Eighth preliminary edition

Arnold, George. See: Book of 500 Puzzles, Boy's Own Conjuring Book, Hanky Panky.

Arrighi, Gino. See: Benedetto da Firenze, Calandri, Pseudo-Dell'Abbaco, della Francesca, Gherardi, Lucca 1754, P. M. Calandri.

Aryabhata. Āryabhata (I)) [NOTE: ţ denotes a t with a dot under it and ş denotes an s with a dot under it.] (476- ). Āryabhatīya. 499. Critically edited and translated into English by Kripa Shankar Shukla, with K. V. Sarma. Indian National Science Academy, New Delhi, 1976. (Volume 1 of a three volume series -- the other two volumes are commentaries, of which Vol. 2 includes the commentary Āryabhatīya-Bhāşya, written by Bhaskara I in 629. Aryabhata rarely gives numerical examples, so Bhaskara I provided them and these were later used by other Indian writers such as Chaturveda, 860. The other commentaries are later and of less interest to us. Prof. Shukla has sent a photocopy of an introductory booklet, which is an abbreviated version of the introductory material of Vol. 1, with some extensions relating Aryabhata to other writers.) The material is organized into verses. There is an older translation by Walter Eugene Clark as: The Âryabhaţîya of Âryabhaţa; Univ. of Chicago Press, Chicago, 1930. (There was an Aryabhata II, c950, but he only occurs in 7.K.1.)

A&N. Wilhelm Ahrens. Altes und Neues aus der Unterhaltungsmathematik. Springer, Berlin, 1918.

Bachet, Claude Gaspar (1581-1638). See: Problemes.

Bachet-Labosne. See: Problemes.

Badcock. Philosophical Recreations, or, Winter Amusements. [1820].

Philosophical Recreations, or, Winter Amusements. Thomas Hughes, London, nd [1820]. [BCB 18-19; OCB, pp. 180 & 197. Heyl 22-23. Toole Stott 75-77. Christopher 54-56. Wallis 34 BAD, 35 BAD. These give dates of 1820, 1822, 1828.] HPL [Badcock] RBC has three versions with slightly different imprints on the title pages, possibly the three dates mentioned.

Wallis 34 BAD has this bound after the copy of: John Badcock; Domestic Amusements, or Philosophical Recreations ...; T. Hughes, London, nd [1823], and it is lacking its Frontispiece and TP -- cf in 6.BH. HPL [Badcock] has both books, including the folding Frontispieces. The earlier does not give an author, but its Preface is signed J. B. and the later book does give his name and calls itself a sequel to the earlier. Toole Stott 75-80 clearly describes both works. Some of the material is used in Endless Amusement II.

Baker. Well Spring of Sciences. 1562?

Humfrey Baker (fl. 1557-1587). The Well Sprynge of Sciences Which teacheth the perfect worke and practise of Arithmeticke both in whole numbers and fractions, with such easye and compendious instruction into the sayde arte, .... Rouland Hall for James Rowbotham, London, 1562. [Smith, Rara, p. 327, says it was written in 1562 but wasn't actually printed until 1568, but a dealer says the 1st ed. was 1564 and there was a 4th ed. in 1574, which I have examined.] Apparently much revised and extended, (1580). Reprinted, with title: The Wel [sic] Spring of Sciences: Which teacheth the perfect worke and practise of Arithmetike; Thomas Purfoote, London, 1591. I have seen Thomas Purfoot, London, 1612, which is essentially identical to 1591. I have also seen: Christopher Meredith, London, 1646; Christopher Meredith, London, 1650; R. & W. L. for Andrew Kemb, London, 1655; which are all the same, but differently paged than the 1591. I have also seen Baker's Arithmetick, ed. by Henry Phillippes, Edward Thomas, London, 1670, which has different pagination and some additional problems compared to the 1646/1655 ed. [Smith, Rara, 327-330 & 537, says it was rewritten in 1580, but there is little difference between the 1580 and the many later editions, so the 1591 ed. is probably close to the 1580 ed. The copy of the 1562 in the Graves collection ends on f. 160r, but an owner has written a query as to whether the book is complete. Neither Smith nor De Morgan seems to have seen a 1562 so they don't give a number of pages for it. (STC records no copies of the 1562, 1564, 1576, 1584, 1607 editions, but there was a 1576 by [T. Purfoote], apparently the 5th ed., of c500pp, in the Honeyman Collection.) Almost all the problems of interest occur on ff. 189r-198r of the 1591 ed. and hence are not in the Graves copy of the 1562 ed., but H&S 61 refers to one of these problems as being in Baker, 1568. The 1574 ends at fol. 200 (misprinted as 19?, where the ? is an undecipherable blob) and Chapter 16, which is headed: The 16 Chapter treateth of sportes and pastime, done by number, is on ff. 189r-200v, and contains just a few recreations, as in Recorde. So I will date the book as 1562?, but most of the later material as 1580?. The problems of 7.AF.1 and 10.A may be in Graves copy of the 1562 ed. -- ??check. I will cite the 1580?, 1646 and 1670 editions, e.g. 1580?: ff. 192r 193r; 1646: pp. 302-304; 1670: pp. 344-345.] Bill Kalush has recently sent a CD with 1574, 1580, 1591, 1598, 1602, 1607, 1612, 1617, 1650, 1655 on it -- ??NYR.

