Eighth preliminary edition

It has been conjectured that this was a pseudonym of Luca Pacioli, but there is no evidence for this [R. Emmett Taylor; No Royal Road Luca Pacioli and His Times; Univ. of North Carolina Press, Chapel Hill, 1942, pp. 60 & 349].

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

Bourdon. Algèbre. 7th ed., 1834.

Louis Pierre Marie Bourdon (1779-1854). Élémens d'Algèbre. 7th ed., Bachelier, Paris, 1834. (1st ed, 1817; 5th, 1828; 6th, 1831; 8th, 1837; 1840. Undated preface in the 7th ed. describes many changes, so I will cite this as 1834, though much of the material would have occurred earlier.)
Boy's Own Book. 1828.

William Clarke, ed. The Boy's Own Book. The bibliography of this book is extremely complex -- by 1880, it was described as having gone through scores of editions. My The Bibliography of Some Recreational Mathematics Books has 11 pages listing 76 English (40 UK, 37 US, 1 Paris) versions and a Danish version, implying 88 English (50 UK, 37 US, 1 Paris) versions, and 10 (or 11) related versions, and giving a detailed comparison of the versions that I have seen. Because of the multiplicity of versions, I have cited it by title rather than by the original editor's name, which is not in any of the books (except the modern facsimile) though this attribution seems to be generally accepted. I have examined the following versions, sometimes in partial photocopies or imperfect copies.

Vizetelly, Branston and Co., London, 1828, 448pp.; 2nd ed., 1828, 462pp.; 3rd ed., 1829, 464pp (has an inserted advertisement sheet); 6th ed??, c1830, 462pp?? (my copy lacks TP, pp. 417-418, 431-436, 461-462); 9th ed., 1834, 462pp. Longman, Brown & Co., London, 24th ed., 1846, 462pp. [The latter five are identical, except for a bit in the Prelude (and the extra sheet in 3rd ed), so I will just cite the first of these as 1828 2. It seems that all editions from the 2nd of 1828 through the 29th of 1848, 462pp. are actually identical except for a bit of the Prelude (and the advertisement sheet in the 3rd ed.)]

First American Edition. Munroe & Francis, Boston & Charles S. Francis, NY, 1829, 316pp. Facsimile by Applewood Books, Bedford, Massachusetts, nd [1998?]. This is essentially an abridgement of the 2nd ed of 1828, copying the Prelude and adding "So far the London Preface. The American publishers have omitted a few articles, entirely useless on this side of the Atlantic, ...." The type is reset, giving some reduction in pages. A number of the woodcuts have been omitted. The section title pages are omitted. Singing Birds, Silkworms, White Mice, Bantams, Magnetism, Aerostatics, Chess and Artificial Fireworks are omitted. Angling, Rabbits, Pigeons, Optics are reduced. Rosamond's Bower is omitted from Paradoxes and Puzzles. Surprisingly, The Riddler is increased in size. The 2pp Contents is omitted and an 8pp Index is added.

Baudry's European Library & Stassin & Xavier, Paris, 1843, 448pp. [The existence of a Paris edition was previously unknown to the vendor and myself, but it is Heyl 354 and he cites Library of Congress. It is very different than the English and US editions, listing J. L. Williams as author. Even when the topic is the same, the text, and often the topic's name, are completely rewritten. See my The Bibliography of Some Recreational Mathematics Books for details -- in it I have found it generally necessary to treat this book separately from all other editions. I will cite it as 1843 (Paris). Much of this, including almost all of the material of interest is copied exactly in Anon: Boy's Treasury, 1844, qv, and in translated form in de Savigny, Livre des Écoliers, 1846, qv. The problem of finding the number of permutations of the letters of the alphabet assumes 24 letters, which makes me wonder if these books are based on some earlier French work. Heyl 355 is probably the same book, with slight variations in the title, by Dean and Munday, London, c1845.]

David Bogue, London, 1855, 611pp. [It seems that this version first appears in 1849 and continues through about 1859, when two sections were appended.]

[W. Kent (late D. Bogue), London, 1859, 624pp??. For almost all material of interest, this is identical to the 1855 ed, so I will rarely (if ever?) cite it.]

