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  -  seems interchangeable and I have used  ^  when different versions use both  ^  and  - , except when quoting a title or passage when I use the author's form.  [Smith, following Suter, uses  ^  for Arabic, but uses  -  for Indian.  Murray uses  -  for both.  Wieber uses  -  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 both Liège and Liége.  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  _  in Polish, and after  o  for  ø  in Scandinavian.

\        denoted accent grave.

^        denoted the circumflex,  ^,  in Czech, etc.; the overbar (macron)  -   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  _)  and the ogonek or Polish hook (Polish  a).

.         denoted the underdot in  h, k, n, r, s, t,  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  h. , etc., so not all of these may be converted.)  This mark vanishes when converted to WordPerfect.

*        denoted the overdot for  _, m, n,  in Sanskrit, Hindu, Arabic.  This vanishes over  m  and  n  in WordPerfect.

~       denoted the Spanish tilde  ~  and the caron or hachek  _,  in  _, š.  The breve is a curved version,  _,  of the same symbol and is essentially indistinguishable from the caron.  It may occur in Russian, but vanishes in WordPerfect.

_        denoted the underbar in  d, j, t.  This mark vanishes in WordPerfect.

'         denotes breathing marks in Arabic, etc.  There are actually two forms of this _ ayn    and alif/hamzah    _ but I didn't have two forms easily available and originally entered both as apostrophe  '  .  These normally occur between letters and I placed the  '  in the same space.  I have converted most of these.


          Commonly occurring words with diacritical marks are: Académie, arithmétique, bibliothèque, Birkhäuser, café, carré, école, Erdös, für, géomètre, géométrie, Göttingen, Hanoï _ in French only, ‑ième, littéraire, mathématique, mémoire, ménage, misère, Möbius, moiré, numérique, Pétersbourg, probabilités, problème (I have seen problêmes??), Rätsel, récréation, Sändig, siècle, société, Thébault, théorie, über, umfüllung.


          I have used  ??  to indicate uncertainty and points where further work needs to be done.  The following symbols after  ??  indicate the action to be done.

          *                  check for diacritical marks, etc.

          NX               no xerox or other copy

          NYS              not yet seen

          NYR   not yet read

          o/o              on order

          SP                check spelling

          Other comments may be given.



          ABBREVIATIONS OF JOURNALS AND SERIES.  See:  AMM,  CFF,  CM,  CMJ,  Family Friend,  G&P,  G&PJ,  HM,  JRM,  MG,  MiS,  MM,  MS, MTg,  MTr,  M500,  OPM,  RMM,  SA,  SM,  SSM  in Common References below.


          ABBREVIATIONS OF PUBLISHERS.  See:  AMS,  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.


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.



                              COMMON REFERENCES.


          NOTES.  When referring to items below, I will usually include the earliest reasonable date, even though the citation may be to a much later edition.  For example, I would say "Canterbury Puzzles, 1907", even though I am citing problem numbers or pages from the 1958 Dover reprint of the 1919 edition.  Sometimes the earlier editions are hard to come by and I have sometimes found that the earlier edition has different pagination _ in that case I will (eventually) make the necessary changes.

          Edition information in parentheses indicates items or editions that I have not seen, though I don't always do this when the later version is a reprint or facsimile.



Abbaco.                        See:  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.

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.]

Adams.  Puzzle Book.  1939.

                                    Morley Adams.  The Morley Adams Puzzle Book.  Faber & Faber, London, 1939.

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 (1872-1927).

                                    See:  A&N,  MUS,  3.B,  7.N.

al‑Karkhi.                     Aboû Beqr Mohammed Ben Alhaçen Alkarkhî [= al‑Karagi  = al‑Karaj_].  Untitled MS called Kit_b al-Fakhr_ (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 [Biblioteca Matematica Italiana, 1952] 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 Poggendorf), but the book gives no such indication.

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 u_ fragstucken begriffen.  Sunderlich was fortl unnd behendigkait in der Welsch_ Practica u_ Tolletn gebraucht wirdt / des gleychen fürmalss wider in Teützscher noch in Welscher sprach nie gedrückt.  durch Petrum Apian_ von Leyssnick / d Astronomei z_ Ingolstat Ordinari_ / 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, HB, 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:  Calandri,  Dell'Abbaco,  Gherardi,  Lucca 1754,  P. M. Calandri.

Aryabhata.                    _ryabhata (I) (476-  ).  _ryabhat_ya.  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 _ryabhat_ya-Bh_sya, 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  Âryabhatîya  of  Âryabhata; 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 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.]

Bakhshali MS.                The Bakhsh_l_ Manuscript, c7C.  This MS was found in May 1881 near the village of Bakhsh_l_, in the Yusufz__ 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 Bakhsh_l_ 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 Bakhsh_l_ 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 Bakhsh_l_ 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 Bakhsh_l_ 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. 

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.


                                    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, 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.]

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.

Bede, The Venerable (c672-735).  (Now St. Bede.)

                                    See:  Alcuin.

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.

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. Bestelmeier.  Magazin von verschiedenen Kunst‑ und andern nützlichen Sachen ....  [Toy catalogues.]  Nuremberg, 1801‑1803.

                    Nine issues 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 a 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.

                                    Bh_skara I.  _ryabhat_ya-Bh_sya.  629.  Critically edited, including an English Appendix of the numerical examples used, by Kripa Shankar Shukla.  Indian National Science Academy, New Delhi, 1976.  (Volume 2 of a three volume series devoted to the _ryabhat_ya (499) of Aryabhata (476-  ).)  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 (Mah_‑Bh_skar_ya) 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, N. L.  See:  BLW.

Bijaganita.                     Bîjaganita of Bhaskara II, 1150 (see Colebrooke).

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.

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.

BMC.           British Museum Catalogue (of books) to 1955.  c1963. 

BMC65.                        Supplement to the above for 1956‑1965.  c1968.

BNC.            Bibliothèque National, Paris.  Catalogue, 1897-1981.

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.


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 (in 4.A.1),  Hanky Panky,  The Sociable.


Borghi.  Arithmetica.  1484.

                                    Pietro Borghi  = Piero Borgo or Borgi (??-1494).  Qui comenza la nobel opera de arithmethica ne la qual se tracta tute cosse amercantia pertinente facta & compilata p Piero borgi da veniesia.  Erhard Ratdolt, Venice, 1484.  2 + 116 numbered ff.  This is the second commercial arithmetic printed in Italy and was reprinted many times.  See Rara 16-22.  This edition was reproduced in facsimile, with notes by Kurt Elfering, as: Piero Borghi; Arithmetica  Venedig 1484; Graphos, Munich, 1964;  in: Veröffentlichungen des Forschungsinstituts des Deutschen Museums für die Geschichte der Naturwissenschaften und der Technik, Reihe C _ Quellentexte und Übersetzunge, Nr. 2, 1965.

                      The 3rd ed of 1491 had a title: Libro dabacho.  From the 4th ed of 1501, the title was Libro de Abacho, so this is sometimes used as the title for the first editions also.  Rara indicates that the printing was revised to 100 numbered ff by the 4th ed. of 1491.  I have examined a 1509 ed. by Jacomo Pentio, Venice, ??NX.  This has 100 numbered ff, but the last three ff contain additional material, though Rara doesn't mention this until the 11th ed of 1540.  H&S discusses a problem and the folio in the 1540 ed is the same as in the 1509 ed.  The locations of interest in the 1509 ed. are c18ff before the corresponding locations of the 1484.

                    See also:  D. E. Smith; The first great commercial arithmetic; Isis 8 (1926) 41-49.


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 (39 UK, 37 US) and a Danish version, implying 86 English (49 UK, 37 US) versions, and 10 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.;  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 four are identical, except for a bit in the Prelude, 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.]

                    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.

                    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 an article on these books: H. Adrian Smith; Dick and Fitzgerald Publishers; Books at Brown 34 (1987) 108-114.]  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.]  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.]

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.


                                    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.

Buteo.  Logistica.  1559.

                                    Johannes Buteo (c1485-c1560).  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 presumbably 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 Medic_ de arimethrica opuscul_."  Lorenzo de Morgiani & Giovanni Thedesco da Maganza, Florence, 1491.  (There must have been a reprint of the 1491 ed as the Graves collection has two copies dated 1491, one with the folio number  c iiii  misprinted as  b iiii  and the other with it correct.  There was a reprint by Bernardo Zuchetta(??), 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); and  in Riccardi [Biblioteca Matematica Italiana, 1952, I, col. 208-209] (giving Bernardo Zuchecta, 1515).)  "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 [Biblioteca Matematica Italiana, 1952, I, col. 208-209] says there may have been a 1490 ed. by Bernardo Zuchecta.

Calandri.  Aritmetica.  c1500.

                                    Filippo Calandri.  Aritmetica.  c1500.  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 _ 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 catlogued 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.

Calandri.  Raccolta.  c1500.

                                    Filippo Calandri.  Una Raccolta di Ragioni.  In: Cod. L.VI.45, Biblioteca Communale di Siena, c1500.  Ed. by D. Santini.  Quaderni del Centro Studi della Matematica Medioevale, No. 4, Univ. di Siena, 1982.

Calandri.                       See also:  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 Antoniius 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 Artihmetical, 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.

Cassell's.  1881.

                                    Cassell's Book of In‑Door Amusements, Card Games, and Fireside Fun.  Cassell, Peter, Gilpin & Co., London, 1881; Cassell, London, 1973.  219pp, of which 211 are text.  [There was a companion volume: Cassell's Book of Sports and Pastimes.  The two were later 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 almost all the text of the Book of In‑Door Amusements, ..., reduced to 209pp and advanced by c745 pages.  Manson (qv) is a 1911 extension to 340pp.]

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. 

Charades, Enigmas, and Riddles.  1859.

                                    Charades, Enigmas, and Riddles.  Collected by a Cantab.  3rd ed., J. Hall and Son, Cambridge, 1860;  5th ed., Bell and Daldy, London, 1865.  BMC says 1st ed. was Cambridge, 1859 and 4th ed. was Bell and Daldy, London, 1862, both ??NYS.  Regarding the 3rd and 5th eds, most of the problems are identical, but the problem numbering and pagination are quite different.  It seems likely that the 3rd ed is identical to the 1st and the 5th ed is identical to the 3rd, so I will cite them as in the following example.  1859?: prob. 28, pp. 59 & 63;  1862?: prob. 573, pp. 107 & 154.

Chaturveda. Chaturveda Prthudakasvâmî.  Commentator on the Brahma‑sphuta‑siddhanta (qv), 860.  Some of these comments are taken from Bhaskara I in 629.  Shukla calls him Prth_daka, 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, HB.  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];  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 some more details.

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 Ji_ Zh_ng 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.)

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.  A second volume has recently appeared and is o/o.

Christopher II.  1998.

                                    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, 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 Villefr_che; 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.  1904.

                                    S. E. Clark.  Mental Nuts.  Can you Crack 'em?  A book of 100 Catch or Trick Problems.  Waltham Watches, Waltham, Massachusetts, (1897), rev. ed. 1904.  (This was an promotional item and jewelers would have their address printed on the cover.  My example has:  With the compliments of  J. H. Allen  Jeweler  Shelbina, Mo.  Thanks to Jerry Slocum for this.)  This actually contains 95 problems since numbers 68, 75, 76, 78, 84 are omitted.  It gives brief solutions.  It includes a number of early examples or distinct variants, which is remarkable for a promotional item.  I have entered 19 of the problems.  Another 25 are standard examples of topics covered in this work, but are not sufficiently early to be worth entering. 

                    Robert L. Helmbold has sent a photocopy of a revised edition of 1916 which is quite different in lay-out and content.  There is no promotional material in it.  It uses 71 of the 1904 problems, combined to form 69 problems and adds 31 new problems.  A few of the problems that are in 1904 and 1916 are much expanded in 1916.

                    I originally cited the 1904 problems as 1897 on the grounds that editions of this period do not change much, but having seen the 1916, I realise that one cannot assume the 1904 problems were in the 1897 ed.  So I will cite the actual dates.  Since neither version is paginated, I will just cite problem numbers, but 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.  c1370.

                                    Anonymous Italian MS, c1370, 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.

               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 H. (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.)

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 II).  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].


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.  Paolo dell'Abbaco (sometimes called Dagomari) (c1281-c1370).  Trattato d'Aritmetica.  c1370.  Codex Magliabechiano XI, 86 at Biblioteca Nazionale di Firenze.  Edited by Gino Arrighi, Domus Galilaeana, Pisa, 1964.  Arrighi gives some black & white reproductions of illustrations.  I examined this MS in Sep 1994 and found the illustrations are often lightly coloured and that Arrighi's illustrations were probably made from poorish photocopies _ the writing on the opposite side shows through much more in several of his illustrations than it does in the originals.  I have colour slides of 11 pages.  (Warren Van Egmond [New light on Paolo dell'Abbaco; Annali dell'Istituto e Museo di Storia della Scienza di Firenze 2:2 (1977) 3‑21] asserts this MS is a 15C compilation and doubts that it is due to dell'Abbaco.)  Smith, Rara, 435‑440 describes a different MS at Columbia, headed 'Trattato d'Abbaco, d'Astronomia e di segreti naturali e medicinali', which he dates c1339.  Van Egmond gives the title of this as 'Trattato di tutta l'arte dell'abacho'.

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.

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 Diophantus 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.            Dictionary of National Biography.  Ed. by Leslie Stephen.  1885‑1901 in 22 volumes.  With Supplements.  Compact Edition, 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 - II.  1971.

                                    Eric Doubleday.  Test Your Wits, Vol. 2.  Ace Publishing, NY, 1971.  [A good collection, with a number of novel variations of standard problems.]

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.

Dudeney, Henry Ernest (1857-1930). 

                                    See:  AM,  CP,  MP,  PCP,  536.


Eadon.  Repository.  1794.

                                    John Eadon.  The Arithmetical and Mathematical Repository, Being a New Improved System of Practical Arithmetic, in all its Branches; Designed for the Use of Schools, Academies, Counting-Houses, and Also for the Benefit of private Persons who have not the Assistance of a Teacher.  In Four Volumes.  Volume 1.  In Three Books.  Printed for the author, and sold by G. G. and J. Robinson, Paternoster Row, London, 1794.

Endless Amusement I.  c1818.

                                    Anonymous.  Endless Amusement; A Collection of Nearly 400 Entertaining Experiments  In various Branches of Science; ..., All the Popular Tricks and Changes of the Cards, ....  3rd ed.(?), Thomas Boys, London, nd [1825].  Frontispiece & TP are missing, but James Dalgety has inserted a photocopy of the TP of the 3rd ed.  [BMC lists  2nd ed., 1819?;  3rd ed., 1825?  BMC65 lists 1st ed. by Thorp & Burch, c1818;  2nd ed., c1820.  Toole Scott 255-267 lists  3rd ed., c1820;  4th ed., 1822;  5th ed., 1830;  6th ed., 1834;  7th ed., 1839.  Hall, BCB 116-123 are:  1st ed., c1815;  2nd ed., c1820;  3rd ed., c1820;  3rd ed., Philadelphia, 1822;  4th ed., c1825;  5th ed., c1830;  6th ed., 1834;  Philadelphia, 1847.  Heyl 110-115, 121 are  1819;  2nd & 3rd ed., M. Carey & Sons, Philadelphia, 1821 & 1822;  3rd ed, C. Tilt, London, 1825;  Borradaile, NY, 1831;  Henry Washburne & Thomas Tegg, London, 1839;  Lea & Blanchard, Philadelphia, 1847.  Almost all of these are listed as 2 + 216 pp, so the editions are probably all the same as the 1st ed., except that Hall notes that the 1st ed. title is slightly different: Endless Amusement; A Collection of Upwards of 400 Entertaining and Astonishing Experiments.  Among a Variety of other Subjects, are Amusements in Arithmetic, Mechanics, Hydraulics ....  All the Popular Tricks and Changes of the Cards, ...,  and Heyl gives a similar title for the 1825 ed. and the 1831 NY ed. has some variations.  Christopher 330-338 are  2nd ed., Philadelphia, 1821;  3rd ed., c1820;  3rd ed., Philadelphia, 1822;  4th ed., c1822;  4th ed., c1822 (slightly different to preceding;  5th ed., c1830;  6th ed., 1834;  7th ed., 1839;  Philadelphia, 1847.  C&B list it under Thorp and Burch, the publishers, with no dates.]

Endless Amusement II.  1826?

                                    Anonymous.  A Sequel to the Endless Amusement, Containing Nearly Four Hundred Interesting Experiments, In various Branches of Science, ..., to Which are Added, Recreations with cards, and a Collection of Ingenious Problems.  Thomas Boys, London, nd [1826?].  Pp. 203-216 are missing, but James Dalgety has inserted photocopies.  [BMC lists one ed., 1826?  Hall, BCB 252 gives c1825.  Heyl says this refers to Thomas Boys ... and Thorp and Burch, London (1925).  Toole Stott 623 gives 1825.]

                                    = Anonymous.  The Endless Amusement.  New Series Containing Nearly Four Hundred Interesting Experiments, ... (as above).  Thomas Tegg & Sons, London, 1837.  Angela Newing has provided a photocopy of the interesting parts of this and it is virtually identical to the 1826? ed., though it has been reset, resulting in an extra word fitting on some lines, and it has rather poorer pictures.  One problem has been replaced by another.  [Heyl 122.]

                                    = Anonymous.  A Companion to the Endless Amusement.  James Gilbert, London, 1831.  [Toole Stott 172 says this is a reprint of A Sequel ..., from the same type, with new TP, and this is clear from examination of the example Wallis 187.5 COM.  Heyl 66 dates it as c1820?]

                                    Some of the material is taken from Badcock.


van Etten.  1624.           The bibliography of this book is very complicated.  I have now made a separate 13pp bibliogrphy listing 40 French editions, 5 English editions, 4 Latin editions and 6 Dutch editions _ a total of 55 editions from 1624 to 1706.  This is part of my The Bibliography of Some Recreational Mathematics Books.

