adam Riese (with Abdruck der Coss) (from the Programm for
1860), pp. 27-62. This gives many numbered problems -- I will cite the problem
number and pages from this.
There is a recent facsimile of the MS which I have just received -- ??NYR.
Riese. Rechnung. 1522.
Adam Riese (c1489-1559). Rechnung auff der Linien unnd Federn ...
Erfurt, 1522. I have two reprinted editions. See Rara 138-143.
Christian Egenolph, Frankfurt, 1544. (Riese's text is dated 1525. There is a
supplement on gauging by Erhard Helm, dated 1544.) Facsimile by Th. Schäfer,
Hannover, 1978.
Christian Egenolff's Erben, Frankfurt, 1574. (Riese's text is dated 1525 and
appears to be the same text as above, but reset. The Supplement has further material.)
Facsimile by Th. Schäfer, Hannover, 1987.
Ripley's Puzzles and Games. 1966.
Ripley's Believe It or Not! Puzzles and Games. Essandess Special
SOURCES - page 80
Edition (Simon & Schuster), New York, 1966. Much of the material occurred in the
various Ripley's Believe it or Not! books. Most of the material is well known, but there
are a number of unusual variations and some interesting incomplete assertions and
mistakes!
RM.
(François-) Édouard (-Anatole) Lucas (1842-1891). Récréations
mathématiques. (Gauthier-Villars, Paris, 4 vols, 1882, 1883, 1893, 1894, 2nd eds. of
vol. 1, 1891, vol. 2, 1893) = Blanchard, Paris, (1960), 1975-1977, using 2nd ed. of vol.
1 and 1st ed. of vol. 2 (however, there seem to be very few differences in the editions).
I will cite the Blanchard reprint volumes as RM1, etc. (Dates are as given in Harkin,
op. cit. in 1 below, and on the books, but I have seen other dates cited.)
Lucas; L'Arithmétique Amusante, 1895, Note IV, pp. 210-260 gives various
fragments of material for further volumes which were found after Lucas's untimely
death. His draft Tables of Contents for volumes 5 and 6 are given on p. 210, but no
material exists for most of the chapters.
RMM.
Recreational Mathematics Magazine. Nos. 1 - 14 (Feb 1961 - Jan/Feb
1964). Quite a bit of the material in this was abstracted and sometimes extended in:
Joseph S. Madachy; Mathematics on Vacation; Scribner's, NY, 1966; somewhat
corrected as: Madachy's Mathematical Recreations; Dover, 1979.
Rocha. Libro Dabaco. 1541. SEE: Tagliente. Libro de Abaco. (1515). 1541.
Rohrbough. Lynn Rohrbough edited a series of 20 booklets, called Handy Series, Kits A-J and
M-V, for Cooperative Recreation Service, Delaware, Ohio, during at least 1925-1941.
Most of these were reprinted and revised several times. Two of these are of especial
interest to us and are listed below. Several others are cited a few times.
Rohrbough. Brain Resters and Testers. c1935.
Lynn Rohrbough, ed. Brain Resters and Testers. Handy Series, Kit M,
Cooperative Recreation Service, Delaware, Ohio, nd [c1935].
Rohrbough. Puzzle Craft. 1932.
Lynn Rohrbough, ed. Puzzle Craft Plans for Making and Solving 40
Puzzles in Wire, Wood and String. Handy Series, Kit U, Cooperative Recreation
Service, Delaware, Ohio, (1930), 1932.
I have another version of this, unfortunately undated, but apparently later, so I
have dated it as 1940s? Jerry Slocum located this by tracking down Rohrbough's
successors. The 1932 version has 39 puzzles in its index, but 4 more that were not
indexed and some Notes which are listed in the index of this version, making 44 items
in all. 13 items are omitted and replaced by 5 in the present version, giving 36 indexed
items. The outside of the back cover of the 1932 version shows a number of puzzles,
including several not described in either version of the booklet.
Rudin. 1936.
Jacob Philip Rudin. So You Like Puzzles! Frederick A. Stokes Co.,
NY, 1936.
SA.
Scientific American, usually Martin Gardner's Mathematical Games
column. For years from at least 1950, SA appeared in two volumes per year, each of six
issues. In year 1950 + n, vol. 182 + 2n covers Jan-Jun and vol. 183 + 2n covers
Jul-Dec. See also under Gardner.
Sanford. 1930.
Vera Sanford. A Short History of Mathematics. Houghton Mifflin,
Boston, 1930 & 1958. See also: H&S.
Santi. 1952.
Aldo Santi. Bibliografia della Enigmistica. Sansoni Antiquariato,
Florence, 1952. 2541 entries, often citing several editions and versions, arranged
chronologically from 1479 onward. My thanks to Dario Uri for providing this. I will
site item numbers. I have only entered part of the information so far.
de Savigny. Livre des Écoliers. 1846.
M. l'Abbé de Savigny. Le Livre des Écoliers Illustré de 400 vignettes.
SOURCES - page 81
Jeux. -- Récréations. Exercises. -- Arts utiles et d'agrément. Amusements de la science.
Gustave Havard, Paris, nd [dealer has written in 1846], HB. [This is almost entirely
the same as Boy's Own Book, 1843 (Paris). Each has a few sections the other does not.
de Savigny's illustrations seem to have been copied by a new hand, generally
simplifying a little. Many of the copies have been done in reverse and this leads to one
erroneous chessboard. However, there is one diagram in Boy's Own Book, 1843
(Paris), which looks like it was badly copied, so it is possible that both these books are
based on an earlier book.]
Schaaf. 1955-1978.
William L. Schaaf. A Bibliography of Recreational Mathematics.
Vol. 1, (1955, 1958, 1963); 4th ed., 1970. Vol. 2, 1970. Vol. 3, 1973. Vol. 4, 1978.
National Council of Teachers of Mathematics, Washington, DC. See Schaaf &
Singmaster in Section 3.B for a Supplement to these.
Schott. 1674.
Gaspare Schott. Cursus Mathematicus. Joannis Arnoldi Cholini,
Frankfurt, 1674. The material of interest is in Liber II, Caput VI: De Arithmetica
Divinatoria, pp. 57-60, and in Liber XXVI: Algebra, Pars III: De Exercitatione
Algebraicam, Caput I, II, IV, VI, pp. 551-563, and Pars V: Exercitationes Algebraicae,
pp. 570-571.
Schwenter. 1636.
Daniel Schwenter (1585-1636). Deliciæ Physico-Mathematicae. Oder
Mathemat- und Philosophische Erquickstunden, Darinnen Sechshundert Drey und
Sechsig, Schöne, Liebliche und Annehmliche Kunststücklein, Auffgaben und Fragen,
auf; der Rechenkunst, Landtmessen, Perspectiv, Naturkündigung und andern
Wissenschafften genomēn, begriffen seindt, Wiesolche uf der andern seiten dieses blats
ordentlich nacheinander verzeichnet worden: Allen Kunstliebenden zu Ehren, Nutz,
Ergössung des Gemüths und sonderbahren Wolgefallen am tag gegeben Durch M.
