SOURCES IN RECREATIONAL
MATHEMATICS
AN ANNOTATED BIBLIOGRAPHY
EIGHTH PRELIMINARY EDITION
DAVID SINGMASTER
Contact via the Puzzle Museum
http://puzzlemuseum.com
Last
updated on 19 March 2004.
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.
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.])
DIACRITICAL MARKS AND NOTATION
SOME OTHER RECURRING REFERENCES
1. BIOGRAPHICAL
MATERIAL -- in chronological order
2. GENERAL
PUZZLE COLLECTIONS AND SURVEYS
3. GENERAL
HISTORICAL AND BIBLIOGRAPHICAL MATERIAL
3.A. GENERAL
HISTORICAL MATERIAL
4.A. GENERAL
THEORY AND NIM‑LIKE GAMES
4.B.1. TIC‑TAC‑TOE =
NOUGHTS AND CROSSES
4.B.5. OVID'S GAME AND NINE MEN'S MORRIS
4.B.12. RITHMOMACHIA
= THE PHILOSOPHERS' GAME
5.A.2. THREE DIMENSIONAL VERSIONS
5.B.1. LOWERING FROM TOWER PROBLEM
5.B.2. CROSSING A BRIDGE WITH A TORCH
5.C. FALSE
COINS WITH A BALANCE
5.C.1RANKING COINS WITH A BALANCE
5.D.2. RULER WITH MINIMAL NUMBER OF MARKS
5.D.3 FALSE COINS WITH A WEIGHING SCALE
5.D.4. TIMING WITH HOURGLASSES
5.E.2. MEMORY WHEELS =
CHAIN CODES
5.F.1. KNIGHT'S TOURS AND PATHS
5.F.2. OTHER HAMILTONIAN CIRCUITS
5.F.3. KNIGHT'S TOURS IN HIGHER DIMENSIONS
5.F.4. OTHER CIRCUITS IN AND ON A CUBE
5.G.1. GAS, WATER AND ELECTRICITY
5.H. COLOURED
SQUARES AND CUBES, ETC.
5.H.1. INSTANT INSANITY =
THE TANTALIZER
5.I. LATIN
SQUARES AND EULER SQUARES
5.I.2. COLOURING CHESSBOARD WITH NO REPEATS
IN A LINE
5.J.3. TILING A SQUARE OF SIDE 70 WITH
SQUARES OF SIDES 1, 2, ..., 24
5.K.1. DERANGED BOXES OF A,
B AND A & B
5.K.2. OTHER LOGIC PUZZLES BASED ON
DERANGEMENTS
5.M. SIX
PEOPLE AT A PARTY -- RAMSEY THEORY
5.N. JEEP OR
EXPLORER'S PROBLEM
5.O. TAIT'S
COUNTER PUZZLE: BBBBWWWW TO
WBWBWBWB
5.P. GENERAL
MOVING PIECE PUZZLES
5.Q. NUMBER
OF REGIONS DETERMINED BY N LINES OR PLANES
5.Q.1. NUMBER
OF INTERSECTIONS DETERMINED BY N LINES
5.R.2. FROGS AND TOADS: BBB_WWW
TO WWW_BBB
5.R.3. FORE AND AFT -- 3
BY 3 SQUARES MEETING AT A CORNER
5.R.4. REVERSING FROGS AND TOADS: _12...n
TO _n...21 , ETC.