                    This book has traditionally been attributed (since 1643) to Père Jean Leurechon, SJ (c1591-1670), who was probably van Etten's university teacher, but the book specifically names van Etten and there seems to be very little real evidence for Leurechon's authorship.  Trevor Hall's booklet and chapter are a substantial study of this question and he concludes that there is no real reason to doubt van Etten's authorship, though he may well have had help or inspiration from his teacher.  Hall has also shown that van Etten and his uncle, the book's dedicatee, were real people.  (Toole Stott 429‑431 dismisses Hall's work as a result of completely misunderstanding it!)  However, the book was amended, revised and translated many times, so that versions may occur under the following names:  Hendrik van Etten;  Jean Leurechon;  D.H.P.E.M.  = Denis (or Didier) Henrion, professeur en mathématique (or Professeur ès Mathematiques), a pseudonym of Clément Cyriaque de Mangin, who also called himself Pierre Hérigone;  Claude Mydorge;  Caspar (or Gaspar) Ens;  Wynant van Westen;  William Oughtred;  William Leake; not to mention Anonymous and versions of the title _ I have found it under Recreations or Récréations and under Vermakelijkheden.  E.g. Lucas, RM1, 239-240, has 7 entries for this book under five different authors and twice under Récréations.  Hall's booklet and chapter are the most detailed study of this book and form the basis of the following discussion, supplemented by the standard catalogues and personal inspection of about a half of the French and English editions _ generally after 1630.


                    Henrik van Etten.  Recreation Mathematicque.  Composee de Plusieurs Problemes Plaisants et Facetieux.  En faict d'Arithmeticque Geometrie, Mechanicque, Opticque, & autres parties de ces belles sciences.  Jean Appier Hanzelet, Pont‑a‑Mousson, 1624 [taken from facsimile of the 1626 ed.].  155pp., ??NYS.

                    2nd ed., 1626, ibid.  = recent facsimile with no details, but with 'Pont à Mousson  13 ‑ 10 ‑ 54' written inside the back cover.  [An apparently identical copy at the Museum of the History of Science, Oxford, has a small insert saying it was reissued by La Compagnie de Pont-à-Mousson, printed by l'Imprimerie Berger-Levrault, nd.].  91 problems on xiv + 144 = 158pp.  [According to Hall, OCB, this edition has only three extra pages, so I have listed the 1624 as 155pp.  A 1630 edition omits parts V and VI of problem 91 which may correspond to these 3 pages.  The BMC says there was another edition in Pont-à-Mousson in 1629.] 


                    After the two Hanzelet editions, there were three editions in Paris in 1626, by Rolet Boutonné (2nd ed.), by Antoine Robinot (2nd ed.) and by Jean Moreau (3rd ed.).  These appear to all have added two further problems to van Etten's 91 (though this may just be a renumbering of parts of prob. 91??) and included Examen (notes) after some problems, signed D.A.L.G.  (Eneström, op. cit. under Leurechon/van Etten in 1, says that though D.A.L.G. was used by Mydorge on one of his other books, it had been conjectured that this stood for  Des Argues Lyonnais Girard (or Géomètre).  Eneström can find no real evidence for this and feels that Mydorge is the most likely person.)  NUC indicates the Robinot had further comments signed D.H.P.E.M., later identified as Denis (or Didier) Henrion Professeur En Mathématique (though Henrion is a pseudonym of Clément Cyraique de Mangin!).  In the next few years, editions appeared in Paris, Rouen and Lyon.  In 1627, Boutonné issued a '4th ed.' with "Nottes sur les recreations mathematiques ... Par D. H. P. E. M." and the D.A.L.G. notes may have been omitted.  In 1627, Claude Rigaud & Claude Obert, Lyon, issued a version with 9pp of Additions relating to 7 of van Etten's problems _ this may be the first to put the illustrations in the text rather than on separate sheets of 8 figures.

                    In 1628, Charles Osmont, Rouen, issued a version augmented by Henrion and Mydorge: Récréations mathématiques ... 1re et 2de partie.  La 3e partie contient un recueil de plusieurs gentilles et récréatives inventions de feux d'artifice ... avec des augmentations dues à Denis Henrion et à Cl. Mydorge.  Part 1 was van Etten's 91 problems, possibly with parts V & VI of prob. 91 omitted, apparently omitting the Examen.  Part 2 had 45 new problems, presumably by Mydorge [and/or Henrion??].  Part 3 is an independent treatise on fireworks which Hall attributes to Hanzelet.  This edition was reissued in Rouen by various publishers in 1629, 1630, 1634,

                    In 1630, Boutonné and/or Robinot (their printing seems indistinguishable and volumes often have parts from both of them) issued an extended version in four parts, titled Examen du Livre des Recreations Mathematiques, stated to be by Mydorge.  Part 1 was van Etten's 91 problems, with parts V & VI of prob. 91 omitted, with Examen signed D.A.L.G.  Part 2 had its own TP and had 45 new problems, presumably by Mydorge and/or Henrion.  Part 3 had its own TP, but doesn't state the publisher, and is the independent treatise on fireworks which Hall attributes to Hanzelet.  Part 4 again has its own TP and is Nottes [sic] sur les Recreation Mathematiques by D.H.P.E.M. and are additions to 27 of van Etten's problems.  The book is also described as 3 parts with the Nottes, but Parts 2 and 3 are consecutively paged, leading to some descriptions of the book as being in 3 parts.  The parts appear to have been issued separately as they sometimes are catalogued separately.  I have photocopy of most of this ed.  This most extended form was reissued by various publishers in Paris: 1634, 1638, 1639, 1649? and in Rouen: 1639 (two publishers), 1643. 

                    In 1642, Claude Prost, Lyon, issued a version titled Recreations Mathematiques, with no author, in three parts.  The Nottes seem to be simply omitted.  This form was reissued in Lyon: 1653, 1658, 1669, 1680.

                    In 1659, Cardin Besonge, Paris, issued  Les Récréations mathématiques, avec l'examen de ses problèmes en arithmétique, géométrie, ....  Premièrement reveu par D. Henrion, depuis par M. Mydorge, et tout nouvellement corrigé et augmenté, 5e et dernière édition.  The Nottes are incorporated in the text (or perhaps omitted??).  The entire text is consecutively page-numbered.  Reissued in Paris: 1660, 1661 and in Rouen as the 6th ed.: 1663?, 1669 (four publishers).


                    The 1630 Paris ed. and the 1626 ed. have the same problem numbers for the first 91 problems, as do almost all French editions.  I will cite the problem number and the pages of the 1626 ed.  I will add reference to the 1630 Paris ed., when the latter has additional information.  Only one of the additional problems in part 2 (prob. 7) is of any interest to us, but several of Henrion's Nottes give corrections, extensions, additional references and even additional problems.  I didn't find any of the D.A.L.G. notes of any interest.


   English editions.

                    Mathematicall Recreations.  Or a Collection of sundrie [1653 has: many] Problemes, extracted out of the Ancient and Moderne Philosophers, as secrets in nature, and experiments in Arithmeticke, Geometrie, Cosmographie, Horologographie, Astronomie, Navigation, Musicke, Opticks, Architecture, Staticke, Machanicks, Chimestrie, Waterworkes, Fireworks, &c.  Not vulgarly made manifest untill this time: Fit for Schollers, Students, and Gentlemen, that desire to know the Philosophicall cause of many admirable Conclusions.  Usefull for others, to acuate and stirre them up to the search of further knowledge; and serviceable to all for many excellent things, both for pleasure and Recreation.  Most of which were written first in Greeke and Latine, lately compiled in French, by Henry Van Etten Gent.  And now delivered in the English tongue, with the Examinations, Corrections, and Augmentations.  Printed by T. Cotes for Richard Hawkins, London, 1633.  328pp.  (This ed. is 'excessively rare'.) 

                    Reissued by William Leake, London: 2nd ed., 1653; (1667(??)); 1674.  344pp.  [Hall, OCB, says the 2nd ed. is similar to the 1633 edition, but with an extra 16pp description (of 1636) of some dials by Oughtred (which led to the book or the translation often being attributed to Oughtred).  Hall also states that the English editions are based on the Rouen ed. of 1628.  Sadly some interesting problems were omitted in the English, leading to confusion in plate numbers.  However, I have just noticed that Prob. 63 is about two pages longer than the corresponding Prob. 70 of the French editions.]  The 1633, 1653 and 1674 editions are identical except for the additional English material in the later editions.  I will add citations to the English editions in parentheses.  I now have an imperfect copy of the 1674 ed, covers missing and lacking the Frontispiece and pp. 273-282 and later material.  Heyl 311 is a 1753 ed., which must be an error for 1653.

                    Leybourn, qv, takes several sections directly from the English editions.


   Latin editions.

                    In 1628(??), Caspar (or Gaspar) Ens made a Latin translation but added some other material, e.g. 49 problems from Alcuin.  I have only studied the 1636 ed. carefully.

                    Thaumaturgus Mathematicus, Id est, Admirabilium Effectorum e Mathematicarum Disciplinarum Fontibus Profluentium Sylloge.  Casparo Ens L. Collectore & Interprete.  1628.  [Taken from 1636 TP.  There is some doubt whether the 1628 edition exists!]

                    Reissued in 1636 and 1651.  It has 89 of van Etten's problems (omitting 38 & 46) and adding 25 new problems, with some numbering errors so the last is numbered 113.  This is followed by 55 problems of Alcuin, using the Bede version of 56 problems, but omitting 18.

                    Thaumaturgus mathematicus Gasparo Ens lectore collectore, & interprete, Nunc denuò Correctus, & Auctus.  Apollonius Zambonus, Venice, 1706.  113 problems + 49 from Alcuin (check??).  There are some differences between this and the 1636 ed.

                    [MUS #30 gives Köln, 1651, and further editions, saying that the first ed. of 1628 is only a translation of van Etten.]


   Dutch editions.

                    In 1641, Wynant van Westen translated van Etten into Dutch.  The title is: Het eerste [- derde] deel van de Mathematische vermaecklyckheden.  Te samen ghevoeght van verscheyden ghenuchlijcke ende boertige werckstucken, soo uyt arithmetica, geometria, astronomie, geographia, cosmographia, musica, physica, optica, catoptrica, architectonica, sciotetica, als uyt andere ongehoorde mysterien meer.  Ghetranslateert uyt het fransch in nederduytsche tale: ende verrijckt, vermeerdert, ende verbetert met verscheyden observatien ende annotatien, dienende tot onderrichtinge van eenige duystere questien, ende mis-slaghen in den franschen druck.  Door Wynant van Westen .... op nieus oversien verbetert.  Jacob van Biesen, Arnhem, 1641.  3 parts with separate title pages and pagination, perhaps in 3 vols, but later in 1 vol. 

                    This was reissued:  Van Biesen, Arnhem, 1641, ??, 1644, 1662, 1671-72; Lootsman and Jacobsz, Amsterdam, 1673.  I haven't examined any of these.


Euler.  Algebra.

                                    Leonard Euler (1707-1783).  Vollständig Anleitung zur Algebra.  Royal Academy of Sciences at Petersburg, 1770.  [A Russian translation appeared in 1768.]  Translated into French by John III Bernoulli, with additions by Bernoulli and La Grange (pp. 463-593 here), 1774.  Translated from French into English, with further notes, by Rev. John Hewlett, with a Memoir of Euler by Francis Horner [Horner actually did the translation; Hewlett edited it.], (1797),  5th ed., Longman, Orme, and Co., London, 1840.  Reprinted, with Introduction by C. Truesdell (1972), omitting 4 pp of Horner, Springer, NY, 1984 [hidden on back of title page].  I will cite part, section, chapter, article and the pages from the Springer ed.  (Part II has no sections.)  Unfortunately these numbers seem to have little connection with other editions.  [Though most of the recreational material in Euler is much older than Euler, I have included it as a representative 18C text.]


Family Friend.               The Family Friend.  This was a magazine founded by Robert Kemp Philp in 1849.  The dating is awkward _ vol. 1 is dated 1850 on the cover, but the Preface is dated 15 Nov 1849 and refers to the success of the past year, when it appeared monthly.  It also says the magazine will henceforth appear twice a month with two volumes per year, due on the first of June and December.  The Gardening section of vol. 1 goes from Jan to Dec.  The Preface of Vol. 2 is dated 10 Jun 1850 and its gardening section covers Jan - Jun.  The Preface of Vol. 3 is dated 15 Dec 1850 and its Gardening section goes Jul - Dec.  BMC shows Philp left in 1852 and the magazine continued with two volumes per year through a fifth series, ending in 1867, then restarted with one volume a year from 1870 until 1921.  I have vols. 1 - 3 & the second half of 1858, which is dated 1858-9, but appears to be Jul-Dec.  None of the text is signed.  At the back of volumes are included answers to correspondents.  The puzzles are often identical to those in The Magician's Own Book or The Illustrated Boy's Own Treasury, etc.

FHM.           Graham Flegg, Cythia Hay & Barbara Moss _ see under Chuquet.

Fibonacci.                     Leonardo Pisano, called Fibonacci (c1170->1240).  Liber Abbaci.  (1202); 2nd ed., 1228.  In: Scritti di Leonardo Pisano; vol. I, ed. and pub. by B. Boncompagni; Tipografia delle Scienze Matematiche e Fisiche, Rome, 1857.  The title pages give 'abbaci', but the text begins 'Incipit liber Abaci ... Anno MCCII.'  Both forms are used, sometimes even in the same article _ e.g. Loria's biographical article, see in Section 1.

                    Richard E. Grimm is working on a critical edition of this and he has kindly given me some details.  There are 15 known MSS.  Six of these consist of 1½ to 3 chapters only; five of the others lack Chapter 10 and the second half of Chapter 9; one lacks Chapter 10 and one lacks much of Chapter 15, leaving two essentially complete texts.  The last four MSS mentioned are the most important:  Siena L.IV.20, c1275, lacking much of Chap. 15, "the oldest and best";  Siena L.IV.21, c1465, which includes much other material from later writers, so it is at least double the size of L.IV.20;  Vatican Palatino #1343, end of 13C, lacking Chap. 10;  Florence Bibl. Naz. Conventi Soppressi C. 1. 2616, early 14C, "handsome but frequently badly faded" so "that a later hand found it necessary to rewrite what he saw there."  When I examined it in Sep 1994, the black ink was indeed sometimes badly faded but the numbers were in a clear red _ perhaps these are what was rewritten??  L.IV.20 has the beginning sentence ending "et correctus ab eodem a MCCXXVIII", but Grimm says all the others are also of the 1228 ed.  Sadly, I heard in Aug 1998 that Grimm has Alzheimer's disease and is now in a nursing home.

                    Boncompagni used only one MS, then denoted Codex Magliabechiana, C. I, 2616, Badia Fiorentina, no. 73, now Conventi Soppressi, C. I. 2616, the badly faded fourth MS described above. 

                    In Sep 1994 and Mar 1998, I examined Siena L.IV.20 and 21 and Conv. Soppr. C.1.2616.  I have slides of the Incipit & Fibonacci numbers from all of these and some other material.

Fibonacci.  Flos  and  Epistola.

                                    Leonardo Pisano, called Fibonacci.  MS of c1225 which begins "Incipit flos Leonardi bigolli pisani ...", Biblioteca Ambrosiana, Milan, E. 75.  In: Scritti di Leonardo Pisano, vol. II, ed. and pub. by B. Boncompagni, Rome, 1862, pp. 227-252.

                    Part of the MS has a separate heading: "Epistola suprascripsit Leonardi ad Magistrum Theodorum phylosophum domini Imperatoris" and is sometimes considered a separate work.  It occupies pp. 247-252 of the printed version.  For an English description, see:  A. F. Horadam; Fibonacci's mathematical letter to Master Theodorus; Fibonacci Quarterly 29 (1991) 103-107.

                    Italian translation (including the Epistola) and commentary: E. Picutti; Il 'Flos' di Leonardo Pisano; Physis 25 (1983) 293-387.

Folkerts, Menso.           See:  Alcuin.

Frikell, Wiljalba (1818 (or 1816) - 1903).  (The given name Gustave sometimes occurs _ I thought Gustave might be a son of Wiljalba, but the son was named Adalbert (  -1889) and his name was pirated by a clumsy imposter in England.)

                                    See the discussion at:  Book of 500 Puzzles,  Boy's Own Conjuring Book,  Hanky Panky,  Magician's Own Book,  The Secret Out (in 4.A.1).  Frikell was a noted conjuror of the time and his name has been associated with the UK versions of these books, but there is no evidence he had anything to do with them.  I think Gustave was his son, though some entries seem to imply it is another of Frikell's names.  The Art of Amusing, by Frank Bellew, Hotten, London, 1866?, op. cit. in 5.E, has a note on the back of the TP saying The Secret Out is a companion volume, just issued, by Hermann Frikell.  C&B, under  Williams, Henry Llewellyn ("W. Frikell")  lists:  Hanky Panky;  Magician's Own Book, London & New York;  (Magic No Mystery);  The Secret Out  and says to also see Cremer.


Gamow & Stern.  1958.

                                    George Gamow & Marvin Stern.  Puzzle‑Math.  Macmillan, London, 1958.


Gardner.                       Martin Gardner (1914-  ).  Many references are to both his SA column, cited by (month & year), e.g. SA (Mar 1982), and to the appearance of the column as a chapter in one of his books, abbreviated as shown below.  In general, I will only give the chapter reference as the various editions and translations are differently paginated.  Answers, comments and extensions appeared in succeeding issues of SA, usually in Gardner's column, but sometimes in the Letters.  All this material is collected in the book chapter, sometimes by rewriting of the article, sometimes as notes or an Addendum at the end of the chapter.  Since many years usually passed before the book version, the Addenda often contain material that never appeared in SA, as well as references to work done as a result of the SA article.  I have not tried to enter all of Gardner's references here, so anyone interested in a topic that Gardner has considered should consult the book version of Gardner's column.  Currently some of the earlier books are being reissued in new editions, with further extensions and updating.  See also the next entry.

                    For years from at least 1950, SA appeared in two volumes per year, each of six issues.  In year  1950 + n,  vol. 182 + 2n  covers  Jan-Jun  and  vol. 183 + 2n  covers  Jul-Dec.