Danielem Schwenterum. Jeremiæ Dümlers, Nuremberg, 1636. [Note: the text is in
elaborate Gothic type with additional curlicues so that it is not always easy to tell what
letter is intended!] Probably edited for the press by Georg Philip Harsdörffer.
Extended to three volumes by Harsdörffer in 1651 & 1653, with vol. 1 being a
reprint of the 1636 vol. Vol. 2 & 3 have titles as follows.
Delitiæ Mathematicæ et Physicæ Der Mathematischen und Philosophischen
Erquickstunden Zweiter Theil: Bestehend in Fünffhundert nutzlichen und lustigen
Kunstfragen / nachsinnigen Aufgaben / und derselben grundrichtigen Erklärungen /
Auss Athanasio Kirchero Petro Bettino, Marion Mersennio, Renato des Cartes, Orontio
Fineo, Marino Gethaldo, Cornelio Drebbelio, Alexandron Tassoni, Sanctorio Sanctorii,
Marco Marco, und vielen anderen Mathematicis und Physicis zusammen getragen durch
Georg Philip Harsdörffern. Jeremia Dümlern, Nürnberg, 1651.
Delitiæ Philosophicæ et Mathematicæ Der Philosophischen und Mathematischen
Erquickstunden / Dritter Theil: Bestehend in Fünffhundert nutzlichen und lustigen
Kunstfragen / und derselben gründlichen Erklärung: Mit vielen nothwendigen Figuren /
so wol in Kupffer als Holz / gezieret. Und Aus allen neuen berühmten Philosophis und
Mathematicis, mit grossem Fleiss zusammen getragen. Durch Georg Philip
Harsdörffern. Wolffgang dess Jüngern und Joh. Andreas Endtern, Nürnberg, 1653.
This 3 vol. version was reprinted in 1677 and 1692. Modern facsimile of the 3
vol. version edited by Jörg Jochen Berns, Keip Verlag, Frankfurt Am Main, 1991, HB.
See also MUS II 325-326. Schott described this as a German translation of van
Etten/Leurechon, but this is quite wrong. V&T, p. 152, say it is 'partially derived from'
van Etten/Leurechon. C&B list just the 1636, under Schwenterum. P. 549 of vol. 1 is
misprinted 249 which indicates that it was the first issue of the 1st ed.
I have not yet entered all the items from this.
The Secret Out. 1859.
SOURCES - page 82
The Secret Out; or, One Thousand Tricks with Cards, And Other
Recreations. Illustrated with over three hundred engravings. And containing Clear and
comprehensive explanations how to perform with ease, all the curious card deceptions,
and slight of hand tricks extant. With an endless variety of entertaining experiments in
drawing room or white magic, including the celebrated science of second sight.
Together with a choice collection of intricate and puzzling questions, amusements in
chance, natural magic, etc., etc., etc. By the Author of "The Sociable, or, One Thousand
and One Home Amusements," "The Magician's Own Book," etc, etc. Dick &
Fitzgerald, NY, 1859.
[Toole Stott 191, listing all versions under Cremer. C&B, under Frikell, have
New York, 1859. H. A. Smith dates this as 1869.]
The Secret Out (UK). c1860.
The Secret Out or, One Thousand Tricks in Drawing-room or White
Magic, with an Endless Variety of Entertaining Experiments. By the author of "The
Magician's Own Book." Translated and edited by W. H. Cremer, Junr. With three
hundred illustrations.
I have seen several editions. [Toole Stott lists all versions under Cremer.]
C&W (based on the John Camden Hotten, London, 1871?) (with ads from Sep
1886 at back and inscription dated 12 Oct 1887 on flyleaf). [NUC; Toole Stott 192;
C&B, under Cremer, have London & New York, 1871, and under Frikell, have London,
1870.]
C&W, nd [1871? -- NUC lists several dates; Toole Stott 1013 is 1870;
Christopher 242 is 1878?].
John Grant, Edinburgh, nd [1872 -- Toole Stott 1014, no ads].
All these copies have identical green covers with five magic tricks on
the cover.
[Toole Stott 192 discusses the authorship, saying that Wiljalba (or Gustave)
Frikell is named on the TP of some editions, but that most of the tricks are taken from
the US ed of The Magician's Own Book. In the US ed, The Author acknowledges his
indebtedness to The Sociable and The Magician's Own Book 'and many other works of
similar character and value', but claims 'that the greater portion of it [i.e. the book] is
entirely original.' In the Preliminary to the UK ed he says he is indebted to '"Le
Magicien des Salons," revised by references to Decremps, Servière, Leopold, Besson,
Kircher, Hildebrandt, Ozanam, &c., &c.' though an 1874 ad by C&W indicates that it is
translated from Le Magicien des Salons. (This may be Le Magicien de Société,
Delarue, Paris, c1860, but see Rulfs, below.) The back of the TP of Bellew's The Art of
Amusing, Hotten, 1866?, says The Secret Out is a companion volume, just issued, by
Hermann Frikell. BMC & Toole Stott say it is also attributed to Henry L. Williams.
Toole Stott 481 cites a 1910 letter from Harris B. Dick, of the publishers Dick &
Fitzgerald, who thinks their version of The Secret Out "was a reprint of an English book
by W. H. Cremer" -- but there seems to be no record of a UK ed before the US one.
NUC says an 1871 ed. gives author as Gustave Frikell. Christopher 240-242 are two
copies from Dick & Fitzgerald, c1859, and a C&W, 1878? He repeats most of the
above comments from Toole Stott and 242 cites the Rulfs article mentioned under
Magician's Own Book, above. Rulfs says The Secret Out is largely taken, illustrations
and all, from Blismon de Douai's Manuel du Magicien (1849) and Richard & Delion's
Magicien des salons ou le diable couleur de rose (1857 and earlier). H. A. Smith [op.
cit. under Magician's Own Book] says the first US ed is 1869 (this must be a misprint or
misreading -- though the date is a little hard to read in my copy, it is clearly 1859) and
the UK eds are basically a condensed version with a few additions. He suggests the
book is taken from DeLion. He doubts whether Cremer ever wrote anything. C&B,
under Gustave Frikell, say it is a translation of Richard & Delion. C&B, under Herrman
SOURCES - page 83
Frikell, list London, 1870. C&B, under Secret, list New York, nd. C&B also list it
under Williams, as London, 1871.]
[Toole Stott 1056 is [Frikell, Wiljalba]; Parlor Tricks with Cards, ...; By the
Author of Book of Riddles and 500 Home Amusements, etc.; Dick & Fitzgerald, 1860?;
which is described as "abridged from The Secret Out. Toole Stott 547 and 1142 are two
versions of 1863, but without the description of the author and hence listed
anonymously.]
The US and UK editions are fairly different. The US ed has 382 sections, of
which 157 (41%) are used in the UK ed. The UK ed has 323 sections, so 51% of it is
taken from the US ed. The US ed seems like a magic book, with chapters on Scientific
Amusements and Miscellaneous Tricks. The UK ed has much less magic and tricks,
adding other general tricks and a lot more scientific tricks. The illustrations for the
common sections are not quite identical -- one was probably copied from the other. The
amount taken from The Magician's Own Book and The Sociable is fairly small, perhaps
10% from each, in either edition.
