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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; Scribner's, NY, 1976. Chaps. 1 7 & 9 previously appeared as: The Numerology of Dr. Matrix; Simon & Schuster, NY, 1967. In contrast to his other books above, the answers and comments occur at the end of this book instead of following the original articles.

Workout A Gardner's Workout Training the Mind and Entertaining the Spirit. A. K. Peters, Natick, Massachusetts, 2001. This comprises 41 chapters of articles written after his retirement from SA.

Gardner. MM&M. 1956.

Martin Gardner. Mathematics, Magic and Mystery. Dover, NY, 1956.
General Trattato. 1556.

Nicolo Tartaglia (c1499-1557). (La Prima Parte del) General Trattato di Numeri et Misure. Curtio Troiano, Venice, 1556. (Modern Italian spells his given name as Niccolò, but it appears as Nicolo on the title page.) Six parts actually appeared in 1556-1560. All references are to Part 1. Unless otherwise specified, reference is to Book 16 (of Part 1), but I also have references to Books 12 and 17. CAUTION -- the running head in Book 17 says Libro Decimosesto for several pages before changing to Libro Decimosettimo. Since it is hard to find the beginnings of books, this can cause confusion. See Rara 275-279; Van Egmond's Catalog 345-346.

In 1578, Guillaume Gosselin produced an annotated translation of parts 1 & 2 into French as: L'Arithmetique de Nicolas Tartaglia -- cf Van Egmond's Catalog 347.

Ghaligai. Practica D'Arithmetica. 1521.

Francesco Ghaligai. Practica D'Arithmetica di Francesco Ghaligai Fiorentino. Nuovamente Rivista, & con somma Diligenza Ristampata. I Giunti, Florence, 1552. Smith, Rara, says that this is identical to the first (Latin?) edition by Bernardo Zucchetta, Florence, 1521, except that edition was titled Summa De Arithmetica, so I will date the entries as 1521. See Rara 132; Van Egmond's Catalog 316-317.

Gherardi. Libro di ragioni and Liber habaci. 1328 & c1310.

Paolo Gherardi. Two Italian MSS in Codici Magliabechiani Classe XI, no. 87 & 88 in Bib. Naz. di Firenze. Van Egmond's Catalog 115-116. The first is dated 1327 (but see below). The second is undated, but clearly of a similar date which I originally denoted 1327? - see below. Transcribed by Gino Arrighi; Collana di Storia della Scienza e della Tecnica, No. 2; Maria Pacini Fazzi, Lucca, 1987. See also: Warren Van Egmond; The earliest vernacular treatment of algebra: the Libro di ragioni of Paolo Gerardi (1328); Physis 20 (1978) 155-189. Van Egmond notes that the date of 30 Jan 1327 is in our year 1328 and uses this in his Catalog. He doubts whether Liber habaci is actually by Gherardi and his Catalog assigns no author to it, so I will put Gherardi? as author. He dates it to c1310. His paper is concerned with the quadratic and cubic equations and hence of little interest to us.

Good, Arthur. See: Tom Tit.

Gori. Libro di arimetricha. 1571.

Dionigi Gori. Libro di arimetricha. 1571. Italian MS in Biblioteca Comunale di Siena, L. IV. 23. ??NYS. Extensively quoted and discussed in: R. Franci & L. Toti Rigatelli; Introduzione all'Aritmetica Mercantile del Medioevo e del Rinascimento; Istituto di Matematica dell'Università di Siena, nd [1980?]. (Later published by Quattroventi, Urbino, 1981.) (I will quote Gori's folios and also give the pages of this Introduzione.) Van Egmond's Catalog 191-192.

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

Guy, Richard Kenneth (1916- ). See: Winning Ways.

G4Gn Gathering for Gardner n, held in Atlanta. 1: Jan 1993; 2: Jan 1996; 3: Jan 1998; 4: Feb 2000; 5: Apr 2002.

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

G&PJ. Games and Puzzles Journal. Successor to Chessics. Ran through 12 issues, Sep 1987 -- Dec 1989, then restarted intermittently in May 1996.
Haldeman-Julius. 1937.

E. Haldeman-Julius. Problems, Puzzles and Brain-teasers. Haldeman-Julius Publications, Girard, Kansas, 1937. Facsimile (I believe) presented by Bob Koeppel at IPP13, 1993.

Hall. BCB. 1957.

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

Hall. OCB. 1972.

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

Halwas. Robin Halwas, Ltd. List XV. American Mathematical Textbooks 1760-1850. Catalogue of 511 items being sold as a collection. London, 1997, 144pp. Quite a number of English works and a few French works had US editions which are detailed in this.

Hanky Panky. 1872.

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

HB.XI.22. 1488.

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

Heath, Sir Thomas L. See: Diophantos; HGM.