   1st Book                    The Scientific American Book of Mathematical Puzzles and Diversions.  Simon & Schuster, 1959.

             UK version: Mathematical Puzzles and Diversions from Scientific American.  Bell, London, 1961; Penguin (without the words 'from Scientific American'), 1965.

   2nd Book   The Second Scientific American Book of Mathematical Puzzles and Diversions.  Simon & Schuster, 1961.

             UK version: More Mathematical Puzzles and Diversions from Scientific American.  Bell, London, 1963.  Penguin (without the words 'from Scientific American'), 1966.  (The UK versions omit Chapter 20: "The Mysterious Dr. Matrix".  The dust wrapper of the HB has a sentence referring to this chapter which has been blacked out.  ??)

   New MD                    Martin Gardner's New Mathematical Diversions from Scientific American.  Simon & Schuster, 1966.

   Unexpected                The Unexpected Hanging and Other Mathematical Diversions.  Simon & Schuster, 1969.

             UK version: Further Mathematical Diversions.  Allen & Unwin, London, 1970; Penguin, 1977.

   6th Book                    Martin Gardner's Sixth Book of Mathematical Games from Scientific American.  Freeman, 1971.

   Carnival                     Mathematical Carnival.  Knopf, NY, 1975; Penguin, 1978.

   Magic Show                Mathematical Magic Show.  Random House, NY, 1978.

   Circus                        Mathematical Circus.  Knopf, NY, 1979.

   Wheels                      Wheels, Life and Other Mathematical Amusements.  Freeman, 1983.

   Knotted                     Knotted Doughnuts and Other Mathematical Entertainments. Freeman, 1986.

   Time Travel               Time Travel and Other Mathematical Bewilderments.  Freeman, 1988.

   Penrose Tiles              Penrose Tiles to Trapdoor Ciphers.  Freeman, 1989.

   Fractal                       Fractal Music, Hypercards and More ....  Freeman, 1992.

   Last           The Last Recreations  Hydras, Eggs, and Other Mathematical Mystifications.  Copernicus (Springer), NY, 1997.  ??NYR.

   Magic Numbers          The Magic Numbers of Dr. Matrix.  Prometheus, Buffalo, 1985.  Chaps. 1-18 previously appeared as: The Incredible Dr. Matrix; Scribners, NY, 1976.  Chaps. 1‑7 & 9 previously appeared as: The Numerology of Dr. Matrix; Simon & Schuster, NY, 1967.  In contrast to his other books above, the answers and comments occur at the end of this book instead of following the original articles.

Gardner.  MM&M.  1956.

                                    Martin Gardner.  Mathematics, Magic and Mystery.  Dover, NY, 1956.


General Trattato.  1556.

                                    Nicolo Tartaglia (c1499-1557).  (La Prima Parte del) General Trattato di Numeri et Misure.  Curtio Troiano, Venice, 1556.  (Modern Italian spells his given name as Niccolò, but it appears as Nicolo on the title page.)  Six parts actually appeared in 1556-1560.  All references are to Part 1.  Unless otherwise specified, reference is to Book 16 (of Part 1), but I also have references to Books 12 and 17.  CAUTION _ the running head in Book 17 says Libro Decimosesto for several pages before changing to Libro Decimosettimo.  Since it is hard to find the beginnings of books, this can cause confusion.  See Rara 275-279.

                    In 1578, Guillaume Gosselin produced an annotated translation of parts 1 & 2 into French as: L'Arithmetique de Nicolas Tartaglia.

Ghaligai.  Practica D'Arithmetica.  1521.

                                    Francesco Ghaligai.  Practica D'Arithmetica di Francesco Ghaligai Fiorentino.  Nuovamente Rivista, & con somma Diligenza Ristampata.  I Giunti, Florence, 1552.  Smith, Rara, says that this is identical to the first (Latin?) edition by Bernardo Zucchetta, Florence, 1521, except that edition was titled Summa De Arithmetica, so I will date the entries as 1521.  See Rara 132.

Gherardi.  Libro di ragioni  and  Liber habaci.  1327 & 1327?

                                    Paolo Gherardi.  Two Italian MSS in Codici Magliabechiani Classe XI, no. 87 & 88 in Bib. Naz. di Firenze.  The first is dated 1327.  The second is undated, but clearly of a similar date which I denote 1327?.  Transcribed by Gino Arrighi; Collana di Storia della Scienza e della Tecnica, No. 2; Maria Pacini Fazzi, Lucca, 1987.  See also:  Warren Van Egmond; The earliest vernacular treatment of algebra: the Libro di ragioni of Paolo Gerardi (1328); Physis 20 (1978) 155-189.  Van Egmond notes that the date of 30 Jan 1327 is in our year 1328.  He doubts whether Liber habaci is actually by Gherardi.  His study is concerned with the quadratic and cubic equations and hence of little interest to us.

Good, Arthur.               See:  Tom Tit.

Gori.  Libro di arimetricha.  1571.

                                    Dionigi Gori.  Libro di arimetricha.  1571.  Italian MS in Biblioteca Comunale di Siena, L. IV. 23.  ??NYS.  Extensively quoted and discussed in: R. Franci & L. Toti Rigatelli; Introduzione all'Aritmetica Mercantile del Medioevo e del Rinascimento; Istituto di Matematica dell'Università di Siena, nd [1980?].  (Later published by Quattroventi, Urbino, 1981.)  (I will quote Gori's folios and also give the pages of this Introduzione.) 

Graves.                         The Graves Collection of early mathematical books at University College London.

Guy, Richard K.            See:  Winning Ways.

G&P.            Games & Puzzles.  The first version ran from 1972 through 1981.  The second series started in Apr 1994 and finished with No. 16 in Jul 1995.

G&PJ.           Games and Puzzles Journal.  Successor to Chessics.  Ran through 12 issues, Sep 1987 _ Dec 1989, then restarted intermittently in May 1996.


Hall.  BCB.  1957.

                                    Trevor H. Hall.  A Bibliography of Books on Conjuring in English from 1580 to 1850.  (Carl Waring Jones, Minneapolis, 1957); Palmyra Press, Lepton, W. Yorks., 1957.  323 entries.  I will cite item numbers.  A Supplement is in Hall, OCB.  See Heyl for a list of items not in BCB.

Hall.  OCB.  1972.

                                    Trevor H. Hall.  Old Conjuring Books.  Duckworth, London, 1972.  This covers books in English up through 1850 and it includes a Supplement to his BCB and should be checked for further information on items in BCB.  This contains 39 new items and additional notes to 36 previous items.  New items are given interpolated item numbers, e.g. 24.5.  OCB also includes his booklet on van Etten, see Section 1 below.

Hanky Panky.  1872.

                                    Hanky Panky  A Book of Easy and Difficult Conjuring Tricks  Edited by W. H. Cremer, Jun.  (John Camden Hotten, London, 1872 [BMC & Toole Stott 193, listed under Cremer, while C&B, under Cremer, give London, 1872]; Hotten was succeeded by Chatto & Windus c1873 and they produced several editions [NUC has 1872, Toole Stott 1017 & Shortz have 1875]).  My copy says: A new edition with 250 practical illustrations.  John Grant, Edinburgh, nd [Toole Stott 1016 gives 1874; NUC gives 1875?  Christopher 235, under Cremer, is c1890.  NUC says it is also attributed to Henry Llewellyn Williams, but their entry under Williams says 'supposed author'.  C&B also list it under Williams.  (This has been attributed to Frikell, but Toole Stott doubts that Frikell had anything to do with this.  I may put this under Cremer.)

HB.XI.22.  1488.

                                    Stuttgart Landesbibliothek German MS HB.XI.22, 1488.  Brief description by E. Rath; Über einen deutschen Algorismus aus dem Jahr 1488; Bibl. Math. (3) 14 (1913‑14) 244‑248.

Heath, Sir Thomas L.

                                    See:  Diophantos, HGM.

Heyl.  1963.  Edgar Heyl (1911-1993).  A Contribution to Conjuring Bibliography.  English Language  1580 to 1850.  Edgar Heyl conjuring books, Baltimore, 1963.  Facsimile edition of 100 copies by Maurizio Martino Fine Books, PO Box 373, Mansfield Center, Connecticut, 06250, nd [1998?].  360 entries + appendix of 14 more, almost all not in Hall, BCB.

HGM.  1921.                Sir Thomas L. Heath.  A History of Greek Mathematics, 2 vols.  (OUP, 1921); corrected reprint, Dover, 1981.

HM.                             Historia Mathematica.

Hoernle, A. F. Rudolf.

                                    See:  Bakhshali MS.

Hoffmann.  1893.          Professor Louis Hoffmann [pseudonym of Angelo John Lewis (1839‑1919)].  Puzzles Old and New.  Warne, London, 1893.  Reprinted with Foreword by L. E. Hordern; Martin Breese, London, 1988.  Hordern published a limited edition of "The Hordern Collection of Hoffmann Puzzles  1850‑1920", in 1984, which gives colour photos of examples from his collection.  I have occasionally cited these pictures _ but these citations will be replaced by the following.  Hordern later produced a corrected edition of Hoffmann with colour illustrations as: Hoffmann's Puzzles Old & New; published by Hordern, 1993.

                                    See also:  Tom Tit.

Hordern, L. Edward.

                                    See under Hoffmann and in 5.A.

HPL.            The Harry Price Library, Senate House, University of London  OR  its catalogues. 

                                    Harry Price (1881-1948).  Short-Title Catalogue and Supplementary Catalogue of Works on Psychical Research, Spiritualism, Magic, Psychology, Legerdemain and Other Methods of Deception, Charlatanism, Witchcraft, and technical Works for the Scientific Investigation of Alleged Abnormal Phenomena from Circa 1450 A.D. to 1935 A.D.  Compiled by Harry Price.  (The first part was originally  ... to 1929 A. D.; Proc. National Lab. of Psychical Research 1:2 (1929); National Laboratory of Psychical Research, London, 1929.  The second part was originally: Short-Title Catalogue of the Research Library, for 1472 A.D. to the Present Day; Bull. Univ. of London Council for Psychical Investigation 1 (1935); Univ. of London Council for Psychical Investigation, 1935.)  New Introduction by R. W. Rieber and Andy Whitehead  With an appendix entitled "The St. Louis Magnet" (which originally appeared in 1845) by T. J. McNair and J. F. Slafter.  Da Capo Press (Plenum), NY, 1982.  NOTE: The works listed here are now in the Harry Price Library, though the editors have added 36 items in their Introduction.

Hutton.  A Course of Mathematics.  1798?

                                    Charles Hutton (1737-1823).  A Course of Mathematics.  Composed for the Use of the Royal Military Academy.  (In 2 vols, plus a third, 1798-1811.)  A New Edition, entirely Remodelled.  By William Ramsay, B. A., Trinity College, Cambridge.  T. T. & J. Tegg, London, and Richard Griffin & Co., Glasgow, 1833 (in one volume).  8 + 822 pp.

Hutton-Rutherford.  A Course of Mathematics.  1841?

                                    Charles Hutton.  A Course of Mathematics,  Composed for the Use of The Royal Military Academy.  By Charles Hutton, LL.D., F.R.S., Late Professor of Mathematics in that Institution.  A new and carefully corrected Edition, Entirely Re-modelled, and Adapted to the Course of Instruction Now Pursued in the Royal Military Academy.  By William Rutherford, F.R.A.S.  Royal Military Academy.  William Tegg, London, 1857 [Preface dated Nov 1840, so probably identical or nearly identical to the 1841 ed].  8 + 895 pp.

                    [Two volume versions:  1798/1801;  3rd, 1800/1801;  4th, 1803/1804;  5th, [1810, NUC gives 1806- and 1807];  6th, [1810-1811 _ NUC].  Three volume versions _ apparently the early forms were just the earlier 2 volumes with an additional third vol:  6th, 1811;  1813;  7th, 1819-1820;  8th, 1824;  9th, 1827/1828.  10th ed by Olinthus Gregory, in 3 vols., 1827-1831.  New ed by William Ramsay in one vol., 1833; 1838.  11th ed by Gregory in 2 vols, 1836-1837.  12th ed, revised by Thomas Stephens Davies, 2 vols., 1841-1843.  Ed by William Rutherford in one vol, 1841; 1843; 1846; 1849; 1851; 1853; 1857; 1860. 

                    This is a pretty straightforward text, but it well illustrates the situation in early 19C England, outside Oxford and Cambridge.  Almost all the material of interest is in the first two sections: Arithmetic and Algebra and is identical in these two editions.  I imagine most of these problems appeared in the first edition, so I will date this as 1798?, citing pages as 1833 and 1857.  However the 1857 has an additional three pages on Practical Questions in Arithmetic which has 44 problems, some of which are recreational, and another new problem.  Assuming the 1857 is essentially the same as the 1841, I will cite this as 1841?.]

                    See also:  Ozanam‑Hutton.

H&S.  1927.  Vera Sanford.  The History and Significance of Certain Standard Problems in Algebra.  (Teachers College, Columbia University, NY, Contributions to Education, No. 251, 1927)  = AMS Press, NY, 1972.


Illustrated Boy's Own Treasury.  c1847.

                                    The Illustrated Boy's Own Treasury of I. - Science, II. - Drawing, III. - Painting, IV. - Constructive Wonders, V. - Rural Affairs, VI. - Wild and Domesticated Animals, Outdoor Sports & Indoor Pastimes forming a Complete Repository of Home Amusements & Healthful Recreations embellished with five hundred descriptive engravings.  (John & Robert Maxwell, London, c1847 [Toole Stott 407]).  Ward and Lock, 1860 [Toole Stott 1091].  (3rd ed, for the Proprietors, 1865? [Toole Stott 408].)  [Toole Stott's descriptions make it seem that these editions are identical.]  See also:  Boy's Own Book,  Boy's Own Conjuring Book.  [Many of the problems are the same as in the other two books, but the illustrations here occasionally omit some labels, so these must be errors in copying from some earlier source.  If the c1847 date is correct, then this considerably changes the chronology of these problems, with this book being the major known intermediate between Boy's Own Book and Magician's Own Book.  I will hold off making these changes until I see the c1847 ed _ this may take some time as the BM copy was lost in the war and the other two copies cited are in the US.  Hall, BCB 187 is: The Illustrated Boys' Own Treasury of Indoor Pastimes; Robson, London, c1845.  This may be related to this book.]

Indoor & Outdoor.  c1859.

                                    Indoor and Outdoor Games for Boys and Girls: Comprising Parlour Pastimes, Charades, Riddles, Fireside Games, Chess, Draughts, &c, &c.  With a Great Variety of Athletic Sports, Parlour Magic, Exercises for Ingenuity, and Much That is Curious, Entertaining, and Instructive.  James Blackwood, London, nd [c1859].  This is a combination of two earlier books, comprising two separately paginated parts.  The earlier books are Parlour Pastime (1857 _ qv) and Games for All Seasons [Toole Stott 311 & BMC give 1858].  There is a later version of the first part _ Parlour Pastimes, qv, which the BMC dates as 1868.  Also there is another version of the combined ed "with additions by Oliver Optic", as Sports and Pastimes for Indoors and Out, G. W. Cottrell, Boston, 1863 [Toole Stott 1186, which identifies Optic as William Taylor Adams.  Both BMC and NUC say Indoor & Outdoor is by George Frederick Pardon.  Hence the problems in the first part will be cited as: Parlour Pastime, 1857  = Indoor & Outdoor, c1859, Part 1  = Parlour Pastimes, 1868.  Many of the problems are identical to Book of 500 Puzzles.


Jackson.  Rational Amusement.  1821.

                                    John Jackson.  Rational Amusement for Winter Evenings; or, A Collection of above 200 Curious and Interesting Puzzles and Paradoxes relating to Arithmetic, Geometry, Geography, &c.  With Their Solutions, and Four Plates.  Designed Chiefly for Young Persons.  By John Jackson, Private Teacher of the Mathematics.  London: Sold by J. and A. Arch, Cornhill; and by Barry & Son, High‑Street; and P. Rose; Bristol.  1821.  [Other copies, apparently otherwise identical, say: London: Sold by Longman, Hurst, Rees, Orme, and Brown; G. and W. B. Whittaker; and Harvey and Darton.  And Barry and Son, High-Street, Bristol.  1821.  [Heyl 185.  Toole Stott 413.]  Will Shortz says this is the first English-language book devoted to non-word puzzles.]

JRM.            Journal of Recreational Mathematics.


Kanchusen.  Wakoku Chiekurabe.  1727.

                                    Tagaya Kanchusen [pseud. of Fuwa Senkuro].  Wakoku Chiekurabe [Japanese Wisdom Competition _ in Japanese].  2 vols, 1727, 12 & 29 pp.  PHOTOCOPY from Shigeo Takagi's copy sent by Naoaki Takashima.  Edited into modern Japanese, with commentary on Kanchusen, by Shigeo Takagi, 1991, 42pp, present from Takagi.  Translated into English by Hiroko Dean, 1999, 15pp plus annotations on the 42pp.  Takagi and Takashima are working on an translation and annotation into modern Japanese.  We intend to produce an English version from Dean's translation with commentary on the puzzles.  I will cite pages from Takagi's edition.  (Partly reproduced in Akira Hirayama; Tôzai Sûgaku Monogatari [Mathematical Stories from East and West]; (1973), 3rd ed., 1981, p. 208, ??NYS, from which it has been reproduced in the exhibition Horizons Mathématiques at La Villette, Paris, and elsewhere.)

Kaye, George R.            See:  Bakhshali MS.

King.  Best 100.  1927?

                                    Tom King.  The Best 100 Puzzles.  W. Foulsham, London, nd [1927, according to BMC _ my copy says 'Wartime reprint'.]  A selection of these are reproduced in a booklet: Foulsham's Games and Puzzles Book; W. Foulsham, London, nd [c1930].  I will indicate this by  = Foulsham's, no. & pp.

Knott, Cargill G.

                                    See:  Tom Tit.


Labosne.                       See:  Problemes.

Landells.  Boy's Own Toy-Maker.  1859.