Bakhshali MS. The Bakhshālī Manuscript, c7C. This MS was found in May 1881 near the village of Bakhshālī, in the Yusufzāī district of the Peshawer division, then at the northwestern frontier of India, but apparently now in Pakistan. This is discussed in several places, such as the following, but a complete translation has only recently appeared. David Pingree says it is 10C, but his student Hayashi opts for 7C which seems pretty reasonable and I will adopt c7C.

1. A. F. Rudolf Hoernle. Extract of his report in some journal of the previous year. The Indian Antiquary 12 (Mar 1883) 89-90. A preliminary report, saying it was found near Bakhshâlî in the Yusufzai District in the Panjâb.

2. A. F. Rudolf Hoernle. On the Bakhshālī Manuscript. Berichte des VII. Internationalen Orientalisten Congresses, Wien, 1886. Alfred Hölder, Vienna, 1889. Arische Section, p. 127-147 plus three folding plates. Cf next item. I will cite this as Hoernle, 1886.

3. A. F. Rudolf Hoernle. The Bakhshali manuscript. The Indian Antiquary 17 (Feb 1888) 33 48 & Plate I opp. p. 46; 275 279 & Plates II & III opp. pp. 276 & 277. This is essentially a reprint of the previous item, with a few changes or corrections, but considerable additional material. He dates it c4C. I will cite this as Hoernle, 1888.

4. G. R. Kaye. The Bakhshālī Manuscript – A Study in Medieval Mathematics. Archæeological Survey of India – New Imperial Series XLIII: I-III, with parts I & II as one volume, (1927 1933). (Facsimile reprint in two volumes, Cosmo Publications, New Delhi, 1981 – this is a rather poor facsimile, but all the text is preserved. I have a letter detailing the changes between the original and this 'facsimile'.) I will only cite Part I – Introduction, which includes a discussion of the text. Part II is a discussion of the script, transliteration of the text and pictures of the entire MS. Part III apparently was intended to deal with the language used, but Kaye died before completing this and the published Part III consists of only a rearranged version of the MS with footnotes explaining the mathematics. Gupta, below, cites part III, as Kaye III and I will reproduce these citations. He dates it c12C.

5. B. Datta. The Bakhshâlî mathematics. Bull. Calcutta Math. Soc. 21 (1929) 1 60. This is largely devoted to dating of the MS and of its contents. He asserts that the MS is a copy of a commentary on some lost work of 4C or 5C (?).

6. R. C. Gupta. Some equalization problems from the Bakhshālī manuscript. Indian Journal of the History of Science 21 (1986) 51-61. Notes that Hoernle gave the MS to the Bodleian Library in 1902, where it remains, with shelf mark MS. Sansk. d.14. He follows Datta in believing that this is a commentary on a early work, though the MS is 9C, as stated by Hoernle. He gives many problems from Kaye III, sometimes restoring them, and he discusses them in more detail than the previous works.

7. Takao Hayashi. The Bakhshālī Manuscript An ancient Indian mathematical treatise. Egbert Forsten, Groningen, Netherlands, 1995. (Based on his PhD Dissertation in History of Mathematics, Brown University, May 1985, 774pp.) A complete edition and translation with extensive discussion of the context of the problems. He dates it as 7C.

Ball, Walter William Rouse (1850-1925). See: Ball FitzPatrick; MRE.

Ball FitzPatrick.

French translation of MRE by J. Fitz Patrick, published by Hermann, Paris.

1st ed., Récréations et Problèmes Mathématiques des Temps Anciens & Modernes. From the 3rd ed, 1896, of MRE, 'Revue et augmentée par l'auteur'. 1898. The Note says 'M. Ball ... a bien voulu apporter à la troisième édition anglaise des additions et des modifications importantes.' 352pp.

2nd ed., Récréations et Problèmes Mathématiques des Temps Anciens et Modernes. From the 4th ed, 1905, of MRE, 'et enrichie de nombreuses additions'.

As three volumes, 1907 09. [I have vol. 1, 1907, which is 356pp. Pp. 327 355 is a note by A. Hermann, Comptabilité d'une persone qui dépense plus que son revenu. I have not yet seen the other volumes to compare with the 1926 reprint, but Strens's notes in his copy indicate that they are identical.]