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

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

HM. Historia Mathematica.

Hoernle, A. F. Rudolf. See: Bakhshali MS.

Hoffmann. 1893. Professor Louis Hoffmann [pseudonym of Angelo John Lewis (1839 1919)]. Puzzles Old and New. Warne, London, 1893. Reprinted with Foreword by L. E. Hordern; Martin Breese, London, 1988.

In 1984, Hordern published a limited edition (15 copies) of "The Hordern Collection of Hoffmann Puzzles 1850 1920", which gives colour photos of examples from his collection and the appropriate text. I often cite these pictures as they often differ from those in the following item, with the heading Hordern Collection. Generally, the next item gives more specific dating and/or older examples.

In 1993, Hordern produced a corrected edition of all of Hoffmann as: Hoffmann's Puzzles Old & New; published by himself. This has colour photos of all puzzles for which known examples exist. I will cite this as Hoffmann-Hordern. The 1893 edition gives solutions for each chapter in a following chapter, but both of Hordern's illustrated versions give each solution immediately after the problem, with colour picture nearby. A small section on Elementary Properties of Numbers is omitted from the 1993 edition.

See also: Ozanam Hutton.

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

Illustrated Boy's Own Treasury. c1847.

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

Indoor & Outdoor. c1859.

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

IPPn n-th International Puzzle Party. 10 = London, 1989; 13 = Amsterdam, 1993; 16 = Luxembourg, 1996; 19 = London, 1999; 20 = Los Angeles, 2000; 22 = Antwerp, 2002. This are the ones I have attended, but some material has appeared at other IPPs.
Jackson. Rational Amusement. 1821.

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

JRM. Journal of Recreational Mathematics.
Kanchusen. Wakoku Chiekurabe. 1727.

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

Kaye, George R. See: Bakhshali MS.

King. Best 100. 1927

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

Knott, Cargill G. See under: Tom Tit.

Labosne. See under: Problemes.

Ladies' Diary. See under: T. Leybourn.

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

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

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

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

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

Leopold. At Ease! 1943.

Jules Leopold. At Ease! Ill. by Warren King. Whittlesey House (McGraw Hill), 1943. [This appears to be largely drawn from Yank, The Army Weekly, over the previous few years.]

Leske. Illustriertes Spielbuch für Mädchen. 1864?

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

Leurechon, Jean (c1591-1670). See: van Etten.

T. Leybourn.

Thomas Leybourn, ed. The Mathematical Questions, proposed in the Ladies' Diary, and Their Original Answers, Together with some New Solutions, from its commencement in the year 1704 to 1816. 4 vols., J. Mawman, London, and two co-publishers, 1817. I have only examined vols. I & II so far. The problems are proposed each year with solutions in the following year. Leybourn puts the solutions just after the problem and numbers almost all the problems consecutively, though I don't know if these numbers are in the Ladies' Diary. Problems do not have any names and sometimes have pseudonyms or vague names, e.g. Mr. Deare. I will give the names of the proposer and solver(s), followed by Ladies' Diary and the two years involved, then = T. Leybourn, his volume and pages and his question number. E.g. Chr. Mason, proposer; Rob. Fearnside, solver. Ladies' Diary, 1732-33 = T. Leybourn, I: 223, quest. 168.

W. Leybourn. Pleasure with Profit. 1694.

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

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

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

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

Lloyd, E. Keith. See: BLW.

Loeb Classical Library.

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

Loyd, Sam (1841-1911) (& Sam Loyd Jr. (1873-1934). See: Cyclopedia, MPSL, OPM, SLAHP.

Lucas, Édouard (1842-1891). See: RM and the following.

Lucas. L'Arithmétique Amusante. 1895.

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

Lucca 1754. c1330.

Scuola Lucchese. Libro d'abaco. c1390. Dal Codice 1754 (sec. XIV) della Biblioteca Statale di Lucca. Edited by Gino Arrighi. Cassa di Risparmio di Lucca, 1973. Arrighi gives folio numbers and I will cite these and the pages of his edition. Arrighi has c1390, but Van Egmond's Catalog 163-164 gives c1330.

MA. Mathematical Association (UK).

MAA. Mathematical Association of America.

Magician's Own Book. 1857.

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

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

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

This is quite different than the previous book.

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

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

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

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

Mair. 1765?.

John Mair. Arithmetic, Rational and Practical. Wherein The Properties of Numbers are clearly pointed out, the Theory of the science deduced from first principles, the methods of Operation demonstratively explained, and the whole reduced to Practice in a great variety of useful Rules. Consisting of Three Parts, viz. I. Vulgar Arithmetic. II. Decimal Arithmetic. III. Practical Arithmetic. A. Kincaid & J. Bell, Edinburgh, in three vols, 1765-1766 (Turner G1.14/1-3); 2nd ed., A. Kincaid & W. Creech, and J. Bell, Edinburgh, 1772; 3rd ed, John Bell and William Creech, Edinburgh, 1777. I have the 3rd ed and have seen the 2nd ed. All the material of interest is in part 3, which first appeared as vol. 3 in 1765 and books of this era often had little or no change between editions, so I will date entries as 1765?