                                    E[benezer] Landells.  The Boy's Own Toy-Maker: A Practical Illustrated Guide to the Useful Employment of Leisure Hours.  Griffith & Farran, London, 1859(1858); Shepard, Clark & Brown, Boston, 1859; Griffith & Farran, 3rd ed., 1860; D. Appleton, NY, 1860; Griffith & Farran, 6th ed., 1863 [Toole Stott 1286‑1290].    [BMC has 1859(1858) and a longer 10th ed, 1881.  NUC has the latter four of the versions given by Toole Stott.]  [The Preface to the Second Edition, reproduced in the 3rd ed., says it appeared just two months after the first edition.  Toole Stott indicates that all the versions he cites are identical.  I have 3rd ed., 1860.  Shortz has Appleton, 1860.]  The date 1859(1858) indicates that the book appeared in late 1858 to catch the Christmas trade, but was postdated 1859 to seem current for the whole of 1859, so I will date this as 1858.  The 2nd ed. must be 1859.  Comparison shows that the section on Practical Puzzles is essentially an exact subset of the material in Boy's Own Conjuring Book.

Leeming.  1946.            Joseph Leeming.  Fun with Puzzles.  (Lippincott, Philadelphia, 1946); Comet Books (Pocket Books), NY, 1949.

Lemon.  1890.              "Don Lemon" [= "The Sphinx"  = Eli Lemon Sheldon], selector.  Everybody's Illustrated Book of Puzzles.  Saxon & Co., London, 1890 (with 1891 on the back cover) and 1892.  The 1892 ed. omits the text on the back cover and adds some pages of publisher's advertisements, but is otherwise identical.  794 problems, about 100 being mathematical, on 125pp.  This looks like a UK reprint of a US book, but the NUC only lists London editions, so perhaps it is just selected from US publications.  Some of the problems are attributed to Golden Days, Good Housekeeping, St. Nicholas, etc.

                    I also have an undated edition which says 'Selected by the Sphinx'.  This has 744 problems on 122pp, about 45% of which come from the other edition.  The NUC dates this as 1895.  I will refer to this edition as:  Sphinx.  1895.

Leske.  Illustriertes Spielbuch für Mädchen.  1864?

                                    Marie Leske.  Illustriertes Spielbuch für Mädchen   Unterhaltende und anregende Belustigungen, Spiele and Beschäftigungen für Körper und Geist, im Zimmer sowie im Freien.  (1864; 19th ed., 1904);  20th ed., Otto Spamer, Leipzig, 1907.  There is no indication of any updating in the Foreword to the 19th ed. which is included here, and it was common to describe new printings as new editions, so I will date this as 1864?  This book is jammed with material of all sorts, including lots of rebuses, riddles and puzzles.  It is a bit like Boy's Own Book.  My copy is lacking pp. 159-160 and 211‑212.

Leurechon, Jean (c1591-1670).

                                    See:  van Etten.

Leybourn.  Pleasure with Profit.  1694.

                                    William Leybourn.  Pleasure with Profit: Consisting of Recreations of Divers Kinds, viz. Numerical, Geometrical, Mechanical, Statical, Astronomical, Horometrical, Cryptographical, Magnetical, Automatical, Chymical, and Historical.  Published to Recreate Ingenious Spirits; and to induce them to make farther scrutiny into these (and the like) Sublime Sciences.  And To divert them from following such Vices, to which Youth (in thei age) are so much Inclin'd.  To this work is also Annext, A Treatise of Algebra, ..., by R, Sault.  Richard Baldwin and John Dunton, London, 1694.  The text consists of several parts, labelled Tract. I, Tract. II, ..., which are separately paginated.  All material is from Tract. I unless otherwise specified.  Several sections are taken from the English editions of van Etten.  [Santi 371.]

Li & Du.  1987.             Li Yan & Du Shiran.  Chinese Mathematics: A Concise History.  (In Chinese: Commercial Press, Hong Kong, c1965.)  English translation by John Crossley & Anthony W.‑C. Lun.  OUP, 1987.

Libbrecht.  1973.          Ulrich Libbrecht.  Chinese Mathematics in the Thirteenth Century.  MIT Press, Cambridge, Mass., 1973.

Lilavati.  1150.              Lîlâvatî of Bhaskara II, 1150 (see Colebrooke).

Lloyd, E. Keith.            See:  BLW.

Loeb Classical Library.

                                    Published by Harvard Univ. Press, or Putnam's, NY, & Heinemann, London.

Loyd, Sam (1841-1911)  (&  Sam Loyd Jr. (1873-1934).

                                    See:  Cyclopedia,  MPSL,  OPM,  SLAHP.

Lucas, Édouard (1842-1891).

                                    See:  RM.

Lucas.  L'Arithmétique Amusante.  1895.

                                    Édouard Lucas.  L'Arithmétique Amusante.  Ed. by H. Delannoy, C.‑A. Laisant & E. Lemoine.  (Gauthier-Villars, Paris, 1895.)  = Blanchard, Paris, 1974.

Lucca 1754.  c1390.

                                    Scuola Lucchese.  Libro d'abaco.  c1390.  Dal Codice 1754 (sec. XIV) della Biblioteca Statale di Lucca.  Edited by Gino Arrighi.  Cassa di Risparmio di Lucca, 1973.  Arrighi gives folio numbers and I will cite these and the pages of his edition.


MA.                             Mathematical Association (UK).

MAA.           Mathematical Association of America.

Magician's Own Book.  1857.

                                    The Magician's Own Book, or The Whole Art of Conjuring.  Being a Complete Hand-Book of Parlor Magic, and Containing over One Thousand Optical, Chemical, Mechanical, Magnetical, and Magical Experiments, Amusing Transmutations, Astonishing Sleights and Subtleties, Celebrated Card Deceptions, Ingenious Tricks with Numbers, Curious and Entertaining Puzzles, Together with All the Most Noted Tricks of Modern Performers.  The Whole Illustrated with over 500 Wood Cuts, and Intended as a Source of Amusement for One Thousand and One Evenings.  Dick & Fitzgerald, NY, ©1857.  12 + 362 pp. + 10 pp. publisher's ads.  My thanks to Jerry Slocum for providing a copy of this.  [Toole Stott 481 lists this as anonymous and entirely different from the UK ed.  He cites a 1910 letter from Harris B. Dick who says H. L. Williams may have edited it, but both Dick's father and John Wyman may also have had a hand in it.  Toole Stott 929, 930, 1378, 931 lists Dick & Fitzgerald, 1862, 1866, 1868, 1870, all apparently identical to the 1857.  929-930 are listed under Arnold and he there cites Cushing's Anonyms as saying the book is by Arnold and Cahill.  Christopher 622-625 are all Dick & Fitzgerald; 622-623 are 1st ed., 624-625 are reprints of about the same time and my copy seems most likely to be 625.  C&B, under Cremer, say "It is believed that they were all written by H. L. Williams, a prolific hack writer of the period."  Christopher 622 says Harold Adrian Smith [Dick and Fitzgerald Publishers; Books at Brown 34 (1987) 108-114] has studied this book and concludes that Williams was the author, assisted by Wyman.  Actually Smith simply asserts: "The book was undoubedly [sic] written by H. L. Williams, a "hack writer" of the period, assisted by John Wyman in the technical details."  He gives no explanation for his assertion, but it may be based on C&B.  NUC lists this as by George Arnold (1834-1865) and Frank Cahill, under both Arnold and Cahill.  C&B list it under Cremer, attributed to Arnold & Cahill, but they give a date of 1851, which must be a transcription error.  C&B also list it under Magician's, from New York, 1857, and under Williams, but as London, 1857.]  See the discussion under Status of the Project in the Introduction for the sources of the material.

                    Boy's Own Conjuring Book, qv, appears to be a UK pirate edition largely drawn from this.  Book of 500 Puzzles copies about 80 pages of this.  See the comments under Book of 500 Puzzles.  A fair number of the problems are identical to or similar to the Boy's Own Book and a woodcut, a poem and the introduction to a section are taken directly from Boy's Own Book.  Otherwise I had thought that this book was the source for the spate of puzzle books in the following 15 years, but I have found that some of the identical puzzles appeared in The Family Friend c1850. 

Magician's Own Book (UK version).  1871.

                                    This is quite different than the previous book.

                                    The Magician's Own Book.  By the Author of "The Secret Out," "The Modern Conjuror," &c.  Edited by W. H. Cremer, Jun.  Containing Ample Instructions for Recreations in Chemistry, Acoustics, Pneumatics, Legerdemain, Prestidigitation, Electricity (with and without apparatus).  (In the middle of the page is an illustration of a wizard in white on red.)  Performances with Cups and Balls, Eggs, Hats, Flowers, Coin, Books, Cards, Keys, Rings, Birds, Boxes, Bottles, Handkerchiefs, Glasses, Dice, Knives, &c., &c.  With 200 Practical Illustrations.  John Camden Hotten, nd [1871].  This has a two page list of Very Important New Books at the beginning on pp. i-ii.  This lists Magician's Own Book as by the Author of "The Secret Out" and The Secret Out as by the Author of the "Magician's Own Book".  But a further note says "Under the title of "Le Magicien des Salons" the first has long been a standard Magic Book with all French and German Professors of the Art." _ see the discussion uner Status of the Project in the Introduction, above.  This list is followed by a half-title, p. iii, whose reverse (p. iv) has the printer's colophon, then a blank page v, backed by a Frontispiece, p. vi, comprising Figures 105 & 110 from the text.  The TP is p. vii,, backed by a blank p. viii.  The Preliminary on pp. ix-x has the address  Piccadilly  at the end and states this is "an Entirely New Edition" and is by the same author as The Secret Out.  It refers to Cremer's display of Toys of the World at the recent International Exhibition (possibly the 1862??) and to [Frank Bellew's] "The Art of Amusing" (of 1866 and published by Hotten in 1870) and Clara Bellew's "The Merry Circle".  Contents are given on pp. xi‑xii and then the text on pp. 13-326.  [Toole Stott 194 lists this under Cremer and says there are 30pp of publisher's catalogue at the end, dated 1872 _ I didn't record these details.  Christopher 239 lists this as "An entirely new edition" with 200 illustrations, 325 pp. + 30 pp. publisher's ads.]

                    I have also seen a John Grant, Edinburgh, ed. which omits pp. i-vi, and has a simplified title page, saying it is A New Edition, and drops the address  Piccadilly.  Otherwise the text appears to be identical.  It has no date but Toole Stott 1015 gives the date 1871.  C&B, under Cremer, have London, 1871 with no indication of the New York ed.  C&B also list it under Williams.

                    I have a Chatto & Windus ed., which omits pp. i-vi, and whose TP has only slight changes from the Hotten TP, saying it is A New Edition, but the text appears to be identical, except for dropping the address  Piccadilly  from the end of the Preliminary.  It is dated 1890, with separately paginated publisher's catalogue of 32pp. dated Apr 1893. 

Mahavira.  850.             Mah_v_r_(c_rya).  Ganita‑s_ra‑sangraha  (= Ganita‑s_ra‑samgraha  = Ganitasar Samgrha).  850.  Translated by M. Rang_c_rya.  Government Press, Madras, 1912.  The sections in this are verses.  I will refer to the integral part of the first verse of the problem.  E.g. where he uses  121½ ‑ 123,  I will use  v. 121.  [This work is described by David Eugene Smith; The Ganita-Sara-Sangraha of Mah_v_r_c_rya; Bibliotheca Mathematica (3) (1908/09) 106-110.  In: [G. R. Kaye;  A brief bibliography of Hindu mathematics;  J. Asiatic Society of Bengal (NS) 7:10 (Nov 1911) 679-686], this work is cited as 1908 with the note: "This is really an advance copy of a work not yet actually published, kindly supplied to me by the author."  See the entry under Pearson, 1907, in 7.E.]

Manson.  Indoor Amusements.  1911.

                                    J. A. Manson, compiler.  Indoor Amusements.  Cassell & Co., London, 1911.  This is an extension of Cassell's Book of In-Door Amusements ..., expanding the earlier 211pp of text to 340pp.  This is partly due to using larger type, getting 47 lines per page instead of 54.  The material which was in Cassell's is generally unchanged.

Manuel des Sorciers.  1825.

                                    Manuel des Sorciers  ou  Cours de Récréations Physiques, Mathématiques, Tours de Cartes et de Gibecière, suive  Des Petits Jeux de Société, et de Leurs Pénitences.  (Conort, Paris, 178?;  2nd ed, Metier & Levacher, Paris, 1802 [Christopher 642, C&B];  4th ed, Ferra Jeune, Paris, 1815 [C&B];  5th ed, Ferra Jeune, 1820 [C&B]);  6th ed, Augmentée d'une Notice sur la Magie noire, Ferra Jeune, Paris, 1825 [Christopher 643, C&B, HPL].  There are a great many French books with similar titles from this era.  They seem to be the predecessors of Magician's Own Book, etc. _ cf the discussion under Status of the Project in the Introduction and under Book of 500 Puzzles and Magician's Own Book.  This is the first that I have found and examined carefully, at HPL.  It is likely that most of the material dates back to the first ed of 178?, but until I see some earlier editions, I'll date it as 1825,  Gaidoz, in Section 7.B, cites the 2nd ed, but the material is on a different page than in the 1825.

McKay.  At Home Tonight.  1940.

                                    Herbert McKay.  At Home Tonight.  OUP, 1940.  Section V: Puzzles and problems, pp. 63-88.

McKay.  Party Night.  1940.

                                    Herbert McKay.  Party Night.  OUP, 1940.  Sections on Dinner-Table Tricks, pp. 134-171;  Some Tricks in English, pp. 174-175;  Arithmetical Catches and Puzzles, pp. 176-184.

Metrodorus.                  c510.  In: The Greek Anthology, W. R. Paton, trans.  Loeb Classical Library, 1916‑1918.  Vol. 5, Book 14.  This contains 44 mathematical problems, most of which are attributed to Metrodorus, though he is clearly simply a compiler and some may be much older.  I have cited the pages of the English translation _ the Greek is on the previous page.  Paton gives English answers, but they are not in the Greek. 

                    The Greek Anthology is the modern name for a combination of two anthologies which were based on earlier compilations dating back to the time of Alexander (-4C), e.g. the Garlands of Meleager (c-95) and Philippus of Thessalonika (c40) and the Cycle of Agathias (c570).  In the late 9C or early 10C, Konstantinos Kephalas assembled these into one collection, but distributed them according to type and then added several other collections _ this was somewhat revised c980.  In 1301, Maximus Planudes re-edited Kephalas' anthology, omitting much and adding some (Paton believes that Planudes' source was missing a book).  The Planudean version replaced Kephalas's version and was printed in 1484.  However a copy of Kephalas's version of c980 was discovered at Heidelberg in the Palatine Library (hence the anthology is sometimes described as Palatine) in 1606 and modern versions now use this version as the first 15 books and put all of Planudes' additions as Book 16, the Planudean Appendix.  The Anthology comprises some 4000 poems.  Modern scholars view Paton as obsolete, but I don't know of any later versions of the Anthology which include the mathematical problems _ e.g. they are not even mentioned in Peter Jay; The Greek Anthology; Allen Lane, 1973; Penguin, 1981.

Meyer.  Big Fun Book.  1940.

                                    Jerome S. Meyer.  The Big Fun Book.  Greenberg : Publisher, NY, 1940.

MG.                             Mathematical Gazette.

Mikami.  1913.             Yoshino Mikami.  The Development of Mathematics in China and Japan.  Teubner, Leipzig, 1913; reprinted, Chelsea, 1961?  See also:  Smith & Mikami.

Minguét.  Engaños.  1733.

                                    Pablo Minguét è (or é) Yról (or Irol).  Engaños à Ojos Vistas, y Diversion de Trabajos Mundanos, Fundada en Licitos Juegos de Manos, que contiene todas las diferencias de los Cubiletes, y otras habilidades muy curiosas, demostradas con diferentes Láminas, para que los pueda hacer facilmente qualquier entretenido.  Pedro Joseph Alonso y Padilla, Madrid, 1733.  Frontispiece + 12 + 218 pp.  My copy has the top half of the TP missing _ photocopy of TP of a copy at HPL inserted.  Imprimaturs or licenses dated 3 Nov 1733, 10 Nov 1733 & 12 Dec 1733. 

                    3rd ptg, Domingo Fernandez de Arrojo, Madrid, 1755, 18 + 157 (+ 3 extra) pp.  (Revised, c1760.  4th ptg, D. Gabriel Ramirez, Madrid, 1766).  Sierra y Martí, Barcelona, 1820, 224pp [Christopher 676].)  (Neuva Edicion corregida y augmentada par D. I. M. de L., Juan Francisco Piferrer, Barcelona, 1822.  (Aumentado nueva edicion, Manuel Sauri, Barcelona, 1847.  8th ed, augmented, ibid, 1888.  9th ed., augmented, ibid, 1888.  There was a 1981 facsimile of an 1864 Barcelona ed.)  See Christopher 672-677.  The early history of this book is confused.  The first edition may have only had 18 + 110 pp (or 105 pp ??), then was apparently reprinted, with additions, without changing the date.  Or it may be that both versions appeared in 1733.  However, this copy is identical to one in HPL which is catalogued as 1733.  Christopher dates the 218 pp versions to c1760.  C&B only give Madrid, 1733, 110pp; another ed., 218pp.

                    HPL [Minguet] has 1733, 1733, 1733, 1755, 1755, 1820.  I have seen one from each year, but the catalogue indicates there may be different issues in the same year.  The 1733 is identical to my copy.  The 1820 is identical except the text has been reset, spelling modernized, the front matter updated and the text starts on p. 10, with everything the same as the 1733 except the page numbers are increased by 9, and the index is reduced in size.  The 1755 seems to have the same material as 1733, but it is reset with smaller type and much rearranged.  It seems to be the same as [Christopher 675].  I have also examined Will Shortz's 1822 ed, which is probably [Christopher 677], but it is quite differently arranged than the 1820 or the 1733.  I wrote to Bib. Nac., Madrid, when I only knew of the 1822 ed. and they said they did not have it, but perhaps they meant this particular edition??  I now see that the BL has 1733, 1755, 1766.  If anyone has access to a copy, I would like a photocopy of the TP and other publishing details and the Indice.]