Reprinted in one vol., Gabay, Paris, 1992, 544pp.

Reprinted, 1926-1927. The only copies that I have seen are bound as one volume, but with separate pagination. My copy has left out the title pages of vols. 2 & 3. The copy in the Strens Collection has these title pages, but its vol. II is 1908. The 1926 vol. 1 says Nouvelle édition française, but the 1927 vol. 3 says Deuxième édition française.

[Vol. 1 is 326pp, omitting the note by Hermann. Vol. 2 is 363pp (pp. 322 355 is a historical note on the cubic, based on Cossali (1797)). Vol. 3 is 363pp including: Notes diverses de M. Aubry, pp. 137 206 (or 340? -- the Table des Matières and the page set up do not make it clear if Aubry's Notes end on p. 206); Note de M. Fitz Patrick, La géométrie par le pliage et découpage du papier, pp. 341 360; A. Margossian, De l'ordonnance des nombres dans les carrés magiques impairs, pp. 1 60 (pp. 61-64 is a Note on the same subject, presumably part of Margossian's material); Capt. Reinhart, some geometric notes, pp. 130-136.]

Barnard. 50 Observer Brain-Twisters. 1962.

Douglas St. Paul Barnard. Fifty Observer Brain Twisters A Book of Mathematical and Reasoning Problems. Faber, 1962. US ed.: A Book of Mathematical and Reasoning Problems: Fifty Brain Twisters; Van Nostrand, 1962. The editions have identical pagination.

Bartl. c1920. János Bartl. Preis-Verzeichnis von Bartl's Akademie für moderne magische Kunst. Hamburg, c1920. Reprinted by Olms Verlag, Zürich, 1983, as: Zauberkatalog Bartl. References are to the section: Vexier- und Geduldspiele, pp. 305 312.

Bartoli. Memoriale. c1420.

Francesco Bartoli ( -1425). Memoriale (= Notebook) containing some 30 mathematical problems copied during 1400?-1425. Ms 1 F 54 of the Archives départementales du Vaucluse, France. ??NYS -- described and quoted in: Jacques Sesiano; Les problèmes mathématiques du Memoriale de F. Bartoli; Physis 26:1 (1984) 129-150.

BC. Binomial Coefficient, i.e. BC(n, k) = n!/k!(n-k)!.

BCB. See: Hall, BCB.

BDM. See under DSB.

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

Benedetto da Firenze. c1465.

Benedetto da Firenze. Trattato d'Abacho. c1465. This was a popular treatise and Van Egmond's Catalog 356 lists 18 copies under Benedetto. Six show B as author, one has Benedetto, one has Benedetto da Firenze, one has P^o M^a and one has Filipo Chalandri, so it seems Benedetto is the most likely author. The MSS date from c1465 to c1525 and contain 9 to 25 chapters.

The version in Cod. Acq. e doni 154, Biblioteca Medicea Laurenziana, Florence, c1480. has been transcribed and edited by Gino Arrighi as: Pier Maria Calandri; Tractato d'Abbacho; Domus Galilaeana, Pisa, 1974. The incipit names P^o M^a as author. Cf Van Egmond's Catalog 96. This version has 23 chapters.

Benson. 1904. J. K. Benson. The Book of Indoor Games for Young People of All Ages. C. Arthur Pearson, London, 1904. [This copies a lot from Hoffmann (or a common ancestor?).]

Much of the material of Indoor Games is repeated in: J. K. Benson, ed.; The Pearson Puzzle Book; C. Arthur Pearson, London, nd [1921 -- BMC]. This is not in BMC or NUC under Benson -- but I have seen an ad listing this as by Mr. X and it is listed under Mr. X in BMC. Puzzle Book pp. 1-96 =  Indoor Games pp. 189-257; Puzzle Book pp. 109-114 = Indoor Games pp. 258-262. The only different material in Puzzle Book is pp. 97-108. Neither book refers to the other. Cf Mr. X in Section 4.A.1

Berkeley & Rowland. Card Tricks & Puzzles. 1892.

"Berkeley" [Peel, Walter H.] & Rowland, T. B. Card Tricks and Puzzles. The Club Series, George Bell & Sons, London, 1892 -- according to BMC, but my copy is 1897. Card Puzzles, etc., pp. 1-74 is by Berkeley; Arithmetical Puzzles, pp. 75-120 is by Rowland.

Berlekamp, Elwyn R. (1940- ) See: Winning Ways.

Bestelmeier. 1801-1803.

G. H. [Georg Hieronimus] Bestelmeier. Magazin von verschiedenen Kunst  und andern nützlichen Sachen .... [Toy catalogues.] Nuremberg, 1801 1803.