Manson. Indoor Amusements. 1911.

J. A. Manson, compiler. Indoor Amusements. Cassell & Co., London, 1911. FP + 8pp + 340pp + 8pp Index (341-348). This is an extension of Cassell's Book of In-Door Amusements ..., expanding the earlier 209pp of main text to 340pp. This is partly due to using larger type, getting 47 lines per page instead of 54. The material which was in Cassell's is generally unchanged.

Manuel des Sorciers. 1825.

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

Marinoni, Augusto. See: Pacioli. De Viribus. c1500.

McKay. At Home Tonight. 1940.

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

McKay. Party Night. 1940.

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

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

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

See also: David Singmaster; Puzzles from the Greek Anthology; Math. Spectrum 17:1 (1984/85) 11-15 for a survey of these problems.

Meyer. Big Fun Book. 1940.

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

MG. Mathematical Gazette.

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

Minguet. 1733.

Pablo Minguet (or Minguét) è (or é or e or y) Yról (or Irol) ( -1801?). Engaños à Ojos Vistas, y Diversion de Trabajos Mundanos, Fundada en Licitos Juegos de Manos, que contiene todas las diferencias de los Cubiletes, y otras habilidades muy curiosas, demostradas con diferentes Láminas, para que los pueda hacer facilmente qualquier entretenido. Pedro Joseph Alonso y Padilla, Madrid, nd [1733]. Frontispiece + 12 + 218 pp. Imprimaturs or licenses dated 3 Nov 1733, 10 Nov 1733 & 12 Dec 1733. [NUC. Christopher 672 for a 18 + 110 pp version. C&B gives versions with 18 + 110 pp and with 12 + 218 pp. HPL has 4 versions -- the one I examined was 12 + 218 pp. The BM has a version, but it is not clear which.]

The early history of this book is confused. The first edition may have only had 18 + 110 pp (or 105 pp ??), then was apparently frequently reprinted, without changing the dates, sometimes with additions. Or it may be that both versions appeared in 1733. However, my copy is identical to one in HPL which is catalogued as 1733 and Palau (a list of Spanish book sales, c1955) lists six sales of the 12 + 218 pp version, dated 1733, and only one sale of the 18 + 110 pp version, dated 1733. Christopher dates the 12 + 218 pp versions to c1760.

I now have discovered 26 editions of this work, and 2 and 9 editions of two derivative works, but I have only seen a few versions. If anyone has access to a copy, I would like a photocopy of the TP and other publishing details and of the Indice.

3rd ed, Domingo Fernandez de Arrojo, Madrid, 1755, 18 + 157 + 3 pp. [This includes the same material as 1733, but it is reset with smaller type and much rearranged and includes some new material. It seems to be the same as the 1766. Palau gives this as 18 + 150 + 10 pp and says there was a cheap edition of 14 + 171 + 10 pp. NUC gives 14 + 171 +11 pp, with publisher Domingo Fernandez. HPL has two 'entirely different' editions of 1755 -- the one I examined was 18 + 157 + 3 pp. BM has a 1755, but it is not clear which.]

3rd ed, Dionisio Hernández, Madrid, 1755? [Palau, with nd.]

Antonio del Valle, Madrid, 1756. 171 + 20 (or 40??) pp. [Palau.]

Revised. Pedro J. Alfonso y Padilla, Madrid, c1760, 14 + 218 pp. [Christopher 673 & 674.]

Idem. Añadido en esta quarta impresion, 18 enigmas, 6 quisicosas muy curiosas. 4th ptg, D. Gabriel Ramirez, Madrid, 1766, 16 + 150 + 10 pp. [BM; Palau; Christopher 675.]

Palau says he has seen a catalogue with a 1793 ed, but thinks this is a printing error for either 1733 or 1893.

Palau lists an 1804 reprint of the 1733, 14 + 218 pp.

Sierra y Martí, Barcelona, 1820, 1 + 224 pp. [Identical to 1733, 12 + 218 pp, except the text has been reset, spelling modernized, the front matter updated and the text starts on p. 10, with everything the same as the 1733, except page numbers are increased by 9, and the index is reduced in size. HPL; Palau; Christopher 676.]

Neuva Edicion corregida y aumentada por D. J. M. de L. Juan Francisco Piferrer, Barcelona, 1822, 1 + 224 pp. [This is quite differently arranged than the 1733, 12 + 218 pp, and 1820 eds, and contains some extra material. Palau, with 1 + 240 pp; NUC; Shortz; Christopher 677.].