                    Pp. 1-25 is a fairly direct translation of the 1725 Ozanam, vol. IV, pp. 393-406.  A number of other pictures and texts also are taken from Ozanam.  I will give the date as 1733, though the expansion may not have occurred until c1755.  I will cite the 1755 and 1822 pages in parentheses, e.g.  Pp. 158-159 (1755: 114-115; 1822: 175-176).

MiS.                             Mathematics in School.

Mittenzwey.  1879.

                                    L. Mittenzwey.  Mathematische Kurzweil.  (1879; 3rd ed., 1903; 4th ed., 1904; 5th ed., 1907; 6th ed., 1912); 7th ed., Julius Klinkhardt, Leipzig, 1918.  I will give the date as 1879?  I now have a photocopy of the 1st ed _ ??NYR.

MM.             Mathematics Magazine.

Montucla, Jean Étienne (1725-1799).

                                    See:  Ozanam,  Ozanam‑Montucla.

MP.  1926.                   H. E. Dudeney.  Modern Puzzles.  C. Arthur Pearson, London, 1926; new ed., nd [1936?].  (Almost all of this is in 536.)

MPSL1.  1959  &  MPSL2.  1960.

                                    Mathematical Puzzles of Sam Loyd, vol. 1 & 2, ed. by Martin Gardner, Dover, 1959, 1960.  (These contain about 2/3 of the mathematical problems in the Cyclopedia, often with additional material by Gardner.)

MRE.           W. W. Rouse Ball (1850-1925).  Mathematical Recreations and Essays.  (First three editions titled Mathematical Recreations and Problems).  I have compiled an 8 page detailed comparison of the contents of all editions as part of my The Bibliography of Some Recreational Mathematics Books.

                    1st ed., Feb 1892, 240pp.

                    2nd ed., May 1892 ('No material changes').

                    3rd ed., 1896, 276pp.

                    4th ed., 1905, 388pp.  [In the 4th ed., it says 'First Edition, Feb. 1892.  Reprinted, May 1892.  Second Edition, 1896.  Reprinted, 1905.'  However, it calls itself the 4th ed. and the 3rd ed. calls itself 3rd and there are substantial changes in the 4th ed.]

                    5th ed., 1911, 492pp.

                    6th ed., 1914, 492pp.

                    7th ed., 1917, 492pp.

                    8th ed., 1919, 492pp.

                    9th ed., 1920, 492pp.

                    10th ed., 1922, 366pp.

                    11th ed., 1939, revised by H. S. M. Coxeter, 418pp. 

          Macmillan (for 1st to 11th ed.).

                    12th ed., 1974, revised by H. S. M. Coxeter, 428pp, U. of Toronto Press.

                    13th ed., 1987, revised by H. S. M. Coxeter, 428pp, Dover.

          A few of the editions are actually reprintings of the previous edition:  2 is the same as 1,

                    6 as 5,  9 as 8,  13 as 12.  Consequently I will not cite editions 2, 6, 9, 13.  For

                    each topic occurring in Ball, I have examined all the editions, so the absence of a

                    reference indicates the topic does not occur in that edition _ unless it is buried in

                    some highly unlikely place.

          See also:  Ball‑FitzPatrick.

MS.                              Mathematical Spectrum (Sheffield, UK).

MTg.            Mathematics Teaching (UK).

MTr.            Mathematics Teacher (US).

Munich 14684.  14C.

                                    Munich Codex Lat. 14684.  14C.  Ff. 30‑33.  Published by M. Curtze; Mathematisch‑historische Miscellan: 6 _ Arithmetische Scherzaufgaben aus dem 14 Jahrhundert; Bibliotheca Math. (2) 9 (1895) 77‑88.  34 problems.  Curtze gives brief notes in German.  Curtze says these problems also appear in Codex Amplonianus Qu. 345, ff. 16‑16', c1325, ??NYS.  Munich 14684 comes from the same monastery (St. Emmeran) as AR and AR incorporates much of it.  In a later paper, Curtze says this is 13C _ ??NYR

Murray.  1913.              Harold James Ruthven Murray.  A History of Chess.  (OUP, 1913); reprinted by Benjamin Press, Northampton, Massachusetts, nd [c1986].

MUS.  1910 & 1918.

                                    Wilhelm Ahrens (1872-1927).  Mathematische Unterhaltungen und Spiele.  2 vol., 2nd ed., 1910, 1918, Teubner, Leipzig.  There is a 3rd ed. of Vol 1, 1921, but it is a reprint of the 2nd ed. with just 2 pages of extra notes.  (The first ed. was 1901.)  I will tend to cite this as e.g. MUS 1 153-155.  MUS #n  denotes item  n  in the substantial Literarischer Index, MUS 2 375-431.

Muscarello.  1478.

                                    Pietro Paolo Muscarello.  Algorismus.  MS of 1478.  Published in 2 vols.: I _ facsimile; II _ transcription with notes and commentaries; Banca Commerciale Italiana, Milan, 1972.  I will cite the folios (given in vol. I) and the pages of the transcribed version in vol. II.

M500.          This is the actual name of the journal of the M500 Society, the Open University student mathematics society.


NCTM.                         National Council of Teachers of Mathematics.

nd.                               no date.  Estimated dates may follow in  [   ].

Needham.  1958.           Joseph Needham (1900-1995).  Science and Civilization in China, Vol. 3.  CUP, 1958.  (Occasional references may be made to other volumes: Vol. 2, 1956;  Vol. 5, Part IV, 1980.)

Northrop.  Riddles in Mathematics.  1944.

                                    Eugene P. Northrop.  Riddles in Mathematics.  Van Nostrand, 1944;  English Universities Press, 1945;  revised ed., Penguin, 1961.  The Van Nostrand ed has the main text on pp. 1-262.  The EUP ed. has it on pp. 1-242.  The Penguin ed. has it on pp. 11-240.  The revision seems to consist of only a few additional notes.  I will cite the dates and pages, e.g.  1944: 209-211 & 239;  1945: 195‑197 & 222;  1961: 197‑198 & 222.

NUC.           National Union Catalogue  Pre‑1956 Imprints.  Library of Congress, USA.  c1960.  ??check details

Nuts to Crack.              Nuts to Crack, Part nn.  Or, Enigmatical Repository; containing near mmm Hieroglyphics, Enigmas, Conundrums, Curious Puzzles, and Other Ingenious Devices.  R. Macdonald, 30 Great Sutton Street, Clerkenwell, London.  These are single broadsheets.  The publisher's details are often trimmed from the bottom of the sheet.  At least 25 annual parts appeared, from Part I of 1832, but the year is not always given.  Answer books _ The Nutcrackers _ also appeared and the publishers kept the old sheets available for some years.  This series is very rare _ Will Shortz and James Dalgety have the only examples known to me.  I have photocopy of almost all from Dalgety and Shortz, ??NYR.  mmm is either 250 or 200 and the problems are individually numbered in each part.  I will cite problems as, e.g. Nuts to Crack I (1832), no. 200.

NX.                              No copy.  Usually prefixed by  ??  as a flag for further action.

NYR.            Not yet read _ i.e. I have a copy which I have not yet studied.  Usually prefixed by  ??  as a flag for further action.

NYS.            Not yet seen.  Usually prefixed by  ??  as a flag for further action.


OCB             See: Hall, OCB.

OED.           Oxford English Dictionary.  (As: New English Dictionary, OUP, 1884‑1928), reprinted with supplements, OUP, 1933 and in various formats since.

o/o.                             On order.

OPM.  1907-1908.        Our Puzzle Magazine.  Produced by Sam Loyd.  The pages were unnumbered.  The Magazine was reprinted as the Cyclopedia as follows, but some pages of the Magazine were omitted and the answers to each magazine were normally in the next one.

          Vol. 1, No. 1 (Jun 1907)  =  Cyclopedia pp. 7‑70.

          Vol. 1, No. 2 (Oct 1907)  =  Cyclopedia pp. 71‑121.

          Vol. 1, No. 3 (Jan 1908)  =  Cyclopedia pp. 122‑178.

          Vol. 1, No. 4 (Apr 1908)  =  Cyclopedia pp. 179‑234.

                    Since the Cyclopedia goes to p. 339, there appear to have been two further issues which have not been seen by anyone??

          (The above data were provided by Jerry Slocum.)

OUP.                           Oxford University Press.

Ozanam.  1694.             The bibliography of this book is a little complicated.  I have prepared a more detailed 7 pp. version covering the 19 (or 20) French and 10 English editions, from 1694 to 1854, as well as 15 related versions _ as part of my The Bibliography of Some Recreational Mathematics Books.

                                    Jacques Ozanam (1640-1717).  Recreations Mathematiques et Physiques, qui contiennent Plusieurs Problémes utiles & agreables, d'Arithmetique, de Geometrie, d'Optique, de Gnomonique, de Cosmographie, de Mecanique, de Pyrotechnie, & de Physique.  Avec un Traité nouveau des Horloges Elementaires.  2 vols., Jombert, Paris, 1694, ??NYS.  [Title taken from my 1696 ed.]

                    [BNC.  NUC _ but NUC lists a 1693 3rd ed. from Amsterdam, which appears to be a misreading for 1698.  MUS II 380 says 1st ed. was Récréations Mathématiques, Paris, 1694, 2 vols.  Serge Plantureux's 1993 catalogue describes a 1694 edition in 2 vols., by Jombert and notes that it is the original edition, that the privilege is dated 11 Jan 1692, but that it was not printed until 30 Apr 1694.  The dating of the privilege may account for some references to the first edition being 1692 _ e.g. the Preface to the 1778 Ozanam-Montucla ed. says the first ed. was 1692, but Hutton changes this to 1694.  MRE, 1st ed, 1892, pp. 3‑4, says the the 1st ed. was 2 volumes, Amsterdam, 1696, but this was amended in his 4th ed., 1905.

                    This first appeared in two volumes, but later versions were sometimes in one volume.  I have references to versions in Paris: 1694, 1696, 1697, 1698, possibly 1700? and apparently 1720; and in Amsterdam: 1696, 1697, 1698, 1700.  There is no indication of any textual changes in these, except that the pages are numbered consecutively in later versions.  Plantureaux describes a 1696 edition as: Paris, Jombert (mais Hollande), so there seems to have been some piracy going on.  I have the 1696 ed.  I will assume that the 1696 is essentially identical in content to the 1694, though in the second volume, the page numbers may be different and there is some confusion of plate numbering.

                    The Traité des Horologes élémentaires, which appears in the 1694 ed., is a translation of Domenico Martinelli's Horologi elementari.  NUC says this was separately paginated in 1694, but it occupies pp. 473-583 of the 1696 ed and pp. 301-482 of vol. 3 of the 1725 ed.]


                    About 1723, the work was revised into 4 vols., sometimes described as 3 vols. and a supplement.  MUS #52 gives 1720, 1723, 1724, 1725 and says the dates vary in the literature.  The 1725 has privilege dated 1720, but I haven't found any catalogue entry for a 1720 ed. of this revision, so it may be a spurious date based on the privilege. 

  Nouv. ed.

                    Recreations Mathematiques et Physiques, qui contiennent Plusieurs Problêmes d'Arithmétique, de Géométrie, de Musique, d'Optique, de Gnomonique, de Cosmographie, de Mécanique, de Pyrotechnie, & de Physique.  Avec un Traité des Horloges Elementaires.  Par feu [misprinted Parfeu in vol. 1] M. Ozanam, de l'Académie Royale des Sciences, & Professeur en Mathematique.  Nouvelle edition, Revûë, corrigée & augmentée.

            Vol. 4 has different title page.

                    Recreations Mathematiques et Physiques, ou l'on traite Des Phosphores Naturels & Artificiels, & des Lampes Perpetuelles.  Dissertation Physique & Chimique.  Avec l'Explication des Tours de Gibeciere, de Gobelets, & autres récréatifs & divertissans.  Nouvelle edition, Revûë, corrigée & augmentée.

          Claude Jombert, Paris, 1723.  [Taken from my 1725 ed.]

                    [Ball and Glaisher [op. cit. in 7.P.5, p. 119] both cite a 1723 ed. as though they had seen it, but there is no BMC entry for this date _ perhaps there is a copy at Cambridge??.  MUS # 52 says it was edited by Grandin.  NUC _ "The editor is said to be one Grandin."  I have a brief 1899 reference to this ed.

                    I have 1725, which is apparently a reprint of the 1723.  The privilege/approbation is dated 16 May 1722 in Vol. 3 and Vol. 4 and also 28 Apr and 15 May 1720 in Vol. 3.  NUC says this is 1723 with new title pages.  BNC has: Nouvelle édition ... augmentée [par Grandin], 4 vols, Paris, 1725.  It was reprinted in 1735, 1737?, 1741, 1750/1749, 1770.

                    The text and plates of the 1725 and 1735 eds. seem identical, though some of the accessory material _ lists of corrections and of plates _ has been omitted and other has been rearranged.  I have seen two versions of the 1735 _ one has the plates inserted in the text, the other has them at the end as ordinary pages, while my 1725 has them at the end on folding pages.  Most of the 1725 plates are identical to the 1696 plates, but there were a number of additions and reorderings.  The 1725 plates have their 1696 plate numbers and 1725 page references at the top with new, more sequential, plate numbers at the bottom.  The 1725 text sidenotes refer to the plate numbers at the top, while the 1735 and later sidenotes refer to the bottom numbers.  (However some of the new illustrations in vol. 4 are not described in the text and this makes me wonder if there was an earlier version with these new plates??)  I will give the 1725 top plate numbers, followed by the bottom numbers in  ( )  _ e.g. plate 12 (14).  The 1741 and the 1750/1749 eds. are essentially identical to the 1735 ed.

                    Ball, MRE, and MUS #52 say the 1750 and/or the 1770 ed. were revised by Montucla, but all other sources say his revision was 1778.  Indeed Montucla was only 25 in 1750.  Inspection of 1750 copies in the Turner Collection and at the Institute für Geschichte der Naturwissenschaft shows the 1750 is identical to my 1725 ed. except for some accents and a new publisher.]

  English versions

                    Recreations Mathematical and Physical; Laying down, and Solving Many Profitable and Delightful Problems of Arithmetick, Geometry, Opticks, Gnomonicks, Cosmography, Mechanicks, Physicks, and Pyrotechny.  By Monsieur Ozanam, Professor of the Mathematicks at Paris.  Done into English, and illustrated with very Many cuts.  R. Bonwick, et al., London, 1708. 

                    [Pp. 130-191 are omitted, but there is no gap in the text and the Contents also shows these pages are lacking.  Ball, MRE.  BMC.  NUC.  Hall, OCB, p. 165.  Hall, BCB 216.  UCL.  Toole Stott 520, noting the gap.  Bodleian.  This is a pretty direct translation of the 1696 French ed. or an early simple revision.  Prob. 18-20 of Cosmographie have been omitted.  C&B list this and say there were three later editions, though they then list the 1756 and 1790 editions.]

  2nd ed.

                    Recreations for gentlemen and ladies: or, Ingenious Amusements.   Being Curious and diverting sports and pastimes, natural and artificial.  With Many Inventions, pleasant Tricks on the Cards and Dice, Experiments, artificial Fireworks, and other Curiosities, affording variety of entertainments.  James Hoey, Dublin, 1756.  [Taken from Toole Stott entry.]

                    [NUC.  Hall, BCB 212.  Hall, OCB, p. 165, but giving the 1790 title.  Toole Stott 518, but he has Hoez, which seems to be either a misreading or a miswriting??]

  3rd ed. 

                    Recreations for Gentlemen and Ladies; being Ingenious Sports and Pastimes.  Containing Many curious Inventions, pleasant Tricks on Cards and Dice; Arithmetical Sports; new Games; Rules for Assuredly winning at all Games, whether of Cards or Dice; Recreative Fire-works; Tricks to promote Diversion in Company, and other Curiosities....  James Hoey, Dublin, 1759.  [Taken from Hall, BCB 213.]

                    [Ball, MRE.  Hall, BCB 213.  Hall, OCB, p. 165.  Bodleian.] 

  4th ed.

                    Recreations for gentlemen and ladies; being ingenious sports and pastimes: containing Many curious Inventions, pleasant Tricks on Cards and Dice; Arithmetical Sports; new Games; Rules for Assuredly winning at all Games, whether of Cards or Dice; Recreative Fire-works; Tricks to promote Diversion in Company, and other Curiosities....  The fourth edition.  Peter Hoey, Dublin, 1790.  [Taken from Toole Stott entry.]

                    [BMC calls it the 4th ed. [abridged].  NUC.  Hall, BCB 214.  Hall, OCB, p. 165.  Toole Stott 519.  Bodleian.]


              I will cite these and the following editions by date, though the varying problem numbers and volume numbers will make this a bit unwieldy.  All references to the 4 volume versions are to vol. I unless specified otherwise.  See the entry in 4.A.1 as an example.  Note that I give the problem number first because this is usually the same in the 1790, 1803 and 1814 editions, and often in the 1840.  Figure numbers will also been given with the problem number, although the 1840 has the figures in the text with different numbers.  Additions will be entered at the relevant point.

Ozanam‑Hutton.  1803.

                                    Recreations in Mathematics and Natural Philosophy: ...  first composed by M. Ozanam, of the Royal Academy of Sciences, &c. Lately recomposed, and greatly enlarged, in a new Edition, by the celebrated M. Montucla.  And now translated into English, and improved with many Additions and Observations, by Charles Hutton, ....  4 vols., T. Davison for G. Kearsley, London, 1803. 

                    [This is a pretty direct translation of the 1790 Ozanam-Montucla ed. with a few changes, and some notes and extra material, generally in sections which do not interest us.  Only one or two plates have been changed.  Erroneous problem numbers have been retained.

                    There was an 1814 ed. by Longman, Hurst, Rees, Orme and Brown, London.  The texts are basically identical, but the 1814 has been reset to occupy about 15% fewer pages, the problem numbers have been corrected, a few corrections/additions have been made and the plates do not fold out.]