[Lockwood & Co., London, 1861, 624pp. Identical to the 1859 ed., so I will not cite it.]

Lockwood & Co., London, 1868, 696pp.

[Lockwood & Co., London, 1870, 716pp. Identical to 1868 with 20pp of Appendices, so page numbers for material of interest are the same as in 1868, so I will not cite it.]

[Crosby Lockwood & Co., London, 1880, 726pp. Identical to 1870, but having the Appendices and 20 more pages incorporated into a new section. For almost all material of interest, the page numbers are 30 ahead of the 1868 & 1870 page numbers, so I will not cite it except when the page numbers are not as expected.]

[5th (US?) ed., Worthington, NY, 1881, 362pp. For almost all material of interest, this is identical to the 1829 (US) ed., so I will rarely (if ever?) cite it.]

I will cite pages with edition dates and edition numbers or locations if needed (e.g. 1828-2: 410 or 1829 (US): 216). See also: Book of 500 Puzzles, Boy's Own Conjuring Book, Illustrated Boy's Own Treasury.

Anonymous. The Riddler; A Collection of Puzzles, Charades, Rebusses, Conundrums, Enigmas, Anagrams, &c. for the Amusement of Little Folks. S. Babcock, New Haven, Connecticut, 1835. 22pp. My copy has leaf 11/12 half missing and leaf 17/18 missing; NUC & Toole Stott 1392 say it should be 24pp, so presumably leaf 23/24 is also missing here. [Toole Stott 1392 has The Riddler: or, Fire-Side Recreations; a collection ..., 1838, also listed in NUC.] Paradoxes and Puzzles section consists of the introduction and 11 puzzles copied almost exactly from the Paradoxes and Puzzles section of Boy's Own Book, 2nd ed. of 1828 and this material is all in the first American edition of 1829. Other material is charades, etc. and is all in both these versions of Boy's Own Book. Shortz states that this is the first American book with puzzles -- but there were at least five American versions of Boy's Own Book before this and all the material in The Riddler, except some woodcuts, is taken from Boy's Own Book, so this pamphlet seems to be a pirate version. NUC also lists a 1838 version.

Boy's Own Conjuring Book. 1860.

The Boy's Own Conjuring Book: Being a Complete Hand-book of Parlour Magic; and Containing over One Thousand Optical, Chemical, Mechanical, Magnetical, and Magical Experiments, Amusing Transmutations, Astonishing Sleights and Subtleties, Celebrated Card Deceptions, Ingenious Tricks with Numbers, Curious and Entertaining Puzzles, Charades, Enigmas, Rebuses, etc., etc., etc. Illustrated with nearly two hundred engravings. Intended as a source of amusement for one thousand and one evenings. Dick and Fitzgerald, NY, 1860. 384pp. [Toole Stott 115, corrected, lists this as (1859), and under 114, describes it as an extended edition of The Magician's Own Book -- indeed the running head of the book is The Magician's Own Book! -- but see below. Toole Stott 481 cites a 1910 letter from Harris B. Dick, of the publishers Dick & Fitzgerald. He describes The Boy's Own Conjuring Book as a reprint of Magician's Own Book "evidently gotten up and printed in London, but singularly enough it had printed in the book on the title-page -- New York, Dick & Fitzgerald." Indeed, all the monetary terms are converted into British. Harold Adrian Smith [Dick and Fitzgerald Publishers; Books at Brown 34 (1987) 108-114] states that this is a London pirate edition. BMC has 384pp, c1860. NUC has a 384pp version, nd. Christopher 145-149 are five versions from 1859 and 1860, though none has the blue cover of my copy. Christopher 145 says the 1859 versions were printed by Milner & Sowerby, Halifax, and describes it as an extraction from Magician's Own Book, but see below. Christopher 148 cites Smith's article.] I also have a slightly different version with identical contents except omitting the date and frontispiece, but with a quite different binding, probably Christopher 149. [NUC lists 334pp, nd; 416pp, nd and 416pp, 1860. Toole Stott 114 is a 416pp version, 1861. Toole Stott 959 is a 534pp version, 1861. C&B cite a New York, 1859 with 416pp, a New York, nd, 334pp and London, c1850 (surely too early?).]