Retitled: Juegos de Manos ó sea Arte de Hacer Diabluras, y Juegos de Prendas. Que contiene varias demonstraciones de mágia, fantasmagoria, sombras y otros entretenimientos de diversion para tertulias y sociedades caseras. ilustrado con láminas Por D. Pablo Minguet, y aumentado considerablemente en esta nueva edicion con infinidad de juegos nuevos, y con laminas intercaladas en el texto. D. Manuel Saurí, Barcelona, 1847, 189 + 10 pp. [Palau; Christopher 678.]

Juegos de manos; ó sea, Arte de hacer diabluras ...ilustrado con 60 grabados.... New ed. Simon Blanquet, Mexico, nd [1856]. 7 + 498 pp. [NUC.]

Palau cites an 1857 reprint of the 1847, presumably the 2nd Saurí ed..

Title varied: Juegos de Manos ó sea Arte de Hacer Diabluras. Contiene: juegos de prendas, de naipes, varias demonstraciones de majia, fantasmagoria, sombras y otros entretenimientos de diversion, para tertulias y sociedades caseras. Por D. Pablo Minguet. Tercera Edicion Aumentada con gran número de Juegos nuevos, y grabados intercalados en el texto. Manuel Saurí, Barcelona, 1864. 1 + 213 pp. [From TP of 1993 facsimile. This omits one problem and some discussion that was in 1733 and adds 22 new problems, but I see some of these already appeared in 1755 and 1822. Palau, noting that this is the 3rd ed from Saurí and mentioning a recent facsimile; HPL.]

Palau cites an 1875 Barcelona reprint as 185pp, but has no publisher's name, probably the 4th Saurí ed.

Title varied: Juegos de manos; ó sea, El arte de hacer diabluras, contiene 150 clases de juegos, de prendas, de naipes, varias demonstraciones de mágia, fantasmagoria, sombras y otros entretenimientos de diversion, para tertulias y sociedades caseras. 5. ed., aumentada con gran numero de juegos nuevos y 70 grabados intercalados en el texto. Manuel Saurí, Barcelona, 1876. 192pp. [NUC.]

Palau confusingly cites Sauri reprints of 192pp: 8th ed, 1885; 8th ed, 1888; 9th ed, 1888. [Christopher 679 & 680 are the latter two. Perhaps there is an error in the dates, e.g. the 1885 might really be the 7th ed.]

Title varied: Juegos de Manos o sea Arte de hacer Diabluras, contiene 150 clases de juegos, de prendas de naipes, varias demonstraciones de magia, fantasmagorias, sombras y otros entretenimientos de mucha diversion, para tertulias y sociedades caseras. Décima edición aumentada con juegos nuevos, y 70 grabados intercalados en el texto. Juan Tarroll y Cla., Barcelona, 1893. 192pp. [Palau.]

Palau lists 11th ed [from Sauri]. Sauri y Sabater, Barcelona, 1896. 192pp. [NUC lists 2 copies of the 11th ed as Sauri y Sabater, 1897, 192pp & 189pp.]

12th ed [from Sauri]. Sauri, Barcelona, 1906. 190pp. [Christopher II 2102. HPL with nd.]

Facsimile of the 1864 ed, with Presentación por Joan Brossa: De la brujería blanca. Editorial Alta Fulla, Barcelona, 1981. 11pp new material + II-VIII + 9-213 pp of facsimile (II is FP; III is TP; V-VIII is Al Lector; 9-12 is a poetic introductory Relacion; 203-213 is Indice).

2nd ed (i.e. printing) of the 1981 facsimile of the 1864 ed, with a new cover, 1993. [DBS.]

Pp. 1-25 is a fairly direct translation of the 1723/1725 Ozanam, vol. IV, pp. 393 406. A number of other pictures and texts also are taken from Ozanam. I will give the date as 1733, though the expansion may not have occurred until c1755. I will cite the 1755, 1822 and 1864 pages in parentheses, e.g. Pp. 158-159 (1755: 114-115; 1822: 175-176; 1864: 151).

MiS. Mathematics in School.

Mittenzwey. 1880.

Louis Mittenzwey. Mathematische Kurzweil. Julius Klinkhardt, Leipzig. 1880; 2nd ed., 1883; 3rd ed., 1895; 4th ed., 1904; 5th ed., 1907; 6th ed., 1912; 7th ed., 1918. I will give the date as 1880 or 1895? I now have copies of the 1st, 4th, 5th and 7th eds. In working through the other editions, I have seen many more items than I had previously recorded and I now think this is one of the most important 19C puzzle books.