Ozanam‑Montucla.  1778.

                                    J. E. Montucla (1725-1799)'s revision of Ozanam. 

                    Récréations Mathématiques et Physiques, Qui contiennent les Problêmes & les Questions les plus remarquables, & les plus propres à piquer la curiosité, tant des Mathématiques que de la Physique; le tout traité d'une maniere à la portée des Lecteurs qui ont seulement quelques connoissances légeres de ces Sciences.  Par feu M. Ozanam, de l'Académie royale des Sciences, &c.  Nouvelle Edition, totalement refondue & considérablement augmentée par M. de C. G. F.  Claude Antoine Jombert, fils aîné, Paris, 1778, 4 vols.  Approbation & privilege dated 5 Aug 1775 & 4 Sep 1775. 

                    [BMC says this is "par M. de C. G. F. [i.e. M. de Chanla, géomètre forézien, pseudonym of J. E. Montucla.]"  BMC, under Montucla, says M. de Chanla is a pseudonym of Montucla.  BNC, under Montucla, describes Montucla as Éd.  Lucas, RM1, p. 242 lists this under Chaula "attribué à Montucla".  MUS #52 has Chaula.  NUC has Chanla.  Montucla's connection with the book was so little known that the 1778 version was sent to him in his role as Mathematical Censor and he made some additions to it before approving it.  Hutton says the 'last edition' (presumably 1790) bears Montucla's initials.  'Forézien' means from Feurs or the Forez region.  Reprinted in 1785-1786 and 1790 (see below).

                    This is a considerable reworking of the earlier versions.  In particular, the interesting material on conjuring and mechanical puzzles in Vol. IV has been omitted.  There are occasional misnumberings of problems.  I recall the plates are folding at the end of each volume, but I didn't note this specifically.]

   Nouv. ed.

                    "Nouvelle édition, totalement refondue et considérablement augmentée par M. de M***" [BMC adds: [i.e. Jean Étienne Montucla]].  Firmin Didot, Paris, 1790. 

                    [NUC lists this as a reissue of 1778 with new TPs.  I have this ed.]

Ozanam‑Riddle.  1840.

                                    (Edward Riddle (1788-1854)'s revision of Ozanam‑Hutton.) 

                    Recreations in mathematics and natural philosophy: translated from Montucla's edition of Ozanam, by Charles Hutton, LL.D. F.R.S. &c.  A new and revised edition, with numerous additions, and illustrated with upwards of four hundred woodcuts,  By Edward Riddle, Master of the Mathematical School, Royal Hospital, Greenwich.  Thomas Tegg, London, 1840.  [Taken from my copy.  MUS #130 asserts this is by a C. Biddle, but this must be due to be a misreading or misprint.]

   Another ed.

                    Recreations in science and natural philosophy: Dr. Hutton's translation of Montucla's edition of Ozanam.  The present new edition of this celebrated work is revised By Edward Riddle, Master of the Mathematical School, Royal Hospital, Greenwich, who has corrected it to the present era, and made numerous additions.  This Edition is also Illustrated by upwards of Four Hundred Woodcuts.  Thomas Tegg, London, 1844.

   Another ed.

                    Recreations in Science and Natural Philosophy.  Dr. Hutton's translation of Montucla's edition of Ozanam.  New Edition, revised and corrected, with numerous additions, by Edward Riddle, Master of the Mathematical School, Royal Hospital, Greenwich.  Illustrated by upwards of Four Hundred Woodcuts.  William Tegg, London, 1851.

   [Reprinted by William Tegg, 1854.]


                    All the printings seem to be from the same plates _ the date of the Prefatory Note and the Erratum given on p. xiv are the same in 1840 and 1851.  Marcia Ascher cites an 1844 edition from Nuttall & Hodgson, but this is the printer.

                    These have the figures in the text, but otherwise seem to be little different than Ozanam-Hutton.  I will generally cite it just as 1840.


P. M. Calandri.  c1480.

                                    Pier Maria Calandri.  Tractato d'Abbacho.  Cod. Acq. e doni 154, Biblioteca Medicea Laurenziana, Florence.  c1480.  Edited and transcribed by G. Arrighi, Domus Galilaeana, Pisa, 1974.

Pacioli.  De Viribus.  c1500.

                                    Luca Pacioli (or Paciuolo) (??-c1509).  De Viribus Quantitatis.  c1500.  Italian MS in Codex 250, Biblioteca Universitaria di Bologna, ??NYR.  Santi 3 dates it as 1498 and describes the later parts which deal with riddles, etc, but include some magic, etc.  This has never been published, but Part 1: Delle forze numerali cioe di Arithmetica is extensively described in: A. Agostini; Il "De viribus quantitatis" di Luca Pacioli; Periodico di Matematiche (4) 4 (1924) 165‑192.  All references are to the problem numbers in this part, as given by Agostini, unless specified otherwise.  There is a microfilm at the Warburg Institute (currently misplaced) and also at Munich and Siena.  I have recently obtained a print of the relevant section, some 125pp, but have not yet read it. 

                    In 1998, an Italian edition by Augusto Marinoni was published, but I haven't been able to get the publisher to reply.  There is a copy in the Warburg, but I haven't had time to study it yet.

Pacioli.  Summa.  1494.

                                    Luca Pacioli (or Paciuolo or Paccioli) (??-c1509).  S_ma de Arithmetica Geometria Proportioni & Proportionalita.  Paganino de Paganini, Venice, 1494; facsimile printed by Istituto Poligrafico e Zecca dello Stato, Rome, for Fondazione Piero della Francesca, Comune di Sansepolcro, 1994, with descriptive booklet edited by Enrico Giusti.  There was a second ed., Paganino de Paganinis, Toscolano, 1523, but the main text seems identical, except for corrections (and errors) and somewhat different usage of initial letters and colour.  For extensive studies of this book, see:  Enrico Narducci; Intorno a due edizioni della "Summa de arithmetica" di Fra Luca Pacioli; Rome, 1863; ??NYS _ cited by Riccardi [Biblioteca Matematica Italiana, 1952]  and:  Fenella K. C. Rankin; The Arithmetic and Algebra of Luca Pacioli; PhD thesis, Univ. of London, 1992 (copy at the Warburg Institute), ??NYR.  The text is in two parts _ the second part is geometry and is separately paged.  All page references will be to the first part unless specified as Part 2.  Problems are numbered at the right hand edge of the last line of the previous problem.  See Rara 54-59.

Panckoucke, André Joseph (1700-1753).

                                    See:  Les Amusemens.

Pardon, George Frederick (1824-1884).

                                    See:  Indoor & Outdoor,  Parlour Pastime,  Parlour Pastimes.

Parlour Pastime.  1857.

                                    Parlour Pastime for the Young: Consisting of Pantomime and Dialogue Charades, Fire-side Games, Riddles, Enigmas, Charades, Conundrums, Arithmetical and Mechanical Puzzles, Parlour Magic, etc. etc.  Edited by Uncle George [NUC says this is George Frederick Pardon].  James Blackwood, London, 1857 [Toole Stott 545; Christopher 724].  This was combined with Games for All Seasons [Toole Stott 311; Christopher 723] into Indoor & Outdoor, c1859, qv.  There is a later edition, Parlour Pastimes, 1868, qv.  Hence the problems will be cited as: Parlour Pastime, 1857  = Indoor & Outdoor, c1859, Part 1  = Parlour Pastimes, 1868.  Many of the problems are identical to Book of 500 Puzzles.

Parlour Pastimes.  1868?

                                    Parlour Pastimes: A Repertoire of Acting Charades, Fire-side Games Enigmas, Riddles, Charades, Conundrums, Arithmetical and Mechanical Puzzles, Parlour Magic, etc., etc.  James Blackwood, London, nd.  [BMC, NUC and Toole Stott 1136 date this 1868 and say it is by George Frederick Pardon.  Toole Stott 1136 indicates that By G. F. P. is on the TP, but it is not in my example.  Toole Stott 1137 is 1870, a slightly smaller ed.]  It is an expanded version of Parlour Pastime, with the material of interest to us being directly copied, though the page layout varies slightly.  The running head of this is actually Parlour Pastime.  Hence the problems will be cited as: Parlour Pastime, 1857  = Indoor & Outdoor, c1859, Part 1  = Parlour Pastimes, 1868.  Many of the problems are identical to Book of 500 Puzzles.

PCP.  1932.  H. E. Dudeney.  Puzzles and Curious Problems.  Nelson, 1932; revised ed., nd [1936?].  (Almost all of this is in 536.)  There are almost no changes in the revised ed., except that problem 175 and its solution have been corrected _ it is a cross number puzzle and the text was for a different diagram.  See:  7.AM.

Peano.  Giochi.  1924.

                                    Giuseppe Peano (1858‑1932).  Giochi di Aritmetica e Problemi Interessanti.  G. B. Paravia, Torino, nd [1924 and later reprints].  (Thanks to Luigi Pepe for a photocopy of this.)

Pearson.  1907.             A. Cyril Pearson.  The Twentieth Century Standard Puzzle Book.  Routledge, London, nd [1907].  Three parts in one volume, separately paginated.  The parts were also published separately.  Each part has several numbered sequences of problems.

Peck & Snyder.  1886.

                                    Price List of Out & Indoor Sports & Pastimes.  Peck & Snyder, 126‑130 Nassau Street, N. Y., 1886.  Reprinted, with some explanatory material, in the American Historical Catalogue Collection, Pyne Press, Princeton, 1971.  Unpaginated _ I have numbered the pages starting with 1 as the original cover.

Perelman.  FFF.  1934.

                                    Yakov Isidorovich Perelman [_. _. ________] (c1890?-1942).  Figures for Fun.  _____ __________ [Zhivaya Matematika], _____ [Nauka], Moscow.  The books give no indication of the original dates, but Tatiana Matveeva has kindly searched the Russian State Library and found it was originally published by ___. ____.-____. _____., Leningrad-Moscow, 1934.  Schaaf I 9 cites Recreational Arthmetic, 6th ed., Leningrad, 1935 and Sphinx 5 (1935) 96 reviews the 5th ed. of L'Arithmétique Récréative, Leningrad, 1934 _ both presumably the same book ??

                    Translated by G. Ivanov‑Mumjiev.  Foreign Languages Publishing House, Moscow, 1957, 120 sections. 

                    (2nd ed., 1973 _ used for MCBF, below, apparently the same as the 3rd ed.) 

                    Translated by G. Ivanov‑Mumjiev.  3rd ed., MIR, 1979, 123 sections.  The 3rd ed. drops 3 sections and adds 6 sections and has some amended English.

Perelman.  FMP.  1984.

                                    Yakov Isidorovich Perelman [_. _. ________].  Fun with Maths and Physics.  MIR, Moscow, 1984.  [This is a translation of _____________ ______ _ _____ [Zanimatel'nye Zadachi i Oryty], _______ __________ [Detskaya Literatura], Moscow.)  (There was a _____________ ______, with 4th ed. in 1935 _ no earlier version in Russian State Library.  This title originally published by ______, 1959.)  Compiled by I. I. Pruskov.  Translated by Alexander Repyev.  This is a compilation from several of his books from 1913 to c1942 (when he died).  I have not yet seen the earlier books (??NYS), but if this is mainly based on the earlier book of the similar title, this would date the material to c1935? and I will use this date.

Perelman.  MCBF.  c1980?

                                    Yakov Isidorovich Perelman [_. _. ________].  Mathematics Can Be Fun.  3rd ed., MIR, 1985.  This consists of the following, originally separate, works, but with the second part having its page and problem numbers continued from the first part.  Both these works exist in many other editions and translations.

                    Figures for Fun, translated from _____ __________ [Zhivaya Matematika], _____ [Nauka], Moscow, translated 1973 _ with 123 sections.  Translator not specified, but presumably G. Ivanov-Mumjiev, as in FFF above.

                    Algebra Can be Fun, translated from _____________ _______ [Zanimatel'naya Algebra] (3rd ed. was published by ____, Leningrad-Moscow, 1937 _ The Russian State Library apparently has no earlier edition), edited and supplemented by V. Boltyansky, _____ [Nauka], Moscow, 1976, translated by G. Yankovsky, 1976. 

                    References to this will be to material not in FFF, so will be dated 1937.

Phillips, Hubert (1891-1964).

                                    See:  Brush,  Week‑End.

Pike.  Arithmetic.  1788.

                                    Nicolas Pike.  A New and Complete System of Arithmetic, composed for the Use of the Citizens of the United States.  John Mycall, Newbury-Port, Massachusetts, 1788.  (There is a 2nd ed., 1797, ??NYR.)

Prévost.  Clever and Pleasant Inventions.  (1584), 1998.

                                    J[ean?] Prévost.  (La Première Partie des Subtiles et Plaisantes Inventions, Contenant Plusieurs Jeux de Récréation.  Antoine Bastide, Lyons, 1584.  ??NYS.)  Translated by Sharon King as:  Clever and Pleasant Inventions  Part One  Containing Numerous Games of Recreations and Feats of Agility, by Which One May Discover the Trickery of Jugglers and Charlatans.  Hermetic Press, Seattle, 1998.  [No Second Part ever appeared.  Hall, OCB, pp. 43, 100 & 113.]  This is apparently the first book primarily devoted to conjuring.  Only five copies of the original are known.  There was a facsimile in 1987.  My thanks to Bill Kalush for bringing this work to my attention.

Price, Harry (1881-1948).  See: HPL.

Problemes.  1612.

                                    Claude‑Gaspar Bachet (c1587-1638).  Problèmes plaisans & délectables qui se font par les nombres.  (1st ed., 1612);  2nd ed., 1624, P. Rigaud, Lyon (for 1 & 2 ed.);  revised by A. Labosne, (3rd ed., 1874; 4th ed., 1879); 5th ed., 1884, Gauthier‑Villars, Paris (for 3, 4, 5 ed.).)  5th ed. reprinted by Blanchard, Paris, 1959 et al., with a Frontispiece portrait and an introduction by J. Itard, based on the article by Collet and Itard cited in 1 below. 

                    I have now obtained a photocopy of the 2nd ed. and have examined a 1st ed.  I had believed that Bachet added 10 problems in the 2nd ed., but the additional section of 10 problems, beginning  "S'Ensuivent quelques autres ..." is already in the 1612 1st ed.  In the 1612, there are two problems  V, but in 1624, these are made into two parts of prob. V.  However, he does extend the initial section of 22 problems to 25 problems, inserting the new material as problems 3, 16 and 21.  Prob. 16 (1612) = 18 (1624) has additional material.  Also, Bachet greatly expands his preliminary material on the properties of numbers from 14 to 52 pages, but Labosne drops this.  Otherwise, the material seems identical and the main text seems pretty much identical with the fifth edition except that orthography is modernised _ e.g. plaisans becomes plaisants, mesme becomes même, luy becomes lui, etc.  I have now compared the 3rd ed with the 5th ed and I could find no differences between them _ though I didn't check every word.  Labosne adds a Supplement of 15 problems, four Notes and a table of contents.  Labosne's Préface given in the 5th ed. is for the 3rd ed.  I will cite problem numbers and pages from the 1st ed., 1612; 2nd ed., 1624 and the 5th ed., 1884 (1959 reprint), e.g.  Prob. XIX, 1612, 99-103.  Prob. XXII, 1624: 170-173;  1884: 115‑117.  I will generally not give problem titles as they usually run to several lines.  I will denote Labosne's supplementary problems as Bachet-Labosne, 1874.

                    I have seen a 4th ed. by Gauthier‑Villars, 1905, no editor named, containing only 37 of the 50 problems in the 5th ed.  A contemporary review by E. Lampe (Fortschritte der Math. 36 (1905) 300‑301) was also mystified by this edition.  C&B list this ed.

Prthudakasvâmî or Prth_daka.  See: Chaturveda.

Putnam.  Puzzle Fun.  1978.

                                    Graham R. Putnam, ed.  Puzzle Fun.  Fun Incorporated, np [Chicago?], 1978.


Rara.  1970.  David Eugene Smith.  Rara Arithmetica.  (1908; with some addenda, 1910; Addenda, 1939, published both separately and with the 1910 ed.); 4th ed., combining the original with both Addenda and with De Morgan's Arithmetical Books of 1847 and a new combined index, Chelsea, 1970.  References are to the main entry of this.  Check the index for references to the Addenda and to De Morgan.

Riddle, Edward (1788-1854).

                                    See:  Ozanam‑Riddle.

The Riddler. See under Boy's Own Book.

Riese.  Coss.  1524.

                                    Adam Riese (c1489-1559).  Die Coss.  German MS of 1524 found at Marienberg in 1855.  Described and abstracted in Programm der Progymnasial‑ und Realschulanstalt zu Annaberg 1860.  Reprinted in 1892.  My reference to this comes from Johannes Lehmann; Rechnen und Raten; Volk und Wissen, Berlin (DDR), 1987, pp. 7‑14, esp. p. 13.  I have since seen the Glaisher paper, op. cit. in 7.G.1 under Widman, esp. p. 37.  Glaisher and Lehmann cite: Bruno Berlet; Adam Riese, sein Leben und seine Art zu rechnen; Die Coss von Adam Riese; Leipzig & Frankfurt, 1892.  Glaisher notes that this was a pamphlet.  BLLD provided a copy from Biblioth. Regia Berolinen. G., but it was lacking a title page.  It seems to have the title: Zur Feier des vierhundertsten Geburtsjahres von Adam Riese.  It was printed by Königl. Universitätsdruckerei von H. Stürtz in Würzburg.  The Vorwort is dated 1892, but only signed 'Der Verfasser' and his name does not appear anywhere except on the spine of the library's cover.  The booklet has two parts.

                    Adam Riese, sein Leben, seine Rechenbücher und seine Art zu rechnen (from the Programm for 1855), pp. 1‑26.  This is a discussion of Riese's Rechnung, but it also mentions some material from his 'grosse Rechenbuch' titled Rechenung nach der lenge, auf den Linihen und Feder, written in 1525 but not published until 1550.  Glaisher, loc. cit., p. 43, says he sees no authority for the date of 1525 and assumes it was written c1550.  (I have recently obtained a 1976 reprint of this work, ??NYR)

                    Die Coss von Adam Riese (with Abdruck der Coss) (from the Programm for 1860), pp. 27‑62.  This gives many numbered problems _ I will cite the problem number and pages from this.