5.S. CHAIN
CUTTING AND REJOINING
5.S.1. USING CHAIN LINKS TO PAY FOR A ROOM
5.W. MAKING
THREE PIECES OF TOAST
5.X. COUNTING
FIGURES IN A PATTERN
5.X.2. COUNTING RECTANGLES OR SQUARES
5.Y. NUMBER
OF ROUTES IN A LATTICE
5.Z. CHESSBOARD
PLACING PROBLEMS
5.AB. FOLDING
A STRIP OF STAMPS
5.AC. PROPERTIES OF THE SEVEN BAR DIGITAL DISPLAY
5.AD. STACKING
A DECK TO PRODUCE A SPECIAL EFFECT
5.AG. RUBIK'S
CUBE AND SIMILAR PUZZLES
6.F.1. OTHER CHESSBOARD DISSECTIONS
6.F.2. COVERING DELETED CHESSBOARD WITH
DOMINOES
6.F.3. DISSECTING A CROSS INTO Zs
AND Ls
6.F.4. QUADRISECT AN L‑TROMINO, ETC.
6.F.5. OTHER DISSECTIONS INTO POLYOMINOES
6.G.2. DISSECTION OF 63 INTO 33, 43 AND 53, ETC.
6.G.3. DISSECTION OF A DIE INTO NINE 1 x 1 x 3
6.G.4. USE OF OTHER POLYHEDRAL PIECES
6.I. SYLVESTER'S
PROBLEM OF COLLINEAR POINTS
6.J. FOUR BUGS
AND OTHER PURSUIT PROBLEMS
6.K. DUDENEY'S
SQUARE TO TRIANGLE DISSECTION
6.N. DISSECTION
OF A 1 x 1 x 2 BLOCK TO A CUBE
6.O. PASSING
A CUBE THROUGH AN EQUAL OR SMALLER CUBE. PRINCE RUPERT'S PROBLEM
6.P.1. PARADOXICAL DISSECTIONS OF THE
CHESSBOARD BASED ON FIBONACCI NUMBERS 286
6.Q. KNOTTING
A STRIP TO MAKE A REGULAR PENTAGON
6.R.1. EVERY TRIANGLE IS ISOSCELES
6.R.2. A RIGHT ANGLE IS OBTUSE
6.R.3. LINES APPROACHING BUT NOT MEETING
6.T. NO THREE
IN A LINE PROBLEM
6.U.2. PACKING BRICKS IN BOXES
6.V. SILHOUETTE
AND VIEWING PUZZLES
6.W.2. SIX PIECE BURR =
CHINESE CROSS
6.W.3. THREE PIECE BURR WITH IDENTICAL
PIECES
6.W.4. DIAGONAL SIX PIECE BURR =
TRICK STAR
6.W.5. SIX PIECE BURR WITH IDENTICAL
PIECES
6.X. ROTATING
RINGS OF POLYHEDRA
6.Z. LANGLEY'S
ADVENTITIOUS ANGLES
6.AD.1. LARGEST PARCEL ONE CAN POST
6.AE. 6" HOLE THROUGH SPHERE LEAVES CONSTANT VOLUME
6.AF. WHAT
COLOUR WAS THE BEAR?
6.AJ.2. TRIBAR AND IMPOSSIBLE STAIRCASE
6.AK. POLYGONAL
PATH COVERING N x N LATTICE OF POINTS,
QUEEN'S TOURS, ETC.
6.AN. VOLUME OF
THE INTERSECTION OF TWO CYLINDERS
6.AO.1. PLACE FOUR POINTS EQUIDISTANTLY =
MAKE FOUR TRIANGLES WITH SIX MATCHSTICKS
6.AO.2. PLACE AN EVEN NUMBER ON EACH LINE
6.AP .