[Ahrens, MUS #363 lists the first ed. being 1879, apparently taking the date of the Foreword. He also has 3rd ed., 1903, but V&T (and another reference) cite 3rd ed., 1895. I think this is a misinterpretation of the last Vorrede in the 4th ed., which is for the 3rd and 4th ed. and dated 1903. Trey Kazee has obtained a copy of the 2nd ed. The first two editions have the author's given name and have 300 problems; the 4th, 5th and 7th have 333. The Vorrede to the 2nd ed in the 2nd ed. says it has no major changes. The Vorrede to the 3rd & 4th eds in the 4th ed says the 3rd ed was extended and the 4th ed. has replaced some problems, so it seems that the 3rd probably had 333 problems. Compared to the 1st ed, the 4th drops 9 problems and adds 42. The Vorrede to the 3rd, 4th and 5th eds in the 5th ed also says some problems have been replaced, but I have not discovered any differences between the 4th and 5th eds except one minor amendment, some resetting which changes the page breaks on pp. 1-10 and 36-37 and a few line breaks. I suspect that the 4th and 5th eds are very similar to the 3rd. The 5th and 7th eds. are very similar, but the 7th is reset with smaller type and occupies five fewer pages. There are a few amendments and reorderings and four problems (36, 92, 122, 137) have been replaced, but a number of simple misprints persist through all editions. I will give pages in 1st, 3rd?, and 7th eds, e.g. Prob. 193 & 194, pp. 36 & 89; 1895?: 218 & 219, pp. 41 & 91; 1917: 218 & 219, pp. 37 & 87.]

MM. Mathematics Magazine.

Montucla, Jean Étienne (1725-1799). See: Ozanam; Ozanam Montucla.

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

MPSL1. 1959 & MPSL2. 1960.

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

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

1st ed., Feb 1892, 240pp.

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

3rd ed., 1896, 276pp.

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

5th ed., 1911, 492pp.

6th ed., 1914, 492pp.

7th ed., 1917, 492pp.

8th ed., 1919, 492pp.

9th ed., 1920, 492pp.

10th ed., 1922, 366pp.

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

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

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

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

A few of the editions are actually reprintings of the previous edition: 2 is essentially the

same as 1, 6 as 5, 9 as 8, 13 as 12. Consequently I will rarely, if ever, cite

editions 2, 6, 9, 13. For each topic occurring in Ball, I have examined all the

editions, so the absence of a reference indicates the topic does not occur in that

edition -- unless it is buried in some highly unlikely place.

See also: Ball FitzPatrick.

MS. Mathematical Spectrum (Sheffield, UK).

MTg. Mathematics Teaching (UK).

MTr. Mathematics Teacher (US).

Munich 14684. 14C.

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

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

MUS. 1910 & 1918.

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

[MUS II vii lists 22 items which he had been unable to see and which he suspected might not exist. I have seen the following items from the list: 86 (= Les Amusemens, above), 102 (Hooper, listed in Some Other Recurring References, below; cf Section 4.A.1), 145 (Jackson, see above), 212 (author's name is Horatio Nelson Robinson); item 32 exists as an English edition of van Etten, but the citation gives the publisher as though he was the author; I have seen a copy of item 82 advertised for sale. A number of items (135, 152, 164, 221, 223, 277, 297, 317) are cited by Wölffing - op. cit. in Section 3.B.]

Muscarello. 1478.

Pietro Paolo Muscarello. Algorismus. MS of 1478. Published in 2 vols.: I -- facsimile; II -- transcription with notes and commentaries; Banca Commerciale Italiana, Milan, 1972. I will cite the folios (given in vol. I) and the pages of the transcribed version in vol. II. Van Egmond's Catalog 275-276.

M500. This is the actual name of the journal of the M500 Society, the Open University student mathematics society.
NCTM. National Council of Teachers of Mathematics.

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

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

The New Sphinx. c1840.

Anonymous. The New Sphinx An elegant Collection of upwards of 500 Enigmas Charades Rebusses Logogriphes Anagrams Conundrums &c. &c. To which are added, a Number of Ingenious Problems. T. Tegg & Son, London, nd, HB with folding frontispiece. [Vendor suggests it is 1840s. Shortz has 4th ed, by Gye & Baine and says it is c1840. He also has 'a new(?) edition', by T. Tegg, and says it is c1843. He says the chapter of geometrical problems and brainteasers was new in the 4th ed. Heyl 238 is a 7th ed., London, 18??, referring to HPL, where I find it in the Supplement.] The chapter of problems has 27 problems, of which 21 are copied from Endless Amusement II, 1837 ed., 20 of which come from the 1826? ed.