Shortz.
Will Shortz's library or his catalogues thereof, called "Puzzleana". The
most recent I have is: May 1992, 88pp with 1175 entries in 26 categories, with indexes
of authors and anonymous titles. Some entries cover multiple items. In Jan 1995, he
produced a 19pp Supplement extending to a total of 1451 entries.
SIHGM. 1939-1941.
Ivor Bulmer Thomas. Selections Illustrating the History of Greek
Mathematics. Loeb Classical Library, 1939-1941, 2 vols. I will give volume and pages
as in SIHGM I 308-309.
Simpson. Algebra. 1745.
Thomas Simpson (1710-1761). A Treatise of Algebra; Wherein the
Fundamental Principles Are fully and clearly demonstrated, and applied to the Solution
of a great Variety of Problems. To which is added, The Construction of a great Number
of Geometrical Problems; with the Method of resolving the same Numerically. John
Nourse, London, 1745.
I also have the 7th ed., with the slightly different title: A Treatise of Algebra.
Wherein the Principles Are Demonstrated, And Applied In many useful and interesting
Enquiries, and in the Resolution of a great Variety of Problems of different Kinds. To
which is added, The Geometrical Construction of a great Number of Linear and Plane
Problems; with the Method of resolving the same Numerically. The Seventh Edition,
carefully Revised. F. Wingrave, Successor to Mr. Nourse, London, 1800.
I have now seen a 6th ed., F. Wingrave, 1790 and it appears identical to the 7th
ed. Both have an Author's Preface to the Second Edition.
I will give the 1745 details with the 1790/1800 details in parenthesis like (1790:
...).
SLAHP. 1928.
Sam Loyd Jr. (1873-1934) Sam Loyd and His Puzzles. An
Autobiographical Review. Barse & Co., NY, 1928. (This contains somewhat more
original material than I expected, but he claims that he devised a lot of his father's
puzzles given in the Cyclopedia, OPM, and even earlier.)
Slocum. Compendium. 1977.
Jerry (= G. K.) Slocum. Compendium of Mechanical Puzzles from
Catalogues. Published by the author, Beverly Hills, 1977, 57pp. This is a compendium
of illustrations and descriptions from 30 catalogues. The earliest ones are Bestelmeier,
1793, 1807 (Jacoby edition); The Youth's Companion, 1875; Montgomery Ward, 1886,
1889, 1903, 1930; Peck & Snyder, 1886; Joseph Bland, c1890. Others of some interest
are: Gamage's, 1913, c1915, c1928; Johnson Smith, 1919, 1935, 1937, 1938, 1942.
Slocum & Gebhardt -- see under Catel.
SM.
Scripta Mathematica.
SOURCES - page 84
Smith, David Eugene (1860-1944). See: Rara and the following four items.
Smith. History. 1923.
David Eugene Smith. History of Mathematics. Two vols. (Ginn, NY,
1923) = Dover, 1958.
Smith. Number Stories. 1919.
David Eugene Smith. Number Stories of Long Ago. NCTM, (1919),
reprinted 1968? Chaps. IX and X.
Smith. Source Book. 1929.
David Eugene Smith. A Source Book in Mathematics. Two vols.
(1929) = Dover, 1959.
Smith & Mikami. 1914.
David Eugene Smith & Yoshio Mikami. A History of Japanese
Mathematics. Open Court, Chicago, 1914.
The Sociable. 1858.
The Sociable; or, One Thousand and One Home Amusements.
Containing Acting Proverbs; Dramatic Charades; Acting Charades, or Drawing-room
Pantomimes; Musical Burlesques; Tableaux Vivants; Parlor Games; Games of Action;
Forfeits; Science in Sport, and Parlor Magic; and a Choice Collection of Curious
Mental and Mechanical Puzzles; &c,&c. Illustrated with nearly three hundred
engravings and diagrams, the whole being a fund of never-ending entertainment. By the
author of "The Magician's Own Book." (Dick & Fitzgerald, NY, 1858 [Toole Stott 640
lists this as anonymous; C&B list it under the title, with no author]); G. G. Evans,
Philadelphia, nd, but the back of the title gives ©1858 by Dick & Fitzgerald, NY, so
this copy seems to be a reprint of the 1858 book. Cf. Book of 500 Puzzles for
discussion of possible authorship. The Preface here says that most of the Parlor
Theatricals are by Frank Cahill and George Arnold -- Toole Stott opines that this
reference led Harry Price to ascribe this and the related books to these authors. My
thanks to Jerry Slocum for providing a copy of this.
The entire section Puzzles and Curious Paradoxes, pp. 285-318, is identical to the
same section in Book of 500 Puzzles, pp. 3-36. Rulfs (see under Status of the Project in
the Introduction) says this draws on the same sources as Magician's Own Book, with
more taken from Endless Amusement and Parlour Magic.
See also: Book of 500 Puzzles; Boy's Own Conjuring Book; Illustrated Boy's
Own Treasury; Indoor and Outdoor; Landells: Boy's Own Toy-Maker; The Secret
Out; Hanky Panky.
SP.
Prefixed by ?? is a flag to check spelling.
"The Sphinx". See: Lemon.
Sridhara. c900.
Śrīdharācārya. Patiganita (= Pâţîgaņita [NOTE: ţ, ņ denote t, n with
underdot.]). c900. Transcribed and translated by Kripa Shankar Shukla. Lucknow
Univ., Lucknow, 1959. The text is divided into verses and examples, separately
numbered by the editor. I will cite verse (v.) and example (ex.) and the page of the
English text. The editor has appended answers on pp. 93-96, some of which were given
by an unknown commentator. (I have seen this dated 8C, which would put it before
Mahavira -- ??)
SSM.
School Science and Mathematics.
Struik. Source Book. 1969.
D. J. Struik (1894- ), ed. A Source Book in Mathematics 1200-1800.
Harvard Univ. Press, 1969.
Sullivan. Unusual. 1943 & 1947.
Orville A. Sullivan. Problems involving unusual situations. SM 9
(1943) 114-118 & 13 (1947) 102-104. (Previously listed in Section 2 below.)
Suter. 1900-1902.
Heinrich Suter. Die Mathematiker und Astronomen der Araber und
SOURCES - page 85
Ihre Werke. (AGM 10 (1900) & 14 (1902)); reprinted by APA -- Academic Publishers
Associated, Amsterdam, 1981. See also: H. P. J. Renaud; Additions et corrections à
Suter "Die Mathematiker und Astronomen der Araber"; Isis 18 (1932) 166-183.
S&B. 1986.
Jerry (= G. K.) Slocum & Jack Botermans. Puzzles Old & New -- How
to Make and Solve Them. Univ. of Washington Press, Seattle, 1986. Slocum had
produced a detailed index for this and has extended it to a joint index with New Book of
Puzzles.
Tabari. Miftāh al-mu‘āmalāt. c1075.
Mohammed ibn Ayyūb Ţabarī [NOTE: Ţ denotes a T with a
underdot.]. Miftāh al-mu‘āmalāt. c1075. Ed. by Mohammed [the h should have an
underdot] Amin Riyāhi [the h should have an underdot], Teheran, 1970. ??NYS -frequently cited and sometimes quoted by Tropfke and others.