DISSECTIONS OF A TETRAHEDRON
6.AQ. DISSECTIONS
OF A CROSS, T OR H
6.AR. QUADRISECTED
SQUARE PUZZLE
6.AS. DISSECTION
OF SQUARES INTO A SQUARE
6.AS.1. TWENTY 1, 2, Ö5
TRIANGLES MAKE A SQUARE OR FIVE EQUAL SQUARES TO A SQUARE
6.AS.1.a. GREEK CROSS TO A SQUARE
6.AS.1.b. OTHER GREEK CROSS DISSECTIONS
6.AS.2. TWO (ADJACENT) SQUARES TO A SQUARE
6.AS.2.a. TWO EQUAL SQUARES TO A SQUARE
6.AS.3. THREE EQUAL SQUARES TO A SQUARE
6.AS.3.a. THREE EQUAL 'SQUARES' TO A HEXAGON
6.AS.4. EIGHT EQUAL SQUARES TO A SQUARE
6.AS.5. RECTANGLE TO A SQUARE OR OTHER
RECTANGLE
6.AT. POLYHEDRA
AND TESSELLATIONS
6.AT.2 STAR AND STELLATED POLYHEDRA
6.AT.5. REGULAR‑FACED POLYHEDRA
6.AT.6.a. TESSELLATING WITH CONGRUENT FIGURES
6.AU. THREE
RABBITS, DEAD DOGS AND TRICK MULES
MODERN VERSIONS OF THE THREE RABBITS PUZZLE
6.AV. CUTTING
UP IN FEWEST CUTS
6.AW. DIVISION
INTO CONGRUENT PIECES
6.AW.3. DIVIDING A SQUARE INTO CONGRUENT
PARTS
6.AW.4. DIVIDING AN L-TROMINO INTO CONGRUENT PARTS
6.AY. DISSECT 3A x 2B
TO MAKE 2A x 3B, ETC.
6.BA. CUTTING
A CARD SO ONE CAN PASS THROUGH IT
6.BB. DOUBLING
AN AREA WITHOUT CHANGING ITS HEIGHT OR WIDTH
6.BD. BRIDGE A MOAT WITH PLANKS
6.BE. REVERSE A
TRIANGULAR ARRAY OF TEN CIRCLES
6.BF.2. SLIDING SPEAR =
LEANING REED
6.BF.3. WELL BETWEEN TWO TOWERS
6.BF.5. TRAVELLING ON SIDES OF A RIGHT
TRIANGLE.
6.BG. QUADRISECT
A PAPER SQUARE WITH ONE CUT
6.BI. VENN DIAGRAMS FOR N SETS
6.BL. TAN-1
⅓ + TAN-1 ½ = TAN-1 1, ETC.
6.BM. DISSECT
CIRCLE INTO TWO HOLLOW OVALS
6.BN. ROUND PEG
IN SQUARE HOLE OR VICE VERSA
6.BP. EARLY MATCHSTICK
PUZZLES
6.BQ. COVERING A
DISC WITH DISCS
6.BR. WHAT IS A
GENERAL TRIANGLE?
6.BS. FORM SIX
COINS INTO A HEXAGON
6.BT. PLACING
OBJECTS IN CONTACT
6.BW. DISTANCES
TO CORNERS OF A SQUARE
7. ARITHMETIC &
NUMBER‑THEORETIC RECREATIONS
7.B. JOSEPHUS
OR SURVIVOR PROBLEM
7.E. MONKEY
AND COCONUTS PROBLEMS
7.E.1. VERSIONS WITH ALL GETTING THE SAME
7.F. ILLEGAL
OPERATIONS GIVING CORRECT RESULT
7.G.1. HALF + THIRD + NINTH, ETC.
7.H. DIVISION
AND SHARING PROBLEMS -- CISTERN PROBLEMS
7.H.1. WITH GROWTH -- NEWTON'S CATTLE
PROBLEM
7.H.3. SHARING UNEQUAL RESOURCES --
PROBLEM OF THE PANDECTS
7.H.4. EACH DOUBLES OTHERS' MONEY TO MAKE
ALL EQUAL, ETC.
7.H.5. SHARING COST OF STAIRS, ETC.
7.H.7. DIGGING PART OF A WELL.
7.I.1. LARGEST NUMBER USING FOUR ONES, ETC.
7.L.1. 1 + 7 + 49 + ... &
ST. IVES
7.L.2.b. HORSESHOE NAILS PROBLEM
7.L.2.c. USE OF 1, 2, 4, ... AS WEIGHTS, ETC.