E. P. Northrop. Riddles in Mathematics. 1944.

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

H. D. Northrop. Popular Pastimes. 1901.

Henry Davenport Northrop. Popular Pastimes for Amusement and Instruction being a Standard Work on Games, Plays, Magic and Natural Phenomena Suitable for All Occasions containing Parlor Games; Charming Tableaux; Tricks of Magic; Charades and Conundrums; Curious Puzzles; Phrenology and Mind Reading; Palmistry, or How to Read the Hand; Humorous and Pathetic Recitations, Dialogues, Etc., Etc. including The Delightful Art of Entertaining The Whole Forming a Charming Treasury of Pastimes for the Home, Public Schools and Academies, Lodges, Social Gatherings, Sunday Schools, Etc., Etc. Frank S. Brant, Philadelphia, 1901. [Not in any of my bibliographies. Vendor says only two copies in NUC, none in BL.]

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

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

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

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

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

OCB. See: Hall, OCB.

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

o/o. On order.

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

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

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

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

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

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

(The above data were provided by Jerry Slocum.)

OUP. Oxford University Press.
Ozanam. 1694.

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

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

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

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

The Traité des Horologes élémentaires, which appears in the 1694 ed., is a translation of Domenico Martinelli's Horologi elementari. NUC says this was separately paginated in 1694, but it occupies pp. 473-583 of the 1696 ed and pp. 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 [sic] d'Arithmétique, de Géométrie, de Musique, d'Optique, de Gnomonique, de Cosmographie, de Mécanique, de Pyrotechnie, & de Physique. Avec un Traité des Horloges Elementaires. Par feu [misprinted Parfeu in vol. 1] M. Ozanam, de l'Académie Royale des Sciences, & Professeur en Mathematique. Nouvelle edition, Revûë, corrigée & augmentée.

Vol. 4 has different title page.

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

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

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

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

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

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

English versions

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

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

2nd ed.

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

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

3rd ed.

Recreations for Gentlemen and Ladies; being Ingenious Sports and Pastimes. Containing Many curious Inventions, pleasant Tricks on Cards and Dice; Arithmetical Sports; new Games; Rules for Assuredly winning at all Games, whether of Cards or Dice; Recreative Fire-works; Tricks to promote Diversion in Company, and other 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 Riddle printings seem to be from the same plates -- the date of the Prefatory Note and the Erratum given on p. xiv are the same in 1840 and 1851. Marcia Ascher cites an 1844 edition from Nuttall & Hodgson, but this is the printer.

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

P. M. Calandri. See: Benedetto da Firenze.

Pacioli. De Viribus. c1500.

Luca Pacioli (or Paciuolo) (c1445-1517). De Viribus Quantitatis. c1500. Italian MS in Codex 250, Biblioteca Universitaria di Bologna. Santi 3 dates it as 1498 and describes the later parts which deal with riddles, etc., but include some magic, etc. However, Pacioli petitioned for a privilege to print this in 1508 and Part 2, Chap. CXXIX, ff 228r-228v, has a date of 1509, so he may have been working on the MS for many years. Van Egmond's Catalog 55-56 is not as helpful as usual.

Part 1: Delle forze numerali cioe di Arithmetica is described in: A. Agostini; Il "De viribus quantitatis" di Luca Pacioli; Periodico di Matematiche (4) 4 (1924) 165 192 (also separately published with pp. 1-28). Agostini's descriptions are sometimes quite brief -- unless one knows the problem already, it is often difficult to figure out what is intended. Further, he sometimes gives only one case from Pacioli, while Pacioli does the general situation and all the cases. All references are to the problem numbers in this part, unless specified otherwise. I will use problem numbers and names as in the MS at the problem -- these often differ considerably from the numbers and names given in the index at the beginning of the MS. There are 81 problems in part 1, but the Index lists 120 -- in a few cases, the Index name clearly indicates a problem similar to an actual problem and I will mention this. There are microfilms at the Warburg Institute (currently misplaced) and at Munich and Siena. I printed Part 1 and some other relevant material from the Warburg microfilm, some 125pp. When I read this, I saw that the material near the last pages I had copied would be of interest, but when I went back to copy this material, the microfilm had been misplaced.

Dario Uri has photographed the entire MS and enhanced the images and put them all on a CD. This has 614 images, including the insides of the covers. This is often more legible than the microfilm, but the folio numbers are often faint, sometimes illegible. It was not until the transcription (below) became available that I could read the material just after this point and see that there were more interesting problems, but I found it difficult to read the Italian (many words are run together and/or archaic) and the diagrams referred to are lacking. Dario was able to carry on and found the Chinese Rings and about a dozen other interesting items. He has put some material up on his website: http://digilander.libero.it/maior2000/. This includes the indexes and a number of the most interesting items, with his comments and diagrams of later examples of the puzzles. I have now gone through all of the text and found a number of problems of interest for this bibliography. Nonetheless, quite a number of problems, some clearly of interest, remain obscure.