I have now compared this with The Magician's Own Book of 1857 and it is essentially a minor reworking of that book. The Magician's Own Book has 17 chapters and an answers chapter and a miscellaneous chapter of items which are almost all also listed in the Contents under earlier sections. All together, there are some 635 items. The Boy's Own Conjuring Book copies about 455 of these items essentially directly, completely omitting the chapters on Electricity, Galvanism, Magnetism, Geometry, Art, Secret Writing and Strength, and almost completely omitting the chapter on Acoustics. Of the 488 items in the other chapters, 453 are copied into the Boy's Own Conjuring Book, and this has in addition two of the acoustic problems, 125 new miscellaneous problems and 38pp of charades, riddles, etc. (The later UK edition of Magician's Own Book is very different from the US edition.) Many of the problems are identical to the Boy's Own Book or the Illustrated Boy's Own Treasury. See also: Book of 500 Puzzles, Boy's Own Book, Illustrated Boy's Own Treasury, Landells: Boy's Own Toy Maker.
Boy's Treasury. 1844.

Anonymous. The Boy's Treasury of Sports, Pastimes, and Recreations. With four hundred engravings. By Samuel Williams. [The phrasing on the TP could be read as saying Williams is the author, but the NUC entry shows he was clearly listed as the designer in later editions and his name appears on the Frontispiece.] D. Bogue, London, 1844. Despite the similarity of title, this is quite different from Illustrated Boy's Own Treasury and the similar books of c1860. [Toole Stott 116. Toole Stott 117 is another ed., 1847, 'considerably extended'. Toole Stott gives US editions: 959; 960; 118; 199 & 961-965 are 1st, 1847; 2nd, 1847; 3rd, 1848; 6 versions of the 4th, 1850, 1848, 1849, 1852, 1854, 1848. Hall, BCB 37 is a US ed. of 1850 = Toole Stott 119. Christopher 151 is a US version of 1850? NUC lists 9 versions, all included in Toole Stott. Toole Stott cites some BM copies, but I haven't found this in the BMC. A section of this, with some additional material, was reissued as Games of Skill and Conjuring: ..., in 1860, 1861, 1862, 1865, 1870 -- see Toole Stott 312-317.]

I have now found that much of this, including all the material of interest, is taken directly from the 1843 Paris edition of Boy's Own Book, qv, by J. L. Williams, including many of the illustrations - indeed they have the same Frontispiece, with S. Williams' name on it.

BR. c1305. Greek MS, c1305, Codex Par. Suppl. Gr. 387, fol. 118v 140v. Transcribed, translated and annotated by Kurt Vogel as: Ein Byzantinisches Rechenbuch des frühen 14.Jahrhunderts; Wiener Byzantinistische Studien, Band VI; Hermann Böhlaus Nachf., Wien, 1968. I will cite problem numbers and pages from this -- Vogel gives analysis of the methods on pp. 149 153 and historical comments on pp. 154 160, but I will not cite these.

Brahmagupta, c628. See: Brahma sphuta siddhanta; Colebrooke.

Brahma sphuta siddhanta.

Bráhma sphuta siddhânta of Brahmagupta, 628 (see Colebrooke). He only states rules, which are sometimes obscure. It appears from Colebrooke, p. v, and Datta (op. cit. under Bakhshali, p. 10), that almost all the illustrative examples and all the solutions are due to Chaturveda Prthudakasvâmî in 860. Brahmagupta's rules are sometimes so general that one would not recognise their relevance to these examples and I have often not cited Brahmagupta. E.g. cistern problems are given as examples to Brahmagupta's verse on how to add and subtract fractions. (See also Datta & Singh, I, p. 248.) Some of these comments are taken from Bhaskara I in 629.

Brush. Hubert Phillips. Brush Up Your Wits. Dent, London, 1936.

BSHM. British Society for the History of Mathematics. The produce a useful Newsletter.

Buteo. Logistica. 1559.