                    There is a recent facsimile of the MS which I have just received _ ??NYR.

Riese.  Rechnung.  1522.

                                    Adam Riese (c1489-1559).  Rechnung auff der Linien unnd Federn ...  Erfurt, 1522.  I have two reprinted editions.  See Rara 138-143.

                    Christian Egenolph, Frankfurt, 1544.  (Riese's text is dated 1525.  There is a supplement on gauging by Erhard Helm, dated 1544.)  Facsimile by Th. Schäfer, Hannover, 1978.

                    Christian Egenolff's Erben, Frankfurt, 1574.  (Riese's text is dated 1525 and appears to be the same text as above, but reset.  The Supplement has further material.)  Facsimile by Th. Schäfer, Hannover, 1987.

RM.                             (François-) Édouard (-Anatole) Lucas (1842-1891).  Récréations mathématiques.  (Gauthier‑Villars, Paris, 4 vols, 1882, 1883, 1893, 1894, 2nd eds. of vol. 1, 1891, vol. 2, 1893)  = Blanchard, Paris, (1960), 1975‑1977, using 2nd ed. of vol. 1 and 1st ed. of vol. 2 (however, there seem to be very few differences in the editions).  I will cite the Blanchard reprint volumes as RM1, etc.  (Dates are as given in Harkin, op. cit. in 1 below, and on the books, but I have seen other dates cited.) 

                    Lucas; L'Arithmétique Amusante, 1895, Note IV, pp. 210-260 gives various fragments of material for further volumes which were found after Lucas's untimely death.  His draft Tables of Contents for volumes 5 and 6 are given on p. 210, but no material exists for most of the chapters.

RMM.          Recreational Mathematics Magazine.  Nos. 1 - 14 (Feb 1961 - Jan/Feb 1964).  Quite a bit of the material in this was abstracted and sometimes extended in: Joseph S. Madachy; Mathematics on Vacation; Scribners, NY, 1966; somewhat corrected as: Madachy's Mathematical Recreations; Dover, 1979.

Rocha.  Libro Dabaco.  1541.  SEE:  Tagliente.  Libro de Abaco.  (1515).  1541.


                                    Lynn Rohrbough edited a series of 20 booklets, called Handy Series, Kits A-J and M‑V, for Cooperative Recreation Service, Delaware, Ohio, during at least 1925-1941.  Most of these were reprinted and revised several times.  Two of these are of especial interest to us and are listed below.  Several others are cited a few times.

Rohrbough.  Brain Resters and Testers.  c1935.

                                    Lynn Rohrbough, ed.  Brain Resters and Testers.  Handy Series, Kit M, Cooperative Recreation Service, Delaware, Ohio, nd [c1935].

Rohrbough.  Puzzle Craft.  1932.

                                    Lynn Rohrbough, ed.  Puzzle Craft  Plans for Making and Solving 40 Puzzles in Wire, Wood and String.  Handy Series, Kit U, Cooperative Recreation Service, Delaware, Ohio, (1930), 1932. 

                    I have another version of this, unfortunately undated, but apparently later, so I have dated it as 1940s?  Jerry Slocum located this by tracking down Rohrbough's successors.  The 1932 version has 39 puzzles in its index, but 4 more that were not indexed and some Notes which are listed in the index of this version, making 44 items in all.  13 items are omitted and replaced by 5 in the present version, giving 36 indexed items.  The outside of the back cover of the 1932 version shows a number of puzzles, including several not described in either version of the booklet. 

Rudin.  1936.                Jacob Philip Rudin.  So You Like Puzzles!  Frederick A. Stokes Co., NY, 1936.


SA.                               Scientific American, usually Martin Gardner's Mathematical Games column.  For years from at least 1950, SA appeared in two volumes per year, each of six issues.  In year  1950 + n,  vol. 182 + 2n  covers  Jan-Jun  and  vol. 183 + 2n  covers  Jul-Dec.  See also under Gardner.

Sanford.  1930.              Vera Sanford.  A Short History of Mathematics.  Houghton Mifflin, Boston, 1930 & 1958.  See also:  H&S.

Santi.  1952. Aldo Santi.  Bibliografia della Enigmistica.  Sansoni Antiquariato, Florence, 1952.  2541 entries, often citing several editions and versions, arranged chronologically from 1479 onward.  My thanks to Dario Uri for providing this.  I will site item numbers.

Schaaf.  1955-1978.

                                    William L. Schaaf.  A Bibliography of Recreational Mathematics.  Vol. 1, (1955, 1958, 1963); 4th ed., 1970.  Vol. 2, 1970.  Vol. 3, 1973.  Vol. 4, 1978.  National Council of Teachers of Mathematics, Washington, DC.  See Schaaf & Singmaster in Section 3.B for a Supplement to these.

Schwenter.  1636.

                                    Daniel Schwenter (1585-1636).  Deliciæ Physico‑Mathematicae.  Oder Mathemat‑ und Philosophische Erquickstunden, Darinnen Sechshundert Drey und Sechsig, Schöne, Liebliche und Annehmliche Kunststücklein, Auffgaben und Fragen, auf; der Rechenkunst, Landtmessen, Perspctiv, Naturkündigung und andern Wissenschafften genom_n, begriffen seindt, Wiesolche uf der andern seiten dieses blats ordentlich nacheinander verzeichnet worden: Allen Kunstliebenden zu Ehren, Nutz, Ergössung des Gemüths und sonderbahren Wolgefallen am tag gegeben Durch M. Danielem Schwenterum.  Jeremiæ Dümleis, Nuremberg, 1636.  [Note: the text is in elaborate Gothic type with additional curlicues so that it is not always easy to tell what letter is intended!]  Probably edited for the press by Georg Philip Harsdörffer.

                    Extended to three volumes by Harsdörffer in 1651 & 1653, with vol. 1 being a reprint of the 1636 vol.  Vol. 2 & 3 have titles as follows.

                    Delitiæ Mathematicæ et Physicæ  Der Mathematischen und Philosophischen Erquickstunden  Zweiter Theil:  Bestehend in Fünffhundert nutzlichen und lustigen Kunstfragen / nachsinnigen Aufgaben / und derselben grundrichtigen Erklärungen / Auss Athanasio Kirchero Petro Bettino, Marion Mersennio, Renato des Cartes, Orontio Fineo, Marino Gethaldo, Cornelio Drebbelio, Alexandron Tassoni, Sanctorio Sanctorii, Marco Marco, und vielen anderen Mathematicis und Physicis zusammen getragen durch Georg Philip Harsdörffern.  Jeremia Dümlern, Nürnberg, 1651.

                    Delitiæ Philosophicæ et Mathematicæ  Der Philosophischen und Mathematischen  Erquickstunden / Dritter Theil:  Bestehend in Fünffhundert nutzlichen und lustigen Kunstfragen / und derselben gründlichen Erklärung: Mit vielen nothwendigen Figuren / so wol in Kupffer als Holz / gezieret.  Und  Aus allen neuen berühmten Philosophis und Mathematicis, mit grossem Fleiss zusammen getragen.  Durch  Georg Philip Harsdörffern.  Wolffgang dess Jüngern und Joh. Andreas Endtern, Nürnberg, 1653.

                    This 3 vol. version was reprinted in 1677 and 1692.  Modern facsimile of the 3 vol. version edited by Jörg Jochen Berns, Keip Verlag, Frankfurt Am Main, 1991, HB.  See also MUS II 325-326.  Schott described this as a German translation of van Etten/Leurechon, but this is quite wrong.  Volkmann & Tummers, p. 152, say it is 'partally derived from' van Etten/Leurechon.  C&B list just the 1636, under Schwenterum. 

                    I have not yet entered all the items from this.

SIHGM.  1939-1941.

                                    Ivor B. Thomas.  Selections Illustrating the History of Greek Mathematics.  Loeb Classical Library, 1939‑1941, 2 vols.

Simpson.  Algebra.  1745.

                                    Thomas Simpson (1710-1761).  A Treatise of Algebra; Wherein the Fundamental Principles Are fully and clearly demonstrated, and applied to the Solution of a great Variety of Problems.  To which is added, The Construction of a great Number of Geometrical Problems; with the Method of resolving the same Numerically.  John Nourse, London, 1745. 

                    I also have the 7th ed., with the slightly different title:  A Treatise of Algebra.  Wherein the Principles Are Demonstrated, And Applied In many useful and interesting Enquiries, and in the Resolution of a great Variety of Problems of different Kinds.  To which is added, The Geometrical Construction of a great Number of Linear and Plane Problems; with the Method of resolving the same Numerically.  The Seventh Edition, carefully Revised.  F. Wingrave, Successor to Mr. Nourse, London, 1800. 

                    I have now seen a 6th ed., F. Wingrave, 1790 and it appears identical to the 7th ed.  Both have an Author's Preface to the Second Edition. 

                    I will give the 1745 details with the 1790/1800 details in parenthesis like (1790: ...).

SLAHP.  1928.              Sam Loyd Jr. (1873-1934)  Sam Loyd and His Puzzles.  An Autobiographical Review.  Barse & Co., NY, 1928.  (This contains somewhat more original material than I expected, but he claims that he devised a lot of his father's puzzles given in the Cyclopedia, OPM, and even earlier.)

Slocum.  Compendium.  1977.

                                    Jerry (= G. K.) Slocum.  Compendium of Mechanical Puzzles from Catalogues.  Published by the author, Beverly Hills, 1977, 57pp.  This is a compendium of illustrations and descriptions from 30 catalogues.  The earliest ones are Bestelmeier, 1793, 1807 (Jacoby edition); The Youth's Companion, 1875; Montgomery Ward, 1886, 1889, 1903, 1930; Peck & Snyder, 1886; Joseph Bland, c1890.  Others of some interest are: Gamage's, 1913, c1915, c1928; Johnson Smith, 1919, 1935, 1937, 1938, 1942.

Slocum & Gebhardt _ see under Catel.

SM.                              Scripta Mathematica.

Smith, David Eugene (1860‑1944).

                                    See the following four items and also:  Rara.

Smith.  History.  1923.

                                    David Eugene Smith.  History of Mathematics.  Two vols.  (Ginn, NY, 1923)  = Dover, 1958.

Smith.  Number Stories.  1919.

                                    David Eugene Smith.  Number Stories of Long Ago.  NCTM, (1919), reprinted 1968?  Chaps. IX and X.

Smith.  Source Book.  1929.

                                    David Eugene Smith.  A Source Book in Mathematics.  Two vols.  (1929)  = Dover, 1959.

Smith & Mikami.  1914.

                                    David Eugene Smith  &  Yoshio Mikami.  A History of Japanese Mathematics.  Open Court, Chicago, 1914.

The Sociable.  1858.

                                    The Sociable; or, One Thousand and One Home Amusements.  Containing Acting Proverbs; Dramatic Charades; Acting Charades, or Drawing-room Pantomimes; Musical Burlesques; Tableaux Vivants; Parlor Games; Games of Action; Forfeits; Science in Sport, and Parlor Magic; and a Choice Collection of Curious Mental and Mechanical Puzzles; &c,&c.  Illustrated with nearly three hundred engravings and diagrams, the whole being a fund of never-ending entertainment.  By the author of "The Magician's Own Book."  (Dick & Fitzgerald, NY, 1858 [Toole Stott 640 lists this as anonymous; C&B list it under the title, with no author]); G. G. Evans, Philadelphia, nd, but the back of the title gives  ©1858 by Dick & Fitzgerald, NY, so this copy seems to be a reprint of the 1858 book.  Cf. Book of 500 Puzzles for discussion of possible authorship.  The Preface here says that most of the Parlor Theatricals are by Frank Cahill and George Arnold _ Toole Stott opines that this reference led Harry Price to ascribe this and the related books to these authors.  My thanks to Jerry Slocum for providing a copy of this.

                    The entire section Puzzles and Curious Paradoxes, pp. 285-318, is identical to the same section in Book of 500 Puzzles, pp. 3-36.  Rulfs (see under Status of the Project in the Introduction) says this draws on tha same sources as Magician's Own Book, with more taken from Endless Amusement and Parlour Magic. 

                    See also:  Book of 500 Puzzles,  Boy's Own Conjuring Book,  Illustrated Boy's Own Treasury,  Indoor and Outdoor,  Landells: Boy's Own Toy-Maker,  The Secret Out (in 4.A.1),  Hanky Panky.

"The Sphinx".               See:  Lemon.

Sridhara.  c900.             _rîdharâcârya.  Pâtîganita.  c900.  Transcribed and translated by Kripa Shankar Shukla.  Lucknow Univ., Lucknow, 1959.  The text is divided into verses and examples, separately numbered by the editor.  I will cite verse (v.) and example (ex.) and the page of the English text.  The editor has appended answers on pp. 93‑96, some of which were given by an unknown commentator.  (I have seen this dated 8C, which would put it before Mahavira _ ??)

SSM.             School Science and Mathematics.

Struik.  Source Book.  1969.

                                    D. J. Struik (1894-  ), ed.  A Source Book in Mathematics 1200‑1800.  Harvard Univ. Press, 1969.

Sullivan.  Unusual.  1943 & 1947.

                                    Orville A. Sullivan.  Problems involving unnusual situations.  SM 9 (1943) 114‑118 & 13 (1947) 102‑104.  (Previously listed in Section 2 below.

Suter.  1900-1902.        Heinrich Suter.  Die Mathematiker und Astronomen der Araber und Ihre Werke.  (AGM 10 (1900) & 14 (1902)); reprinted by APA _ Academic Publishers Associated, Amsterdam, 1981.  See also:  H. P. J. Renaud; Additions et corrections à Suter "Die Mathematiker und Astronomen der Araber"; Isis 18 (1932) 166-183.

S&B.  1986.  Jerry (= G. K.) Slocum & Jack Botermans.  Puzzles Old & New _ How to Make and Solve Them.  Univ. of Washington Press, Seattle, 1986.  Slocum had produced a detailed index for this and has extended it to a joint index with New Book of Puzzles.


Tabari.  Mift_h al-mu‘_mal_t.  c1075.

                                    Mohammed ibn Ayy_b Tabar_.  Mift_h al-mu‘_mal_t.  c1075.  Ed. by Mohammed Amin Riy_hi, Teheran, 1970.  ??NYS _ frequently cited and sometimes quoted by Tropfke and others.

Tagliente.  Libro de Abaco.  (1515).  1541.

                                    Girolamo & Giannantonio Tagliente.  Libro de abaco che insegnia a fare ogni raxone marcadantile & apertegare le terre con larte di la giometria & altre nobilissime raxone straordinarie c_ la tarifa come raspondeno li pexi & monete de molte terre del mondo con la inclita citta de. Venetia.  El qual Libro se chiama Texauro universale ...; Venice, 1515.  See Rara 114-116, 495, 511‑512, which seems to confuse this with another work whose title starts:  Opera che insegna ....  Riccardi [Biblioteca Matematica Italiana, 1952] lists  27  editions of this and three editions of the other work.  He says Boncompagni has studied this work and found that Giovanni Rocha made some corrections and that several editions have only his name, so it is sometimes catalogued under Rocha _ cf below.  Smith mentions  25  editions under Tagliente and says Riccardi mentions  11  others.  It is clear that this was a major book of its time.  I have briefly looked at a few examples and they seem to have the same material, though the woodcuts were often changed.

                    I have examined:  Giovanne Rocha;  Libro Dabaco che insegna a fare ogni ragione mercadãtile: & a ptegare le terre cõ larte di la geometria: & altre nobilissime ragione straordinarie cõ la Tariffa come respõdeno li pesi & mone de molte terre del mõdo con la inclita di Vinegia.  El qual Libro se chiama Thesauro universale.  Venturino Rossinello, Venice, 1541.  Smith, Rara, p. 529, only records a 1550 ed. printed by Giovanni Padovano in Venice.  The Crawford Collection has 1544 & 1550.  Not under Rocha in Riccardi.  I found this in the Turner collection at Keele as A4.32, but it is not under Rocha in Hill's Catalogue (listed in 3.B), but is under Tagliente.  It has nice woodcut(?) illustrations in the text _ see Rara 512 for an example.  Having first found this book on the shelf at the Turner Collection, I originally thought it was by Rocha and hence an extraordinarily rare book.  I am grateful to Bill Kalush for identifying this as a version of Tagliente and for pointing out its importance.

Tartaglia, Nicolo (or Niccolò) (c1506-1559).

                                    See:  General Trattato.

Thomas, Ivor B.             See:  SIHGM.

Tissandier.  Récréations Scientifiques.  1880.

                                    Gaston Tissandier.  Les Récréations Scientifiques ou L'Enseignement par les Jeux.  G. Masson, Paris, (1880);  2nd ed., 1881;  3rd ed., 1883;  (4th ed., 1884);  5th ed., 1888;  (6th ed., 1893;  7th ed., 1894.)  I have seen 3rd ed., 1883, and I have 2nd ed., 1881, & 5th ed., 1888.  Tissandier was editor of La Nature and the articles often have fine illustrations by L. Poyet and others, often copied elsewhwere.  See Tom Tit for more of Poyet's work.  I have seen the date of the first two editions as 1881 & 1882, but the Avertissement of the 2nd ed. says the 1st ed. was Nov 1880 and the Avertissement is dated Apr 1881.  [C&B only list 1881.]

Tissandier.  Popular Scientific Recreations.  1881.

                                    Translation and enlargement of the above.  Ward Lock, London, ([1881, 1882]); New enlarged ed., nd [1890, 1891].  [Not clear which French edition the translation is based on.  The new enlarged ed. contains a Supplement on pp. 775‑876 which includes material which is in the 5th French ed. of 1888, but not in the 3rd French ed. of 1883, so it seems the the main text is c1885 and the supplement is c1890.  C&B list a London edition, nd, 780pp.]  The index refers to a puzzle of knots and cords on p. 775 which is not present.  Most of the Supplement appeared as a series of Scientific Amusements in (Beeton's) Boy's Own Magazine from 1889 _ I have vol. 3 (1889) which has the first 10 articles, comprising 62 pages and 67 problems. 