Tagliente. Libro de Abaco. (1515). 1541.
Girolamo [& Giannantonio] Tagliente. Libro de abaco che insegnia a
fare ogni raxone marcadantile & apertegare le terre con larte di la giometria & altre
nobilissime raxone straordinarie cō la tarifa come raspondeno li pexi & monete de
molte terre del mondo con la inclita citta de. Venetia. El qual Libro se chiama Texauro
universale ...; Venice, 1515. See Rara 114-116, 495, 511-512, which seems to confuse
this with another work whose title starts: Opera che insegna .... Riccardi lists 27
editions of this and three editions of the other work. He says Boncompagni has studied
this work and found that Giovanni Rocha made some corrections and that several
editions have only his name, so it is sometimes catalogued under Rocha -- cf below.
Smith mentions 25 editions under Tagliente and says Riccardi mentions 11 others.
Van Egmond's Catalog 334-344 lists 31 editions to 1586. It is clear that this was a
major book of its time. I have briefly looked at a few examples and they seem to have
the same material, though the woodcuts were often changed.
I have examined: Giovanne Rocha; Libro Dabaco che insegna a fare ogni
ragione mercadãtile: & a ptegare le terre cõ larte di la geometria: & altre nobilissime
ragione straordinarie cõ la Tariffa come respõdeno li pesi & mone de molte terre del
mõdo con la inclita di Vinegia. El qual Libro se chiama Thesauro universale.
Venturino Rossinello, Venice, 1541. Smith, Rara, p. 529, only records a 1550 ed.
printed by Giovanni Padovano in Venice. The Crawford Collection has 1544 & 1550.
Not under Rocha in Riccardi. I found this in the Turner Collection at Keele as A4.32,
but it is not under Rocha in Hill's Catalogue (listed in 3.B), but is under Tagliente. It
has nice woodcut(?) illustrations in the text -- see Rara 512 for an example. Having
first found this book on the shelf at the Turner Collection, I originally thought it was by
Rocha and hence an extraordinarily rare book. I am grateful to Bill Kalush for
identifying this as a version of Tagliente and for pointing out its importance. Cf Van
Egmond's Catalogue 338, item 15.
Tartaglia, Nicolo (or Niccolò) (c1506-1559). See: General Trattato.
Thomas, Ivor B. See: SIHGM.
Tissandier. Récréations Scientifiques. 1880.
Gaston Tissandier. Les Récréations Scientifiques ou L'Enseignement
par les Jeux. G. Masson, Paris, (1880); 2nd ed., 1881; 3rd ed., 1883; (4th ed., 1884);
5th ed., 1888; (6th ed., 1893; 7th ed., 1894.) I have seen 3rd ed., 1883, and I have 2nd
ed., 1881, & 5th ed., 1888. Tissandier was editor of La Nature and the articles often
have fine illustrations by L. Poyet and others, frequently copied elsewhere. See Tom
Tit for more of Poyet's work. I have seen the date of the first two editions as 1881 &
1882, but the Avertissement of the 2nd ed. says the 1st ed. was Nov 1880 and the
Avertissement is dated Apr 1881. [C&B only list 1881.]
Tissandier. Popular Scientific Recreations. 1881.
SOURCES - page 86
Translation and enlargement of the above. Ward Lock, London,
([1881, 1882]); New enlarged ed., nd [1890, 1891]. [Not clear which French edition the
translation is based on. The new enlarged ed. contains a Supplement on pp. 775-876
which includes material which is in the 5th French ed. of 1888, but not in the 3rd
French ed. of 1883, so it seems the the main text is c1885 and the supplement is c1890.
C&B list a London edition, nd, 780pp.] The index refers to a puzzle of knots and cords
on p. 775 which is not present. Most of the Supplement appeared as a series of
Scientific Amusements in (Beeton's) Boy's Own Magazine from 1889 -- I have vol. 3
(1889) which has the first 10 articles, comprising 62 pages and 67 problems.
Some of the material appeared in: Marvels of Invention and Scientific Puzzles.
Being A Popular Account of Many Useful and Interesting Inventions and Discoveries.
Ward, Lock, & Co., nd [c1890]. My copy has no authors listed, but Jerry Slocum has a
copy with Tissandier and Firth on the TP, though it is difficult to see what Firth could
have done to warrant his inclusion. This consists of Chapters 56-60, pp. 726-774, and
Chap. 32, pp. 448-465, of Popular Scientific Recreations, set on smaller pages, plus a
few extra items: An economical mouse-trap (pp. 57-58); Flying bridges (pp. 64-66);
Performing fleas (pp. 77-79); Knots and cords and A Curious Toy (pp. 83-85). This
last must be what was on pp. 775-776 of the earlier edition of Popular Scientific
Recreations and the other material seems to have come from some edition of that work
or from the articles in (Beeton's) Boy's Own Magazine. I won't bother to cite this
version.
Tom Tit. 1890-1893?
Arthur Good [= "Tom Tit"]. La Science Amusante. 3 vols., Larousse,
Paris, 1890, 1892, 1893? [I have seen the dates given as 1889, 1891, 1893, but the
Introductions are dated as I have given, the last being Dec 1893.] The material
originally appeared in the magazine L'Illustration with classic engravings by Poyet
which have been often reproduced, e.g. in: Beeton's Boy's Own Magazine; The Boy's
Own Paper; Kolumbus-Eier (1890, 1976) -- translated as: Columbus' Egg (1978).
Arthur Good's name is clearly English and I have wondered if the articles were written
originally in French or if they were translated from his English.
I have the three volume set and five one volume selections/adaptations. I will
give references to these by the initials shown below.
C.
François Caradec, ed. La Science Amusante -- 100 Experiences de
Physique. Les Editions 1900 [no accent], Paris, 1989. [This consists of all of
Vol. 1, reordered, but otherwise little changed. Caradec's Preface gives a little
about the author. The illustrations are a bit dark.]
H.
Magic at Home. A Book of Amusing Science. Annotated translation of La
Science Amusante, vol. 1, by Prof. Hoffmann. Cassell, 1891. Cf. VBM below.
VBM.
The Victorian Book of Magic Illustrated or Professor Hoffman's [sic]
Curious & Innocent Diversions for Parlour & Refined Gatherings. Selected [from
the above] & with a note to readers by C. Raymond Reynolds. (Stephen Greene
Press, Japan, 1969); Hugh Evelyn, London, nd [c1970]. [This has 26 of the items
in Vol. 1. Illustrations are small but good.]
K.
Tom Tit. Scientific Amusements. Selected and translated by Cargill G.
Knott. Nelson, nd [1918]. [This contains 178 items, mostly from Vols. 2 & 3,
but Knott has added a few others, possibly taken from Tom Tit's later articles?
Knott has also extended some items. Sadly, the illustrations were poorly redrawn
for this edition.]
R&A.
David Roberts & Cliff Andrew, eds. 100 Amazing Magic Tricks. Cape,
London, 1977. [Selections from all three volumes. Although this refers to the
original books and L'Illustration, it avoids mentioning the original author's name!