Johannes Buteo (= Jean Borrel, c1485-c1560 or c1492-1572). Ioan. Buteonis Logistica, quæ & Arithmetica vulgò dicitur in libros quinque digesta: quorum index summatim habetur in tergo. Gulielmus Rovillius, Lyons, 1559. Most of the material is in books IV and V. H&S cites some problems in the 1560 ed with the same pages as in the 1559 ed, so these editions are presumably identical. See Rara 292-294.
c. circa, e.g. c1300. Also c= means "approximately equal", though  will be used in mathematical contexts.

C. Century, e.g. 13C, -5C.

Calandri. Arimethrica. 1491.

Philippo Calandri. Untitled. Frontispiece is labelled "Pictagoras arithmetrice introductor". Text begins: "Philippi Calandri ad nobilem et studiosus Julianum Laurentii Medicē de arimethrica opusculū." Lorenzo de Morgiani & Giovanni Thedesco da Maganza, Florence, 1491. Van Egmond's Catalog 298-299. The Graves collection has two copies dated 1491, one with the folio number c iiii misprinted as b iiii - cf Van Egmond for other differences in this unique variant. There was a reprint by Bernardo Zucchetta, Florence, 1518 -- ??NYS but mentioned: in a handwritten note in one of the Graves copies of the 1491 (giving Bernardo Zucchecta, 1517); in Smith, Rara, p. 48 (giving Bernardo Zuchetta, 1518); in Riccardi [I, col. 208-209] (giving Bernardo Zuchecta, 1515) and in Van Egmond's Catalog 299. "It is the first printed Italian arithmetic with illustrations accompanying problems, ...." (Smith, Rara, pp. 46 49). There are about 50 of these illustrations, which appear to be woodcuts, but they are quite small, about 25mm (1") square, and the same picture is sometimes repeated for a related but inappropriate problem. Rara reproduces some of these, slightly reduced. Riccardi [I, col. 208-209] says there may have been a 1490 ed. by Bernardo Zuchecta, but Van Egmond did not find any example.

Calandri. Aritmetica. c1485.

Filippo Calandri. Aritmetica. c1485 [according to Van Egmond's Catalog 158-159]. Italian MS in Codex 2669, Biblioteca Riccardiana di Firenze. Edited by Gino Arrighi, Edizioni Cassa di Risparmio di Firenze, Florence, 1969. 2 vol.: colour facsimile; transcription of the text. Copies of the facsimile were exhausted about 1980 and repeated requests to the Cassa di Risparmio have not produced a reprint, though they usually send a copy of the text volume every time I write! I have now (1996) acquired a example of the 2 vol. set and I find that copies of the text volume which are not part of a set have 8 colour plates inserted, but these are not in the copy in the set.

I cite folios from the facsimile volume and pages from the text volume. These are in direct correspondence with the original except for those pages with full page illustrations. The original begins with a blank side with a Frontispiece verso, then 9 sheets (18 pp.) of full page tables, then two blank sheets. The numbered folios then begin and go through 110. Ff. 1r - 32r are pp. 3 - 65 of the text. F. 32v is a full page calculation which is not in the text. Then ff. 33r - 110r are pp. 66 - 220 of the text. F. 110v is a full page illustration omitted in the text. The first 80 folio numbers are in elaborate Roman numerals centred at the head of the page. (These are sometimes unusually written -- e.g. XXIIIIII.) The later folios were not originally numbered and were later numbered in the top right corner using Hindu-Arabic numerals.

In Sep 1994, I examined the original MS, though it is on restricted access. The original colours are rather more luminous than in the facsimile, but the facsimile is a first class job. The history of this codex is obscure. It is said to have belonged to Piero di Lorenzo dei Medici and it may be the book catalogued in the library of Francesco Pandolfini, c1515, as 'uno libretto ... di Filippo Calandri in arithmetica'. The Riccardi family collected continuously from their rise in the mid 15C until the library was acquired by the city in 1813. A number of items from the Pandolfini catalogue can be identified as being in the Riccardiana. Van Egmond's dating may be early as some claim this was produced for Giuliano de' Medici, who was born in 1479.

Calandri. Raccolta. c1495.