                    Some of the material appeared in an anonymous book: Marvels of Invention and Scientific Puzzles.  Ward, Lock, & Co., nd [c1890].  This consists of Chapters 56-60, pp. 726-774, and Chap. 32, pp. 448-465, of Popular Scientific Recreations, set on smaller pages, plus a few extra items:  An economical mouse-trap (pp. 57-58);  Flying bridges (pp. 64-66);  Performing fleas (pp. 77-79);  string puzzles and an air toy (pp. 83‑85).  The string puzzles are probably what was on p. 775(-776?) of the earlier edition of Popular Scientific Recreations and the other material seems to have come from some edition of that work or from the articles in (Beeton's) Boy's Own Magazine.

Tom Tit.  1890-1893?

                                    Arthur Good [= "Tom Tit"].  La Science Amusante.  3 vols., Larousse, Paris, 1890, 1892, 1893?  [I have seen the dates given as 1889, 1891, 1893, but the Introductions are dated as I have given, the last being Dec 1893.]  The material originally appeared in the magazine L'Illustration with classic engravings by Poyet which have been often reproduced, e.g. in:  Beeton's Boy's Own Magazine;  The Boy's Own Paper;  Kolumbus‑Eier (1890, 1976) _ translated as: Columbus' Egg (1978).  Arthur Good's name is clearly English and I have wondered if the articles were written originally in French or if they were translated from his English.

                    I have the three volume set and five one volume selections/adaptations.  I will give references to these by the initials shown below.

C.                 François Caradec, ed.  La Science Amusante _ 100 Experiences de Physique.  Les Editions 1900 [no accent], Paris, 1989.  [This consists of all of Vol. 1, reordered, but otherwise little changed.  Caradec's Preface gives a little about the author.  The illustrations are a bit dark.]

H.                Magic at Home.  A Book of Amusing Science.  Annotated translation of La Science Amusante, vol. 1, by Prof. Hoffmann.  Cassell, 1891.  Cf. VBM below.

VBM.           The Victorian Book of Magic Illustrated or Professor Hoffman's Curious & Innocent Diversions for Parlour & Refined Gatherings.  Selected [from the above] & with a note to readers by C. Raymond Reynolds.  (Stephen Greene Press, Japan, 1969); Hugh Evelyn, London, nd [c1970].  [This has 26 of the items in Vol. 1.  Illustrations are small but good.]

K.                Tom Tit.  Scientific Amusements.  Selected and translated by Cargill G. Knott.   Nelson, nd [1918].  [This contains 178 items, mostly from Vols. 2 & 3, but Knott has added a few others, possibly taken from Tom Tit's later articles?  Knott has also extended some items.  Sadly, the illustrations were poorly redrawn for this edition.]

R&A.           David Roberts & Cliff Andrew, eds.  100 Amazing Magic Tricks.  Cape, London, 1977.  [Selections from all three volumes.  Although this refers to the original books and L'Illustration, it avoids mentioning the original author's name!  Illustrations are very good.]

[I have also seen an Italian translation.  There was a US ed., trans. by Camden Curwen & Robert Waters; Magical Experiments or Science in Play; (© Worthington, 1892); David McKay, Philadelphia, 1894, 329 pp. [Christopher 398.]]

Tonstall.  De Arte Supputandi.  1522.

                                    Cuthbert Tonstall [often spelled Tunstall] (c1474-1559).  De Arte Supputandi Libri Quatuor.  ([With Quattuor] Richard Pynson, London, 1522 _ the first arithmetic printed in England.)  I have seen:  Robert Stephan, Paris, 1538.  Though the pagination is different, Smith, Rara, gives no indication that the 1538 text is any different than the 1522, so I will cite this as 1522.  Most citations are to Book III, whose problems are numbered.  See Rara 132-136.

Toole Stott.  1976-1978.

                                    Raymond Toole Stott.  A Bibliography of English Conjuring  1581‑1876.  2 vols., published by the author, Derby, 1976, 1978; distributed by Harpur & Sons, Derby.  1414 entries.  References are to the item number.

TP                                Title Page.

Tropfke.  1980.             Johannes Tropfke, revised by Kurt Vogel, Karin Reich and Helmuth Gericke.  Geschichte der Elementarmathematik.  4th ed., Vol. 1: Arithmetik und Algebra.  De Gruyter, Berlin, 1980.  (Prof. Folkerts says (1994) that vol. 2 is being edited.)

                    [The 1st ed. was De Gruyter?, Leipzig, 1902, 2 vols.  2nd ed., De Gruyter, Berlin & Leipzig, 1921-1924, 7 vols.  3rd ed., De Gruyter, Berlin & Leipzig, 1930-1940, vols. 1-4 (the MSS of the remaining volumes were lost in 1945).]

Tunstall, Cuthbert _ see:  Tonstall, Cuthbert.


Uncle George.               See:  Parlour Pastime.

Unger.  Arithmetische Unterhaltungen.  1832.

                                    Ephraim Salomon Unger.  Arithmetische Unterhaltungen, bestehend in einer systematisch geordneten Sammlung von mehr als 900 algebraischen Aufgaben, verbunden mit einer Anleitung, diese Aufgaben mittelst der einfachsten Regeln der Arithmetick zu lösen.  (Erfurt, 1832, 4 + 253 pp., ??NYS);  2nd ed., Keysersche Buchhandlung, Erfurt, 1838, 10 + 268pp.  MUS 166 only mentions the 1838 ed. but a copy of the 1st ed. was advertised by Sändig in Jun 1997.  I haven't seen any other reference to this work.  In general, this book believes in beating problems to death _ each type of problem is done several times.  E.g. there are 10 problems of the Chinese Remainder Theorem with two moduli.  Hence I will generally not describe all the problems.


van Etten.                     See:  Etten above.

Vogel, Kurt. See:  AR,  BR,  Chiu Chang Suan Ching,  Columbia Algorism,  Tropfke,  items in 7.K under al‑Khwârizmî,  items in 7.P.7 and 7.R.2 under Fibonacci.

Vyse.  Tutor's Guide.  1771?

                                    Charles Vyse (fl. 1770-1815).  The Tutor's Guide, being a Complete System of Arithmetic; with Various Branches in the Mathematics.  In Six Parts, ....  To which is added, An Appendix, Containing Different Forms of Acquittances, Bills of Exchange, &c. &c.  The whole being designed for the Use of Schools, ....  10th ed., ed. by J. Warburton.  S. Hamilton for G. G. and J. Robinson, London, 1799.  12 + 335 pp.  [1st ed. was 1770 or 1771;  2nd ed., 1772;  4th ed., 1779;  6th ed., 1785;  1790;  8th ed., 1793;  1799;  12th ed., 1804;  13th ed., 1807;  14th ed., 1810;  15th ed., 1815;  1817;  16th ed., 1821.]  Since books of this nature rarely had major changes, I will date this as 1771? until I see further editions.

                                    The Key to the Tutor's Guide; or the Arithmetician's Repository: containing Solutions to the Questions, &c. in the Tutor's Guide, with references to the pages where they stand.  To which are added Some Useful Rules, &c.  Likewise An Appendix; showing the Combination of Quantities; The different Ways they may be varied; with the method of filling the magic squares, &c.  ....  Eighth edition; Carefully revised, corrected, and augmented.  G. & J. Robinson, London, 1802.  8 + 370 pp + 2pp publisher's ads.  [1st ed., 1773;  3rd ed., 1779;  4th ed., 1785;  7th ed., 1799;  8th ed., 1802;  9th ed., 1807;  11th ed., 1818.] 

                    Despite the claim in the title of the Key, the references to the answers are in the text at the beginning of each set of exercises.  I have the 8th and 9th eds. of the Key and have not seen any difference between them _ indeed I have found a common misprint _ and they give the answers to the 10th ed. of the text, on the pages cited in the text, so I assume they are essentially identical to the 7th ed. of the Key. 


Walkingame.  Tutor's Assistant.

                                    Francis Walkingame.  The Tutor's Assistant; Being a Compendium of Arithmetic, and a Complete Question-Book.  ...  To which are added, A new and very short Method of extracting the Cube Root, and a General Table for the ready calculating the Interest ....  The Fifteenth Edition.  Printed for the Author, London (Great Russel-Street, Bloomsbury), 1777.  [First ed. was 1751.  There were about a hundred editions in all.  See Wallis's article on this book in MG 47 (No. 361) (1963) 199-208.]

                                    The Tutor's Assistant.  Being a Compendium of Arithmetic, and a Complete Question-Book.  ...  To which are added, A new and very short Method of extracting the Cube Root, and a General Table for the ready calculating the Interest ....  The Twentieth Edition.  Printed for the Author, London (Kensington), 1784.  Appears to be identical to the 15th ed., except for resetting and some small changes, both corrections and errors, so I won't cite this separately.

                                    The Tutor's Assistant, being a Compendium of Arithmetic, and Complete Question-Book; ...; to which is added, A Compendium of Book-keeping, by Single Entry, by Isaac Fisher.  Thomas Richardson, Derby; Simpkin, Marshall & Co., London, 1835.  [The first Derby edition by Fisher was 1826.] 

                                    The Tutor's Companion; or, Complete Practical Arithmetic.  To which is added A Complete Course of Mental Arithmetic, ..., by Isaac Butler.  Webb, Millington, and Co., London, 1860.

                    The editions are pretty similar, but the interesting collection of problems at the end is much shortened in the 1835 ed. and a few are omitted in the 1860 ed.  Consequently I will assume the problems date from 1751, unless they vary in some important way.  I also have a Key to Walkingame from 1840, but it does not correlate with any of the editions I have!

Wallis.                          The Wallis Collection of early English mathematics books.  Gathered by Peter J. Wallis and left to the University of Newcastle upon Tyne in 1992.  A typical catalogue entry is  Wallis 227 CAR  and there are special sections for Newtoniana and Record(e).

Week‑End.  1932.         Hubert Phillips.  The Week‑End Problems Book.  Nonesuch Press, London, 1932.

Wehman.  New Book of 200 Puzzles.  1908.

                                    Wehman Bros.'  New Book of  200 Puzzles.  Wehman Bros., 126 Park Row, NY, 1908.  Largely copied from various 19C works: Boy's Own Book, Magician's Own Book, The Sociable, sometimes with typographical omissions.

Western Puzzle Works.  1926.

                                    Western Puzzle Works, 979 Marshall Avenue, St. Paul, Minnesota.  1926 Puzzle Catalogue.  Photocopy provided by Slocum.  Unpaginated, 8pp.

Williams.  Home Entertainments.  1914.

                                    Archibald & F. M. Williams.  Home Entertainments.  The Hobby Books, ed. by Archibald Williams.  Nelson, London, nd [1914 _ BMC].

Williams, Henry Llewellyn, Jr. (1842-??).  Books by Frikell?, particularly Magician's Own Book, are often attributed to him.  [C&B, under  Williams, Henry Llewellyn ("W. Frikell")  lists:  Hanky Panky;  Magician's Own Book, London & New York;  (Magic No Mystery);  The Secret Out  and says to also see Cremer.]

Wilson, R. J. See:  BLW.

Wingate/Kersey.  1678?.

                                    Edmund Wingate (1596-1656).  Mr. Wingate's Arithmetick; Containing A Plain and Familiar Method For Attaining the Knowledge and Practice of Common Arithmetick.  (1629.)  The Seventh(?) Edition, very much Enlarged.  First Composed by Edmund Wingate, late of Gray's-Inn, Esquire.  Afterwards, upon Mr. Wingate's Request, Enlarged in his Life-time: Also since his Decease carefully Revised, and much Improved; ... By John Kersey, late Teacher of the Mathematicks.  My copy is lacking the TP and pp. 345+, but it appears to be identical to The Tenth Edition; J. Philips, J. Taylor & J. Knapton, London, 1699 _ though reset, it has the same pagination throughout except for the Dedication.  A Librarian's note suggests my earlier version is the 7th ed. of 1678.  This would be the fourth and last of Kersey's versions.  Kersey began editing from the second or third (1658) ed. and did four versions, the last in 1678. 

                    The material of interest is almost all in Chapter 10 of Kersey's Appendix: A Collection of subtil Questions to exercise all the parts of Vulgar Arithmetick; to which also are added various practical Questions about the mensuration of Superficial Figures and Solids, with the Gauging of Vessels, pp. 475-527, 75 questions.  There are a few further items in Chapter 11: Sports and Pastimes, pp. 528-544, 7 problems.  Chapter 11 is not clearly marked as being by Kersey in these copies, but is so marked in later editions and it is pretty clear that the entire Appendix is due to Kersey.  At the end, he says he has taken the problems of Cahp. 11 from Bachet's Problemes.

                    I have seen a 14th ed. of 1720 which has the same text, reset and repaginated, with some supplementary material by George Shelley.  I have also seen a 19th ed. of 1760 which has been considerably reorganized by James Dodson.  The two chapters of puzzle problems have become Chapters XLIII and XLIV and the material has been changed, generally omitting some problems of interest and only adding two.

Winning Ways.  1982.  

                                    Elwyn R. Berlekamp, John H. Conway & Richard K. Guy.  Winning Ways for Your Mathematical Plays: Vol. 1: Games in General; Vol. 2: Games in Particular.  2 vols, Academic Press, NY, 1982.

Witgeest.  Het Natuurlyk Tover-Boek.  1686.

                                    Simon Witgeest.  Het Natuurlyk Tover-Boek, Of't Nieuw Speel-Toneel Der Konsten.  Verhandelende over de agt hondert natuurlijke Tover-Konsten. so uyt de de Gogel-tas, als Kaartspelen, Mathematische Konsten, en meer andered diergelijke aerdigheden, die tot vermaek, en tijtkorting verstrecken.  Mitsgaders eenTractaet van alderley Waterverwen, en verligteryen;  Als oock Een verhandelinge van veelderley Blanketsels. Om verscheyde wel-ruykende Wateren, Poederen en Balsemen, als ook kostelijke beeydselen, om het Aensicht, Hals en Handen, wit en sagt te maecken, door Simon Witgeest.  Jan ten Hoorn, Amsterdam, 1686.  ??NYS _ some photocopies sent by Jerry Slocum.  'Boek' is 'Boeck' on the frontispiece and running heads.  This is a much expanded and retitled 3rd edition of Witgeest's 1679 work.  The new material is stated to already be in the 2nd ed. of 1682. 

                    [There were many later editions:  1695;  1698;  G. de Groot Keur, Amsterdam, 1725 (10th ed.), 1739;  1749;  1760;  Amsterdam, 1773;  1815  [Christopher 1098-1099, C&B, HPL].  It was translated as: Naturliches Zauber-Buch oder neuer Spiel-Platz der Künste; Hoffmanns sel Wittw. & Engelbert Streck, Nürnberg, 1702.  There were later editions (all in Nürnberg?) of 1713 (in 1 or 2 vols), 1730, 1739, 1740, 1745, 1753, 1760-1762, 1763, 1766, 1781, 1786, 1798 and a Lindau reprint of 1978  [Christopher 1092-1097, C&B, V&T], all apparently based on the 1682 Dutch ed.]

Witgeest.  Het Nieuw Toneel der Konsten.  1679.

                    Simon Witgeest.  Het Nieuw Toneel der Konsten, Bestaande uyt Sesderley Stukken: het eerste, handelt van alderley aardige Speeltjes en Klugjes: het tweede, van de Verligt-konst in 't Verwen en Schilderen: het derde, van het Etzen en Plaat-shijden: het vierde, van de Glas-konst: het vijfde, heest eenige aardige remedien tegen alderley Ziekten: het sesde, is van de Vuur-werken.  Uyt verscheyde Autheuren by een vergadert, door S. Witgeest, Middel-borger.  Jan ten Hoorn, Amsterdam, 1679;  facsimile with epilogue by John Landwehr, A. W. Sijthoff's Uitgeversmaatschappij N. V., Leiden, 1967 (present from Bill Kalush). 

                    There were many later editions, but Nanco Bordewijk has examined these and discovered that the 3rd ed. of 1686 (I can't recall if he saw the 1682 ed.) was so extensively revised and extended as to constitute a new book, and it has the different title given in the previous entry.  (Other sources indicate these revisions are already in the 2nd ed. of 1682.)  Landwehr has written a bibliographical article on this book _ ??NYR.

Wood.  Oddities.          Clement Wood.  A Book of Mathematical Oddities.  Little Blue Book 1210.  Haldemann-Julius, Girard, Kansas, nd [1927].


Young Man's Book.  1839.

                                    Anonymous.  The Young Man's Book of Amusement.  Containing the Most Interesting and Instructive Experiments in Various Branches of Science.  To Which is Added All the Popular Tricks and Changes in Cards; and the Art of Making Fire Works.  William Milner, Halifax, 1844, HB.  2 + 384 pp + folding plate (originally a frontispiece).  My copy has a number of annotations as though in preparation for another edition.  [Hall BCB 322.  Toole Stott 751.  BCB 320-323 are  1839, 1840, 1844, 1848.  Heyl 358-360 are  1846, 1846 (Milner & Sowerby ??), 1850.  Toole Stott 749-752, 1216 are  1839, 1840, 1844, 1846, 1850.  Christopher 1111-1113 are 1839, 1846, 1859 (Milner & Sowerby).  All these are apparently the same except for the publisher's name change.]


536.                             H. E. Dudeney.  536 Puzzles and Curious Problems.  Ed. by M. Gardner.  Scribners, NY, 1967.  (This consists of almost all the puzzles from Modern Puzzles (MP) and Puzzles and Curious Problems (PCP).)  [There is also a Fontana, London, 1970, edition in two volumes: Puzzles and Curious Problems (258 problems); More Puzzles and Curious Problems (261 problems).]


                                   BC, e.g.  ‑330  is  330 BC  and  ‑5C  is  5th century BC.

¹                                  Inequality or incongruence (mod m).  (My word processor does not have an incongruence sign.)