Illustrations are very good.]
SOURCES - page 87
[I have also seen an Italian translation. There was a US ed., trans. by Camden Curwen
& Robert Waters; Magical Experiments or Science in Play; (© Worthington,
1892); David McKay, Philadelphia, 1894, 329 pp. [Christopher 398.]]
Todhunter. Algebra, 5th ed. 1870.
Isaac Todhunter (1820-1884). Algebra For the Use of Colleges and
Schools. With Numerous Examples. Macmillan, (1858; 5th ed, 1870); new edition,
1879, HB. [1st ed was 1858; 2nd, 1861; 5th, 1870. The Preface in my 1879 copy is
dated 1870 and says the work has been carefully revised, with two chapters and 300
miscellaneous examples added, so it was quite different than previous editions and I
will date citations as 1870.]
Tonstall. De Arte Supputandi. 1522.
Cuthbert Tonstall [often spelled Tunstall] (c1474-1559). De Arte
Supputandi Libri Quatuor. ([With Quattuor] Richard Pynson, London, 1522 -- the first
arithmetic printed in England, with TP engraved by Holbein.) I have seen: Robert
Stephan, Paris, 1538. Though the TP and pagination are different, Smith, Rara, gives
no indication that the 1538 text is any different than the 1522, so I will cite this as 1522.
Most citations are to Book III, whose problems are numbered. See Rara 132-136.
Toole Stott. 1976-1978.
Raymond Toole Stott. A Bibliography of English Conjuring
1581-1876. 2 vols., published by the author, Derby, 1976, 1978; distributed by Harpur
& Sons, Derby. 1414 entries. References are to the item number.
TP
Title Page.
Tropfke. 1980.
Johannes Tropfke, revised by Kurt Vogel, Karin Reich and Helmuth
Gericke. Geschichte der Elementarmathematik. 4th ed., Vol. 1: Arithmetik und
Algebra. De Gruyter, Berlin, 1980. (Prof. Folkerts says (1994) that vol. 2 is being
edited.)
[The 1st ed. was De Gruyter?, Leipzig, 1902, 2 vols. 2nd ed., De Gruyter, Berlin
& Leipzig, 1921-1924, 7 vols. 3rd ed., De Gruyter, Berlin & Leipzig, 1930-1940, vols.
1-4 (the MSS of the remaining volumes were destroyed in 1945).]
Tunstall, Cuthbert -- see: Tonstall, Cuthbert.
Turner.
The Turner Collection, formerly at University of Keele. Sadly this
collection was secretly sold by the University in 1998 and has now been dispersed. A
useful catalogue was prepared: Susan Hill; Catalogue of the Turner Collection of the
History of Mathematics Held in the Library of the University of Keele; University
Library, Keele, 1982.
UCL.
University College London or its Library, which includes the Graves
Collection, cf Graves.
Uncle George. See: Parlour Pastime.
Unger. Arithmetische Unterhaltungen. 1832.
Ephraim Salomon Unger. Arithmetische Unterhaltungen, bestehend in
einer systematisch geordneten Sammlung von mehr als 900 algebraischen Aufgaben,
verbunden mit einer Anleitung, diese Aufgaben mittelst der einfachsten Regeln der
Arithmetick zu lösen. (Erfurt, 1832, 4 + 253 pp., ??NYS); 2nd ed., Keysersche
Buchhandlung, Erfurt, 1838, 10 + 268pp. MUS 166 only mentions the 1838 ed. but a
copy of the 1st ed. was advertised by Sändig in Jun 1997. I haven't seen any other
reference to this work. In general, this book believes in beating problems to death -each type of problem is done several times. E.g. there are 10 problems of the Chinese
Remainder Theorem with two moduli. Hence I will generally not describe all the
problems.
van Etten. See: Etten, above.
SOURCES - page 88
Van Egmond's Catalog.
Warren Van Egmond. Practical Mathematics in the Italian
Renaissance: A Catalog of Italian Abbacus Manuscripts and Printed Books to 1600.
Supp. to Annali dell'Istituto e Museo di Storia della Scienza (1980), fasc. 1. = Istituto e
Museo di Storia della Scienza, Monografia N. 4. Florence, 1980. I have consulted this
for (almost?) all MSS cited in these Sources and have made a number of changes of
dates and even authorship based on it. Like any such catalog, there are some omissions
and errors, but it is by far the most authoritative listing of the material and I have
adopted his dates and attributions -- cf Benedetto da Firenze, P. M. Calandri,
dell'Abbaco, pseudo-dell'Abbaco.
Vinot. 1860.
Joseph Vinot. Récréations Mathématiques Nouveau Recueil de
Questions Curieuses et Utiles Extraites des Auteurs Anciens et Modernes. Larousse &
Boyer, Paris, 1860, (3rd ed., Larousse, Paris, 1893; 1898; 1902; 6th ed., nd [1911]). I
have found no difference between the 1st and 6th eds -- indeed I have found a simple
typographical error repeated.
Vogel, Kurt (1888-1985). See: AR; BR; Chiu Chang Suan Ching; Columbia Algorism;
Tropfke; items in 7.K under al-Khwârizmî; items in 7.P.7 and 7.R.2 under Fibonacci.
Vyse. Tutor's Guide. 1771?
Charles Vyse (fl. 1770-1815). The Tutor's Guide, being a Complete
System of Arithmetic; with Various Branches in the Mathematics. In Six Parts, .... To
which is added, An Appendix, Containing Different Forms of Acquittances, Bills of
Exchange, &c. &c. The whole being designed for the Use of Schools, .... The Eighth
Edition, corrected and improved, with Additions. G. G. J. and J. Robinson, London,
1793, HB. 12 + 324 pp. [1st ed. was 1770 or 1771; 2nd ed., 1772; 4th ed., 1779; 6th
ed., 1785; 1790; 8th ed., 1793; 1799; 12th ed., 1804; 13th ed., 1807; 14th ed., 1810;
15th ed., 1815; 1817; 16th ed., 1821.] Since books of this nature rarely had major
changes, I will date this as 1771? until I see further editions.
Charles Vyse (fl. 1770-1815). The Tutor's Guide, being a Complete
System of Arithmetic; with Various Branches in the Mathematics. In Six Parts, .... To
which is added, An Appendix, Containing Different Forms of Acquittances, Bills of
Exchange, &c. &c. The whole being designed for the Use of Schools, .... 10th ed., ed.
by J. Warburton. S. Hamilton for G. G. and J. Robinson, London, 1799. 12 + 335 pp.
[Dedication removed; Preface by the Editor and references to the Key added. Though
the text is reset with one or two more lines per page, the text seems to be preserved,
though the editor has added substantial footnotes in places.]
The Key to the Tutor's Guide; or the Arithmetician's Repository:
containing Solutions to the Questions, &c. in the Tutor's Guide, with references to the
pages where they stand. To which are added Some Useful Rules, &c. Likewise An
Appendix; showing the Combination of Quantities; The different Ways they may be
varied; with the method of filling the magic squares, &c. .... Eighth edition; Carefully
revised, corrected, and augmented. G. & J. Robinson, London, 1802. 8 + 370 pp + 2pp
publisher's ads. [1st ed., 1773; 3rd ed., 1779; 4th ed., 1785; 7th ed., 1799; 8th ed.,
1802; 9th ed., 1807; 11th ed., 1818.]