Filippo Calandri. Una Raccolta di Ragioni. In: Cod. L.VI.45, Biblioteca Comunale di Siena. Ed. by D. Santini. Quaderni del Centro Studi della Matematica Medioevale, No. 4, Univ. di Siena, 1982. Van Egmond's Catalog 193 identifies this as ff. 75r-111v of the codex, titles it Ragone Varie and gives a date of c1495.

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

Cardan. Ars Magna. 1545.

Jerome Cardan = Girolamo Cardano = Hieronymus Cardanus (1501 1576). Artis Magnae sive de Regulis Algebraicis Liber Unus. Joh. Petreium, Nuremberg, 1545, ??NYS Included in Vol. IV of the Opera Omnia, Joannis Antonius Huguetan & Marcus Antonius Ravaud, Lyon, 1663, and often reprinted, e.g. in 1967. NEVER CITED??

Cardan. Practica Arithmetice. 1539.

Jerome Cardan = Girolamo Cardano = Hieronymus Cardanus (1501 1576). Practica Arithmetice, & Mensurandi Singularis. (Or: Practica Arithmeticae Generalis Omnium Copiosissima & Utilissima, in the 1663 ed.) Bernardini Calusci, Milan, 1539. Included in Vol. IV of the Opera Omnia, 1663, see above. Some of the section numbers are omitted in the Opera Omnia and have to be intuited. I will give the folios from the 1539 ed. followed by the pages of the 1663 ed., e.g. ff. T.iiii.v-T.v.r (p. 113).

Cardan. De Rerum Varietate. 1557.

Jerome Cardan = Girolamo Cardano = Hieronymus Cardanus (1501 1576). De Rerum Varietate. Henricus Petrus, Basel, 1557; 2nd ed., 1557; 5th ed., 1581, ??NYS. Included in Vol. III of the Opera Omnia, 1663, see above.

Cardan. De Subtilitate. 1550.

Jerome Cardan = Girolamo Cardano = Hieronymus Cardanus (1501 1576). De Subtilitate Libri XXI. J. Petreium, Nuremberg, 1550; Basel, 1553; 6th ed., 1560; and five other 16C editions, part ??NYS. Included in Vol. III of the Opera Omnia, 1663, see above. French ed. by Richard Leblanc, Paris, 1556, 1584, titled: Les Livres d'Hieronymus Cardanus: De la Subtilité et subtiles Inventions, ensemble les causes occultes et les raisons d'icelles; 9th ed., 1611. I have seen a note that the 1582 ed. by Henricus Petrus, Basel, was augmented by a riposte to attacks by Scaliger with further illustrations.

Carlile. Collection. 1793.

Richard Carlile. A Collection of One Hundred and Twenty Useful and Entertaining Arithmetical, Mathematical, Algebraical, and Paradoxical Questions: With the Method of Working Each. Printed by T. Brice for the author, Exeter, 1793. Wallis 227 CAR, ??NX. Includes a number of straightforward problems covered here, but I have only entered the more unusual examples.

Carroll-Collingwood. 1899.

The Lewis Carroll Picture Book. Stuart Dodgson Collingwood, ed. T. Fisher Unwin, London, 1899. = Diversions and Digressions of Lewis Carroll, Dover, 1961. = The Unknown Lewis Carroll, Dover, 1961(?). Reprint, in reduced format, Collins, c1910. The pagination of the main text is the same in the original and in both Dover reprints, but is quite different than the Collins. I will indicate the Collins pages separately. The later Dover has 42 additional photographs.

Carroll-Gardner. c1890? or 1996

Martin Gardner. The Universe in a Handkerchief. Lewis Carroll's Mathematical Recreations, Games, Puzzles and Word Plays. Copernicus (Springer, NY), 1996. As with Carroll-Wakeling, Carroll material will be dated as 1890?, but there is much material by Gardner which is dated 1996.

Carroll-Wakeling. c1890?