7.L.3. 1 + 3 + 9 + ... AND OTHER SYSTEMS OF
WEIGHTS
7.M. BINARY
SYSTEM AND BINARY RECREATIONS
7.M.2.a. TOWER OF HANOI WITH MORE PEGS
7.M.4.b. OTHER DIVINATIONS USING BINARY OR
TERNARY
7.M.5. LOONY
LOOP =
GORDIAN KNOT
7.N.3. ANTI‑MAGIC SQUARES AND
TRIANGLES
7.P.1. HUNDRED FOWLS AND OTHER LINEAR
PROBLEMS
7.P.2. CHINESE REMAINDER THEOREM
7.P.3. ARCHIMEDES' CATTLE PROBLEM
7.P.5 . SELLING DIFFERENT AMOUNTS 'AT SAME
PRICES' YIELDING THE SAME
7.P.6. CONJUNCTION OF PLANETS, ETC.
7.Q.1. REARRANGEMENT ON A CROSS
7.Q.2. REARRANGE A CROSS OF SIX TO MAKE TWO
LINES OF FOUR, ETC.
7.R. "IF
I HAD ONE FROM YOU, I'D HAVE TWICE YOU"
7.R.1. MEN FIND A PURSE AND 'BLOOM OF
THYMARIDAS'
7.R.2. "IF I HAD 1/3
OF YOUR MONEY, I COULD BUY THE HORSE"
7.R.4. "IF I SOLD YOUR EGGS AT MY
PRICE, I'D GET ...."
7.S. DILUTION
AND MIXING PROBLEMS
7.S.1. DISHONEST BUTLER DRINKING SOME AND
REPLACING WITH WATER
7.S.2. WATER IN WINE VERSUS WINE IN WATER
7.V. XY = YX AND ITERATED EXPONENTIALS
7.X. HOW OLD
IS ANN? AND OTHER AGE PROBLEMS
7.Y. COMBINING
AMOUNTS AND PRICES INCOHERENTLY
7.Y.1. REVERSAL OF AVERAGES PARADOX
7.Z. MISSING
DOLLAR AND OTHER ERRONEOUS ACCOUNTING
7.AC. CRYPTARITHMS,
ALPHAMETICS AND SKELETON ARITHMETIC
7.AC.1. CRYPTARITHMS: SEND + MORE
= MONEY, ETC.
7.AC.2. SKELETON ARITHMETIC: SOLITARY SEVEN, ETC.
7.AC.3.a INSERTION OF SIGNS TO MAKE 100,
ETC.
7.AC.6. OTHER PAN‑DIGITAL AND SIMILAR
PROBLEMS
7.AC.7. SELF-DESCRIPTIVE NUMBERS, PANGRAMS,
ETC.
7.AD. SELLING, BUYING AND SELLING
SAME ITEM
7.AE. USE OF
COUNTERFEIT BILL OR FORGED CHEQUE
7.AH. MULTIPLYING
BY REVERSING
7.AH.1. OTHER REVERSAL PROBLEMS
7.AI.
IMPOSSIBLE EXCHANGE RATES
7.AJ.1. MULTIPLYING BY APPENDING DIGITS
7.AN. THREE
ODDS MAKE AN EVEN, ETC.
7.AO. DIVINATION
OF A PERMUTATION
7.AP. KNOWING SUM
VS KNOWING PRODUCT
7.AQ. NUMBERS IN
ALPHABETIC ORDER
7.AU. NUMBER OF
CUTS TO MAKE N PIECES
7.AV. HOW LONG
TO STRIKE TWELVE?
7.AZ.