Transcription by Maria Garlaschi Peirani, with Preface and editing by Augusto Marinoni. Ente Raccolta Vinciana, Milano, 1997. (The publisher did not reply to a letter, but Bill Kalush kindly obtained a copy for me. Dario Uri says it can be bought from: Libreria Pecorini, 48 foro Buonaparte, Milano; tel: 02 8646 0660; fax: 02 7200 1462; web: www.pecorini.com.) I will cite the text as Peirani and any references to Marinoni's work as Marinoni. The transcription is not exactly literal in that Peirani has expanded abbreviations and inserted punctuation, etc. Also, Peirani seems to have worked from the microfilm or a poor copy as she sometimes says the manuscript has an incorrect form which she corrects, but Dario Uri's version clearly shows the MS has the correct form. Peirani uses the problem numbers and names in the MS (see comment above about these differing from those in the Index), but with some amendments. I will probably give problem names as in the MS, with some of Peirani's amendments. I will give translations of the names, but some of them are pretty uncertain and some have defeated me completely. Marinoni, pp. VIII IX indicates the MS was written in about 1496-1509.

The title is a bit cryptic, but I think the best English version is: On the Powers of Numbers, but Pacioli [f. Ir] has 'forze numerali' and R. E. Taylor [op. cit. in Section 1, pp. 307 & 339] follows Agostini and uses: On the Forces of Quantity.

Pacioli. Summa. 1494.

Luca Pacioli (or Paciuolo or Paccioli) (??-c1509). Sūma de Arithmetica Geometria Proportioni & Proportionalita. Paganino de Paganini, Venice, 1494 -- cf Van Egmond's Catalog 325-326; facsimile printed by Istituto Poligrafico e Zecca dello Stato, Rome, for Fondazione Piero della Francesca, Comune di Sansepolcro, 1994, with descriptive booklet edited by Enrico Giusti. There was a second ed., Paganino de Paganinis, Toscolano, 1523, but the main text seems identical, except for corrections (and errors) and somewhat different usage of initial letters and colour. For extensive studies of this book, see the works by Narducci, Taylor, Davis and Rankin given in Section 1. Davis identifies material taken from Piero della Francesca's works. Taylor says 99 copies of the 1494 and 36 copies of the 1523 are known. The text is in two parts -- the second part is geometry and is separately paged. All page references will be to the first part unless specified as Part II. Problems are numbered at the right hand edge of the last line of the previous problem. See Rara 54-59.

Davis notes that Pacioli's Summa, Part II, ff. 68v - 73v, prob. 1-56, are essentially identical to della Francesca's Trattato, ff. 105r - 120r.

Panckoucke, André Joseph (1700-1753). See: Les Amusemens.

Pardon, George Frederick (1824-1884). See: Indoor & Outdoor; Parlour Pastime; Parlour Pastimes.

Parlour Pastime. 1857.

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

Parlour Pastimes. 1868?

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

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

Peano. Giochi. 1924.

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

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

Peck & Snyder. 1886.

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

Peirani, Maria Garlaschi. See: Pacioli. De Viribus. c1500.

Perelman. FFF. 1934.

Yakov Isidorovich Perelman [Я. И. Перелман] (1882-1942). Figures for Fun. Живая Математика [Zhivaya Matematika], Наука [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 Гос. техн.-теор. издат., Leningrad-Moscow, 1934. Schaaf I 9 cites Recreational Arithmetic, 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 [Я. И. Перелман]. Fun with Maths and Physics. MIR, Moscow, 1984. [This is a translation of Занимательныи Задачи и Оыты [Zanimatel'nye Zadachi i Oryty], Детская Литературы [Detskaya Literatura], Moscow.) (There was a Занимательныи Задачи, with 4th ed. in 1935 – no earlier version in Russian State Library. This title originally published by Деттиз, 1959.) Compiled by I. I. Pruskov. Translated by Alexander Repyev. This is a compilation from several of his books from 1913 to c1942 (when he died). I have not yet seen the earlier books (??NYS), but if this is mainly based on the earlier book of the similar title, this would date the material to c1935? and I will use this date.

Perelman. MCBF. c1980?

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

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

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

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

Phillips, Hubert (1891-1964). See: Brush; Week End.

Pike. Arithmetic. 1788.

Nicolas Pike (1743-1819). A New and Complete System of Arithmetic, composed for the Use of the Citizens of the United States. John Mycall, Newbury-Port, Massachusetts, 1788. (I have a 2nd ed., 1797, [Halwas 318], ??NYR. This went through at least 5 editions and then at least six variants, often abridged for schools [Halwas 318-326].)

Poggendorff. J. C. Poggendorff. Biographisch-Literarisches Handwörterbuch zur Geschichte der Exacten Wissenschaften enthaltend Nachweisungen über Lebensverhältnisse und Leistungen von Mathematikern, Astronomen, Physikern, Chemikern, Mineralogen, Geologen usw aller Völker und Zeiten. Johann Ambrosius Barth, Leipzig. Facsimile by Maurizio Martino, Storrs-Mansfield (later Mansfield Center), Connecticut.