Lewis Carroll's Games and Puzzles. Newly Compiled and Edited by Edward Wakeling. Dover and the Lewis Carroll Birthplace Trust, 1992. This is mostly assembled from various manuscript sheets of Carroll's containing problems which he intended to assemble into a puzzle book. Wakeling has examined a great deal of such material, including a mass of Carroll's notes to Bartholomew Price (1818 1898) who was Sedleian Professor of Natural Philosophy at Oxford in 1853-1898. Price was at Pembroke College, becoming the Master, adjacent to Carroll's Christ Church. He had tutored Carroll (1833 1898) and they were close friends and in continual contact until their deaths, both in 1898. However, few of the papers are dated and they are simply loose sheets with no indication of being in order, so there is no way to date the undated sheets and I have given a fairly arbitrary date of c1890? for these, though Carroll was more active before then rather than after. Some items are taken from Carroll's youthful magazines or his correspondence and hence are more precisely dated. The correspondence is more fully given in Carroll-Collingwood.

In response to an inquiry, Wakeling wrote on 28 May 2003 and said that some of the Carroll-Price notes were typewritten 'probably using Dodgson's Hammond typewriter, purchased in 1888.' This gives a somewhat more precise dating than my c1890? and I will give: 1888 to 1898 for such items, unless there is other evidence.

Carroll-Wakeling II. c1890?

Rediscovered Lewis Carroll Puzzles. Newly Compiled and Edited by Edward Wakeling. Dover, 1995. See the notes to Carroll-Wakeling, above.

Cassell's. 1881.

Cassell's Book of In Door Amusements, Card Games, and Fireside Fun. Cassell, Peter, Gilpin & Co., London, 1881; Cassell, London, 1973. 217pp [probably + 1p + 6pp Index] (pp. 1-8 are preliminary matter). [There was a companion volume: Cassell's Book of Sports and Pastimes. In 1887, the two were combined, with the spine titled Cassell's Book of Outdoor Sports and Indoor Amusements. The front cover says Out Door Sports, the back cover says Indoor Amusements, while the title page says Cassell's Book of Sports and Pastimes. It contains all the main text of Book of In Door Amusements, ..., advanced by 744 pages. From at least 1896, Card Games and Parlour Magic were completely revised and later there were a few other small changes. The title varies slightly. Manson (qv) is a 1911 revision and extension to 340pp of main text.]

Catel. Kunst-Cabinet. 1790.

Peter Friedrich Catel. Mathematisches und physikalisches Kunst-Cabinet, dem Unterrichte und der Belustigung der Jugend gewidmet. Nebst einer zweckmässigen Beschreibung der Stücke, und Anzeige der Preise, für welche sie beim Verfassser dieses Werks P. F. Catel in Berlin zu bekommen sind. [I.e. this is a catalogue of items for sale by post!] Lagarde und Friedrich, Berlin & Libau, 1790. [MUS #113.] P. iv says he started his business in 1780.

There is a smaller Vol. 2, with the same title, except 'beim Verfasser dieses Werkes P. F. Catel' is replaced by 'in der P. F. Catelschen Handlung', and the publisher is F. L. Lagarde, Berlin, 1793.

My thanks to M. Folkerts for getting a copy of the example in the Deutsches Museum made for me.

All citations are to vol. 1 unless specified.

Many of Bestelmeier's items are taken from Catel. Sometimes the figure is identical (often reversed) or is a poor copy. Texts are often copied verbatim, or slightly modified, but usually abbreviated. E.g. Catel often explains the puzzle and this part is frequently omitted in Bestelmeier. Bestelmeier was the successor to Catel. Dieter Gebhardt has searched for the various editions and associated price lists of the Catel and Bestelmeier catalogues in German libraries and he and Jerry Slocum have published the details in: Jerry Slocum & Dieter Gebhardt. Puzzles from Catel's Cabinet and Bestelmeier's Magazine 1785 to 1823. English translations of excerpts from the German Catel-Katalog and Bestelmeier-Katalog. Intro. by David Singmaster. History of Puzzles Series. The Slocum Puzzle Foundation, PO Box 1635, Beverly Hills, California, 90213, USA, 1997. I have not yet made detailed entries from this which gives precise dates for the various parts of these catalogues.

CFF. Cubism for Fun. This is the Newsletter of the Nederlandse Kubus Club (NKC) (Dutch Cubists Club) which has been in English since the mid 1980s.