DIVINATION OF A PAIR OF CARDS FROM ITS ROWS
7.BA. CYCLE OF
NUMBERS WITH EACH CLOSER TO TEN THAN THE PREVIOUS
7.BB. ITERATED
FUNCTIONS OF INTEGERS
7.BC. UNUSUAL DIFFICULTY
IN GIVING CHANGE
8.D. ATTEMPTS
TO MODIFY BOY‑GIRL RATIO
8.G. PROBABILITY
THAT THREE LENGTHS FORM A TRIANGLE
8.H.2. BERTRAND'S CHORD PARADOX
8.J. CLOCK
PATIENCE OR SOLITAIRE
9.A. ALL
CRETANS ARE LIARS, ETC.
9.B. SMITH
-- JONES -- ROBINSON PROBLEM
GENERAL STUDIES OF KINSHIP RELATIONS
9.E.1. THAT MAN'S FATHER IS MY FATHER'S SON,
ETC.
9.E.2. IDENTICAL SIBLINGS WHO ARE NOT TWINS
10.A. OVERTAKING
AND MEETING PROBLEMS
10.A.3. TIMES FROM MEETING TO FINISH GIVEN
10.A.6. DOUBLE CROSSING PROBLEMS
10.C. LEWIS
CARROLL'S MONKEY PROBLEM
10.D.1 MIRROR REVERSAL PARADOX
10.E.1. ARISTOTLE'S WHEEL PARADOX
10.E.2. ONE WHEEL ROLLING AROUND ANOTHER
10.E.4. RAILWAY WHEELS PARADOX
10.H. SNAIL
CLIMBING OUT OF WELL
10.I. LIMITED
MEANS OF TRANSPORT -- TWO MEN AND A BIKE, ETC.
10.K. PROBLEM
OF THE DATE LINE
10.L. FALLING
DOWN A HOLE THROUGH THE EARTH
10.N. SHIP'S
LADDER IN RISING TIDE
10.O. ERRONEOUS
AVERAGING OF VELOCITIES
10.U. SHORTEST
ROUTE VIA A WALL, ETC.
10.V. PICK UP
PUZZLES = PLUCK IT
10.X. HOW FAR
DOES A PHONOGRAPH NEEDLE TRAVEL?
10.Y. DOUBLE
CONE ROLLING UPHILL
10.AB. BICYCLE
TRACK PROBLEMS.
11.B. TWO
PEOPLE JOINED BY ROPES AT WRISTS
11.C. TWO BALLS
ON STRING THROUGH LEATHER HOLE AND STRAP
= CHERRIES PUZZLE
11.H. REMOVING
WAISTCOAT WITHOUT REMOVING COAT
11.H.1. REMOVING LOOP FROM ARM
11.I. HEART
AND BALL PUZZLE AND OTHER LOOP PUZZLES
11.K.1. RING AND SPRING PUZZLE
11.K.2. STRING AND SPRING PUZZLE
11.K.3. MAGIC CHAIN =
TUMBLE RINGS
11.K.6. INTERLOCKED NAILS, HOOKS, HORNS,
ETC.
11.L. JACOB'S
LADDER AND OTHER HINGING DEVICES
11.N. THREE
KNIVES MAKE A SUPPORT
11.Q. TURNING AN
INNER TUBE INSIDE OUT
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 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.
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.
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.
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 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.
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 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 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.
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 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.
[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; 11.N, 11.O, 11.P, 11.Q, 11.R,
11.S. (65 new sections)
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.
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.
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.
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,
̀.
^ 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.
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.
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.
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, 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 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.
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 Āryabhatīya-Bhāşya, 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. 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
75-77. 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 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 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; 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 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 95-97. 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
(1797-1840), 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 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
Shakespeare-Gesellschaft 42 (1906) 1-64 (with the 1631 ed on pp. 53-63). ??NYR.
[Santi 235 & 237.]
Borghi. Arithmetica. 1484.
Pietro
Borghi = Piero Borgo or Borgi (?? - ³1494). 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 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
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, 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.
c. 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 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., 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?
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 Kunst-Cabinet, 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.
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-in-Publication
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. 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 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, 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.
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
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?