Vols. I (A - L) and II (M - Z). (1863), nd [bought in 1996].

Vol. III (1858-1883), edited by B. W. Feddersen & A. J. von Oettingen;

Parts I (A - L) and II (M - Z). (1898), nd [bought in 1998].

Vol. IV (1883-1904), edited by Arthur von Oettingen;

Parts I (A - L) and II (M - Z). (1904), nd [bought in 1998].

[Vol. V covers 1904-1922. Vol. VI covers 1922-1949. One can get I-VI on microfiche. Vol. VIIa covers 1932-1953 and apparently comprises 5 volumes. There is also a VIIa Supplement which gives material supplementary to vols. I-VI.]

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

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

Price, Harry (1881-1948). See: HPL.

Problemes. 1612.

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

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

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

Pŗthudakasvâmî or Pŗthūdaka. See: Chaturveda.

Pseudo-dell'Abbaco. c1440.

This is attributed to Paolo dell'Abbaco (sometimes called Dagomari) (c1281-1367). Trattato d'Aritmetica. (c1370, according to Arrighi, but see below). Codex Magliabechiano XI, 86 at Biblioteca Nazionale di Firenze. Edited by Gino Arrighi, Domus Galilaeana, Pisa, 1964. Arrighi gives some black & white reproductions of illustrations. I examined this MS in Sep 1994 and found the illustrations are often lightly coloured and that Arrighi's illustrations were probably made from poorish photocopies -- the writing on the opposite side shows through much more in several of his illustrations than it does in the originals. I have colour slides of 11 pages.

Warren Van Egmond [New light on Paolo dell'Abbaco; Annali dell'Istituto e Museo di Storia della Scienza di Firenze 2:2 (1977) 3 21 and Van Egmond's Catalog 114-115] asserts this MS is a c1440 compilation, based on watermark evidence, and doubts that it is due to dell'Abbaco, giving the author as pseudo-dell'Abbaco.

Smith, Rara, 435 440 describes a different MS at Columbia, headed 'Trattato d'Abbaco, d'Astronomia e di segreti naturali e medicinali', which he dates c1339. Van Egmond, above, gives the title of this as 'Trattato di tutta l'arte dell'abacho', but Van Egmond's Catalog 254-255 describes it as Plimpton 167, a codex containing two works. The first is the dell'Abbaco: Trattato di tutta l'arte dell'abacho; the second is Rinaldo da Villanova: Medichamento Generale, which has the title Trattato d'Abbaco, d'Astronomia e di segreti naturali e medicinali added in a later hand. The first includes the Regoluzze which is sometimes cited separately. This is quite a different book than the c1440 Trattato. There is a c1513 version at Bologna, MS B 2433, which is dated 1339 -- Dario Uri has sent a CD of images of it. See the entry for dell'Abbaco in 7.E.

Putnam. Puzzle Fun. 1978.

Graham R. Putnam, ed. Puzzle Fun. Fun Incorporated, np [Chicago?], 1978.
Rara. 1970. David Eugene Smith. Rara Arithmetica. (1908; with some addenda, 1910; Addenda, 1939, published both separately and with the 1910 ed.); 4th ed., combining the original with both Addenda and with De Morgan's Arithmetical Books of 1847 and a new combined index, Chelsea, 1970. References are to the main entry of this. Check the index for references to the Addenda and to De Morgan.

Rational Recreations. 1824.

Rational Recreations. Midsummer MDCCCXXIV. Knight and Lacey, London. This is a six part work, but is bound together -- perhaps the parts were issued monthly. The parts are consecutively paginated. [Toole Stott 590. Toole Stott 591 is 2nd ed, 1825 and 592 is 3rd ed, 1825, copublished in Dublin. Hall BCB 235, 236 are 1824 and 1825. C&B. HPL. Not in Christopher. I have examined the BL copy.]

Recorde. First Part. 1543.

Recorde. Second Part. 1552.

Recorde-Mellis. Third Part. 1582.

Recorde (or Record), Robert (1510?-1558). The Grounde of Artes Teaching the worke and practice of Arithmetike. .... The dating of this book is uncertain. Smith, Rara, p. 526 records a 1540 edition. An edition by Reynold Wolff, London, at the Bodleian (Douce R.301) has generally been dated as 1542 and there is a facsimile by Theatrum Orbis Terrarum, Amsterdam & Da Capo Press, NY, 1969, with the date 1542. There were reprints in 1543 and 1549. However, the DSB entry for Recorde ignores the Smith 1540 edition (presumably because it has not been confirmed) and says the 1542 is now dated as 1550?, making the

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