Despite the claim in the title of the Key, the references to the answers are in the
text of the 10th ed at the beginning of each set of exercises. There is no mention of the
Key in the 8th ed of the book. I have the 8th and 9th eds. of the Key and have not seen
any difference between them -- indeed I have found a common misprint -- and they give
the answers to the 10th ed. of the book, on the pages cited in the book, so I assume they
are essentially identical to the 7th ed. of the Key.
V&T, 1952.
Volkmann, Kurt & Tummers, Louis. Bibliographie de la
Prestidigitation Tome I Allemagne et Autriche. Cercle Belge d'Illusionnisme,
SOURCES - page 89
Bruxelles, 1952. With a 2 page list of Bibliographies of Conjuring.
Walkingame. Tutor's Assistant.
Francis Walkingame. The Tutor's Assistant; Being a Compendium of
Arithmetic, and a Complete Question-Book. ... To which are added, A new and very
short Method of extracting the Cube Root, and a General Table for the ready calculating
the Interest .... The Fifteenth Edition. Printed for the Author, London (Great RusselStreet, Bloomsbury), 1777. [First ed. was 1751. There were about a hundred editions
in all. See Wallis's article on this book in MG 47 (No. 361) (1963) 199-208.]
The Tutor's Assistant. Being a Compendium of Arithmetic, and a
Complete Question-Book. ... To which are added, A new and very short Method of
extracting the Cube Root, and a General Table for the ready calculating the Interest ....
The Twentieth Edition. Printed for the Author, London (Kensington), 1784. Appears
to be identical to the 15th ed., except for resetting and some small changes, both
corrections and errors, so I won't cite this separately.
The Tutor's Assistant, being a Compendium of Arithmetic, and
Complete Question-Book; ...; to which is added, A Compendium of Book-keeping, by
Single Entry, by Isaac Fisher. Thomas Richardson, Derby; Simpkin, Marshall & Co.,
London, 1835. [The first Derby edition by Fisher was 1826.]
The Tutor's Companion; or, Complete Practical Arithmetic. To which
is added A Complete Course of Mental Arithmetic, ..., by Isaac Butler. Webb,
Millington, and Co., London, 1860.
The editions are pretty similar, but the interesting collection of problems at the
end is much shortened in the 1835 ed. and a few are omitted in the 1860 ed.
Consequently I will assume the problems date from 1751, unless they vary in some
important way. I also have a Key to Walkingame from 1840, but it does not correlate
with any of the editions I have!
Wallis.
The Wallis Collection of early English mathematics books. Gathered
by Peter J. Wallis and left to the University of Newcastle upon Tyne in 1992. A typical
catalogue entry is Wallis 227 CAR and there are special sections for Newtoniana and
Record(e).
Week-End. 1932.
Hubert Phillips. The Week-End Problems Book. Nonesuch Press,
London, 1932.
Wehman. New Book of 200 Puzzles. 1908.
Wehman Bros.' New Book of 200 Puzzles. Wehman Bros., 126 Park
Row, NY, 1908. Largely copied from various 19C works: Boy's Own Book, Magician's
Own Book, The Sociable, sometimes with typographical omissions. I only count 130
puzzles! There seems to have been a Johnson Smith reprint at some time.
Wells. 1698.
Edward Wells. Elementa Arithmeticæ Numerosæ et Speciosæ. In
Usum Juventutis Academicæ. At the Sheldonian Theatre (i.e. OUP), Oxford, 1698.
(My copy was previously in the Turner Collection, Turner D1.1.) All the material cited
is in Appendix Posterior: Viz. Problemata sive Quæstiones ad exercendas Regulas
Arithmeticæ.
Western Puzzle Works. 1926.
Western Puzzle Works, 979 Marshall Avenue, St. Paul, Minnesota.
1926 Puzzle Catalogue. Photocopy provided by Slocum. Unpaginated, 8pp.
Williams. Home Entertainments. 1914.
Archibald & F. M. Williams. Home Entertainments. The Hobby
Books, ed. by Archibald Williams. Nelson, London, nd [1914 -- BMC].
Williams, Henry Llewellyn, Jr. (1842-??). Books by Frikell?, particularly Magician's Own
Book, are often attributed to him. [C&B, under Williams, Henry Llewellyn ("W.
Frikell") lists: Hanky Panky; Magician's Own Book, London & New York; (Magic
SOURCES - page 90
No Mystery); The Secret Out and says to also see Cremer.]
Williams, J. L. See: Boy's Own Book, 1843 (Paris) edition, which lists him as author.
Wilson, Robin J. See: BLW.
Wingate/Kersey. 1678?.
Edmund Wingate (1596-1656). Mr. Wingate's Arithmetick; Containing
A Plain and Familiar Method For Attaining the Knowledge and Practice of Common
Arithmetick. (1629.) The Seventh(?) Edition, very much Enlarged. First Composed by
Edmund Wingate, late of Gray's-Inn, Esquire. Afterwards, upon Mr. Wingate's
Request, Enlarged in his Life-time: Also since his Decease carefully Revised, and much
Improved; ... By John Kersey, late Teacher of the Mathematicks. My copy is lacking
the TP and pp. 345+, but it appears to be identical to The Tenth Edition; J. Philips,
J. Taylor & J. Knapton, London, 1699 -- though reset, it has the same pagination
throughout except for the Dedication. A Librarian's note suggests my earlier version is
the 7th ed. of 1678. This would be the fourth and last of Kersey's versions. Kersey
began editing from the second or third (1658) ed. and did four versions, the last in 1678.
The material of interest is almost all in Chapter 10 of Kersey's Appendix: A
Collection of subtil Questions to exercise all the parts of Vulgar Arithmetick; to which
also are added various practical Questions about the mensuration of Superficial Figures
and Solids, with the Gauging of Vessels, pp. 475-527, 75 questions. There are a few
further items in Chapter 11: Sports and Pastimes, pp. 528-544, 7 problems. Chapter 11
is not clearly marked as being by Kersey in these copies, but is so marked in later
editions and it is pretty clear that the entire Appendix is due to Kersey. At the end, he
says he has taken the problems of Chap. 11 from Bachet's Problemes.
I have seen a 14th ed. of 1720 which has the same text, reset and repaginated,
with some supplementary material by George Shelley. I have also seen a 19th ed. of
1760 which has been considerably reorganized by James Dodson. The two chapters of
puzzle problems have become Chapters XLIII and XLIV and the material has been
changed, generally omitting some problems of interest and only adding two.
Winning Ways. 1982.
Elwyn R. Berlekamp, John H. Conway & Richard K. Guy. Winning
Ways for Your Mathematical Plays: Vol. 1: Games in General; Vol. 2: Games in
Particular. 2 vols, Academic Press, NY, 1982.
Witgeest. Het Natuurlyk Tover-Boek. 1686.
Simon Witgeest. Het Natuurlyk Tover-Boek, Of't Nieuw Speel-Toneel
Der Konsten. Verhandelende over de agt hondert natuurlijke Tover-Konsten. so uyt de
de Gogel-tas, als Kaartspelen, Mathematische Konsten, en meer andered diergelijke
aerdigheden, die tot vermaek, en tijtkorting verstrecken. Mitsgaders een Tractaet van
alderley Waterverwen, en verligteryen; Als oock Een verhandelinge van veelderley
Blanketsels. Om verscheyde wel-ruykende Wateren, Poederen en Balsemen, als ook
kostelijke beeydselen, om het Aensicht, Hals en Handen, wit en sagt te maecken, door
Simon Witgeest. Jan ten Hoorn, Amsterdam, 1686. ??NYS -- some photocopies sent
by Jerry Slocum. 'Boek' is 'Boeck' on the frontispiece and running heads. This is a
much expanded and retitled 3rd edition of Witgeest's 1679 work. The new material is
stated to already be in the 2nd ed. of 1682.
[There were many later editions: 1695; 1698; Ten Hoorn, 1701; G. de Groot
Keur, Amsterdam, 1725 (10th ed.), 1739; 1749; 1760; Amsterdam, 1773; 1815
[Christopher 1098-1099, C&B, HPL]. It was translated as: Naturliches Zauber-Buch
(or Zauber=Buch) oder neuer Spiel-Platz der Künste; Hoffmanns sel Wittw. &
Engelbert Streck, Nürnberg, 1702. There were later editions (all in Nürnberg?) of 1713
(in 1 or 2 vols); Hoffmann, Nürnberg, 1718; 1730; 1739; 1740; 1745; 1753; Johann
Adam Stein, Nürnberg, 1755; 1760-1762; 1763; 1766; 1781; 1786; 1798 and a Lindau
SOURCES - page 91
reprint of 1978 [Christopher 1092-1097, C&B, V&T], all apparently based on the 1682
Dutch ed.]
Witgeest. Het Nieuw Toneel der Konsten. 1679.
Simon Witgeest. Het Nieuw Toneel der Konsten, Bestaande uyt
Sesderley Stukken: het eerste, handelt van alderley aardige Speeltjes en Klugjes: het
tweede, van de Verligt-konst in 't Verwen en Schilderen: het derde, van het Etzen en
Plaat-shijden: het vierde, van de Glas-konst: het vijfde, heest eenige aardige remedien
tegen alderley Ziekten: het sesde, is van de Vuur-werken. Uyt verscheyde Autheuren by
een vergadert, door S. Witgeest, Middel-borger. Jan ten Hoorn, Amsterdam, 1679;
facsimile with epilogue by John Landwehr, A. W. Sijthoff's Uitgeversmaatschappij N.
V., Leiden, 1967 (present from Bill Kalush).
There were many later editions, but Nanco Bordewijk has examined these and
discovered that the 3rd ed. of 1686 (I can't recall if he saw the 1682 ed.) was so
extensively revised and extended as to constitute a new book, and it has the different
title given in the previous entry. (Other sources indicate these revisions are already in
the 2nd ed. of 1682.) Landwehr has written a bibliographical article on this book -??NYR.
Wood. Oddities.
Clement Wood. A Book of Mathematical Oddities. Little Blue Book
1210. Haldeman-Julius, Girard, Kansas, nd [1927].
Young Man's Book. 1839.
Anonymous. The Young Man's Book of Amusement. Containing the
Most Interesting and Instructive Experiments in Various Branches of Science. To
Which is Added All the Popular Tricks and Changes in Cards; and the Art of Making
Fire Works. William Milner, Halifax, 1844, HB. 2 + 384 pp + folding plate (originally
a frontispiece). My copy has a number of annotations as though in preparation for
another edition. [Hall BCB 322. Toole Stott 751. BCB 320-323 are 1839, 1840,
1844, 1848. Heyl 358-360 are 1846, 1846 (Milner & Sowerby ??), 1850. Toole Stott
749-752, 1216 are 1839, 1840, 1844, 1846, 1850. Christopher 1111-1113 are 1839,
1846, 1859 (Milner & Sowerby). All these are apparently the same except for the
publisher's name change.]
Young World. c1960.
Young World Productions. Tricks and Teasers. 303 Gags Games
Tongue Twisters Problems Tricks. Young World Productions, London, nd [inscribed
1965 on first page, so probably c1960; BLC-Ø].
536.
H. E. Dudeney. 536 Puzzles and Curious Problems. Ed. by M.
Gardner. Scribner's, NY, 1967. (This consists of almost all the puzzles from Modern
Puzzles (MP) and Puzzles and Curious Problems (PCP).) [There is also a Fontana,
London, 1970, edition in two volumes: Puzzles and Curious Problems (258 problems);
More Puzzles and Curious Problems (261 problems).]
??

indicates uncertainty and points where further work needs to be done.
BC, e.g. -330 is 330 BC and -5C is 5th century BC.
Inequality or incongruence (mod m). (My word processor does not
have an incongruence sign. I may change this in Word using an Arial character.)
Nothing, used after catalogues, etc., to indicate that I have looked in
that catalogue and found no entry. E.g. BLC-Ø.
Ø
SOME OTHER RECURRING REFERENCES
SOURCES - page 92
Details of these items are given under the first reference in Sources. Later references
often cite the first reference. I tend to make entries below when I use the item, but sometimes
I have entered the entry long after the first usage of the item, and I haven't searched the text
for other (perhaps entered long ago) appearances of these items.
For:
Anon: Home Book ..., 1941
Anon: Treatise, 1850
Allen, 1991
See Sections:
4.B.1, 4.B.3, 5.U, 6.AO, 6.BF.4, 7.B, 7.AT, 9.E.1
7.H, 7.P.6, 7.S, 7.X, 10.A, 10.R
5.B, 5.I.1, 5.N, 6.L, 7.E, 7.I, 7.P.1, 7.R.3, 7.AC.6, 7.AH,
7.AL, 9.B, 10.A.4
Always: More Puzzles to Puzzle You, 1967
6.BF.4,
Always: Puzzles for Puzzlers, 1971
5.D.2, 5.D.5, 7.G.1, 7.AC.1, 9.J, 10.I, 10.K
Always: Puzzles to Puzzle You, 1965
5.K.2, 5.W.1, 5.X.2, 7.AC.3, 7.AC.6, 7.AS,
Always: Puzzling You Again, 1969
5.C, 6.BD, 7.AH,
Ananias of Shirak, c640
7.E, 7.H, 10.A
André, 1876
7.H, 7.H.1, 7.S.1, 7.S.2, 7.AF, 7.AF.2
August, 1939
5.X.1, 6.BE, 7.I, 7.X, 7.Z, 7.AL, 7.AN, 7.AT, 7.AV, 10.H
Badcock, 1823
6.BH, 7.H.3, 7.P.5, 7.Q
Bagley: Paradox Pie, 1944
6.BN, 7.Z, 7.AI, 7.AW, 10.F, 10.Q, 10.S
Bagley: Puzzle Pie, 1944
5.D.5, 6.O, 6.P.1, 6.P.2, 6.R.1, 6.R.2, 6.Y, 6.AF, 6.AI,
7.AV, 10.L
Bath, 1959
5.C, 7.G.1, 7.I, 7.P.5, 7.AC.3, 7.AC.6, 7.AM
Bellew, 1866
5.E, 6.AO.1, 6.AQ
Berloquin, 1981
5.N, 7.H.5, 7.N.3, 10.R
Black, 1952 [1946?]
5.T, 6.F.2, 9.D, 9.F
Bourdon, 1834
7.E.1, 7.H, 7.P.1, 7.S, 7.X, 7.AF.1, 7.AK, 10.A, 10.R
Brandreth Puzzle Book [1895]
5.B, 5.B.1, 5.O, 6.AW.1, 6.AY.1, 7.B, 7.G.1
Bullen, 1789
7.G.1, 7.H, 7.H.5, 7.L.2.b, 7.S.1, 7.AF.1
Bullivant, 1910
5.S, 6.T, 6.AK
[Chambers], 1866?
7.H, 7.L.2.a, 7.L.2.b, 7.Y, 7.AF.2
Chang Chhiu-Chien -- see Zhang Qiujian
Colenso, Algebra, 1849
7.P.1, 10.G
Colenso, Arithmetic, 1853
7.H, 7.X, 10.G, 10.R
Devi, 1976
5.D.1, 5.X.1, 7.E, 7.P.1, 7.AC.3, 7.AC.6, 7.AE, 10.A.3;
10.K
Dresner, 1962
5.B.1, 5.C, 5.D.4, 5.K.1, 5.W
Dudeney: World's best puzzles, 1908
2, 5.P.1, 5.S, 6.P.1, 6.S, 6.AI, 6.AO, 6.AW
Elliott, 1872
6.V, 6.AQ, 6.AV, 6.AZ, 11.B, 11.C, 11.D
Filipiak, 1942
5.H.1, 6.W.1, 6.W.2, 6.AK
Fisher, 1968
6.E, 6.P.2, 7.M.4, 7.AI
Fisher, 1973
1, 5.E, 7.S.2, 10.L
Fourrey, Cur. Geom., 1907
6.S.1, 8.G (also 6.R.1)
Fourrey, Rec. Arith., 1899
4.A.1, 5.B, 5.P.1, 5.U, 7.N.1
Fuss, 1843
5.F.1
Goldston, nd [1910?]
6.AK, 11.E
SOURCES - page 93
Gomme, 1894/98
Greenblatt, 1965
Heald, 1941
Hooper, 1774
Hutton, 1804
Kamp, 1877
Kraitchik, MJ, 1930
Kraitchik, MR, 1943
Laisant, 1906
Larte de labbacho, 1478
Von der Lasa, 1897
Licks, 1917
Van der Linde, 1874
Littlewood, 1953
Lucas, Théorie, 1891
Madachy, 1966
Meyer, 1965
Milne, 1881
W. O. J. Moser, 1981
Nordmann, 1927
Papyrus Rhind, c-1650
Phillips: Playtime Omnibus, 1933
Phillips: Question Time, 1937
Ransom, 1955
Smith: Origin, 1917
Steinhaus: 1938,1950,1960,1969
Strutt, 1791?, 1801
Strutt-Cox, 1903
Trenchant, 1566
Treviso Arithmetic, 1478
Trigg: Quickies, 1967
Wagner, Rechenbuch, 1483
Wecker, (1582), 1660
A. C. White, 1913
Widman(n), 1489
Williams & Savage, 1940
Wolff, 1937
Workman, 1902
Wyatt, 1928
Mr. X, 1903, 1911
Yang Hui, 1275
Zhang Qiujian, 468
4.B.1, 5.R.5 (Also 4.A.3)
6.U.2, 6.AE, 7.AG
7.Z, 10.E.3, 10.G, 10.0
4.A.1, 5.AA, 6.F, 6.P.2, 7.B, 7.AO, 7.AZ
7.G.2, 7.H, 7.X, 7.AF.1, 7.AK, 10.A, 10.R
5.B, 5.D.1, 5.E, 5.R.7, 7.B, 7.L, 7.Q
4.A.2, 5.J, 7.E, 7.G.1, 7.H.3, 7.AR, 10.B, 10.P
4.A.2, 5.J, 6.M, 7.H.2, 7.H.3, 9.D, 9.G, 10.P
6.P.1, 7.AR, 10.A.2, 10.B, 10.H, 10.I
See: Treviso Arithmetic.
5.F.1, 7.B (Also 4.B.1, 4.B.5)
5.A, 6.R.4, 6.AG, 7.P.3, 7.S.2, 7.AC, 7.AD
5.F.1, 7.N (Also 4.B.1, 4.B.5)
5.C, 5.W, 6.J, 8.B, 9.C, 9.D
5.L, 5.Z.5, 5.AB
5.O, 6.D, 6.X, 7.N.3, 7.N.4, 7.AC.3, 7.BB
7.I, 7.AC.4, 7.AH, 7.AR, 7.AX
7.E, 7.H, 7.R, 7.X, 7.Y, 10.A, 10.A.3, 10.G, 10.R
6.I, 6.T
4.A.4, 5.G.1, 6.AR, 7.AC.3, 7.AR, 11.C, 11.E
7.C, 7.G.1, 7.L, 7.S.1
6.AF, 7.S.2, 7.AC.1, 7.AD.1, 7.AE, 9.D
5.U, 7.E, 7.AG, 9.G
6.M, 7.F, 7.X, 7.AC.2, 8.B, 10.A.1, 10.B, 10.I
3A, 7.G.2, 7.H, 10.A
5.C.1, 6.E, 6.G.1, 6.H, 6.AB
4.B.1, 5.R.1, 5.R.5 (Also 4.A.3)
4.B.1, 5.R.1, 5.R.5 (Also 4.A.3)
7.L.2.a, 7.S.1 (also 5.B, 5.D.1, 7.E, 7.S.1, 7.AF.1)
7.H, 7.K.1, 7.AL, 10.A
5.Q, 6.AE, 6.AN, 7.N.3, 7.W
7.G.1, 7.G.2, 7.H, 7.AK, 10.A
7.L.3, 7.AO, 10.P, 11.I, 11.N
1, 5.I.1, 6.T, 6.AK, 7.X, 11.E
7.G.1, 7.H, 7.L.2, 7.P.1, 7.P.5, (7.AL)
7.P.5, 7.X, 7.AC.2, 7.AM, 7.AP, 8.I, 10.E.2
7.R.3, 7.S.2, 7.AC.1, 7.AE, 9.E, 9.E.1, 10.O
7.H.1, 7.H.4, 7.J, 7.S.2, 7.AC.2, 10.G
5.H.1, 6.V, 6.W.1, 6.W.2, 6.AI
4.A.1, 5.B, 5.P.1, 5.S, 6.AF, 6.AU, 7.H.3, 7.I, 7.J, 7.M.4,
9.E, 9.J, 10.H
7.N, 7.P.1, 7.P.2, 10.A
7.E, 7.L, 7.P.1, 7.P.6, 10.A