Eight issues and cumulative classified index reprinted by Olms, Zurich, 1979. Issue VII is 1801; the others are 'neue verbesserte Auflage', 1803. This includes items numbered 1 through 1111.

Selections, with English translations. Daniel S. Jacoby, ed. The Amazing Catalogue of the Esteemed Firm of George Hieronimus Bestelmeier. Selected Excerpts from Editions of 1793 and 1807. [A comment inside makes me wonder if 1793-1807 is meant??] Merrimack Publishing Corp., NY, 1971, 82pp. The numeration is the same as in the Olms edition, but the Jacoby continues to item 1321. Obviously these later items come from the 1807 edition, but we cannot tell if they might date from 1805, say, nor whether all the earlier items go back to 1793. Jerry Slocum uses Jacoby in his Compendium and has kindly provided photocopies of Jacoby's pp. 70-82 containing all the items after 1111 and some examples of the earlier items. Jacoby does not translate the texts, but just provides English labels for each picture and these labels are sometimes unconnected with the text.

Many of Bestelmeier's items are taken from Catel; Kunst-Cabinet; 1790. Sometimes the figure is identical (often reversed) or is a poor copy. Texts are often copied verbatim, or slightly modified, but often abbreviated. E.g. Catel often explains the puzzle and this part is frequently omitted in Bestelmeier. Bestelmeier was the successor to Catel, qv. The booklet by Slocum & Gebhardt (qv under Catel) gives precise datings for the various parts of these catalogues, but I have not yet entered these details.

Bhaskara I. 629.

Bhāskara I. Āryabhaţīya-Bhāşya. [NOTE: ţ denotes a t with a dot under it and ş denotes an s with a dot under it.] 629. Critically edited, including an English Appendix of the numerical examples used, by Kripa Shankar Shukla. Indian National Science Academy, New Delhi, 1976. (Vol. 2 of a three volume series devoted to the Āryabhaţīya (499) of Aryabhata (476- ), qv.) Bhaskara I repeats and exposits Aryabhata verse by verse, but Aryabhata rarely gives numerical examples, so Bhaskara I provided them and these were later used by other Indian writers such as Chaturveda, 860. His earlier Maha-Bhaskariya (Mahā Bhāskarīya) of c629 is cited in 7.P.2. Shukla's Appendix is sometimes brief, but sometimes very detailed, e.g. on the 26 examples of Chinese remainder problems.

Bhaskara II (1114-c1185).

Bhâskara II (1114-c1185, see Colebrooke).

Biggs, Norman L. See: BLW.

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

The Bile Beans Puzzle Book. 1933.

Bile Beans (C. E. Fulford, Ltd., Leeds, England). The Bile Beans Puzzle Book. 1933.

Birtwistle. Math. Puzzles & Perplexities. 1971.

Claude Birtwistle. Mathematical Puzzles and Perplexities How to Make the Most of Them. George Allen & Unwin, London, 1971.

Birtwistle. Calculator Puzzle Book. 1978.

Claude Birtwistle. The Calculator Puzzle Book. Paperfronts (Elliot Right Way Books), Kingswood, Surrey, 1978. (There is a US ed. by Bell, NY, 1978.)

BL(LD). British Library (Lending Division).

Blasius. 1513. Johannis (or Joannes) Martinus Blasius (later denoted Sileceus or Sciliceus). Liber Arithmetice Practice Astrologis Phisicis et Calculatioribus admodum utilis. Thomas Kees for Joannis Parui & Joannis Lambert (in colophon; TP has Jehanlambert), Paris, 1513. Facsimile by Heffer Scientific Reprint, Cambridge, 1960. See Smith, Rara, pp. 95-97. The Glaisher article in 7.P.5 [Messenger of Mathematics 53 (1923-24) 1 131] discusses this book and says he only knows one example of it, which he has in front of him, so I suspect this facsimile is from that copy. See Rara 95-97. The Honeyman Collection had a copy, saying it was printed for J. Petit and J. Lambert and that copy had Petit's device on the TP while the TP shown in Rara has Lambert's device, which is as in this facsimile. There was a reprinting in 1514 and extended editions in 1519 (ed. by Oronce Finé) and 1526 (ed. by T. Rhaetus) [Honeyman Collection, nos. 350-352].

BLC. British Library Catalogue, replacing BMC, in progress since 1970s.

BLC-Ø Indicates that I could not find the item in the BLC.

BLW. 1976. Norman L. Biggs, E. Keith Lloyd & Robin J. Wilson. Graph Theory 1736 1936. OUP, 1976.

Blyth. Match-Stick Magic. 1921.

Will Blyth. Match-Stick Magic. C. Arthur Pearson, London, 1921, reprinted 1923, 1939.

BM(C). British Museum (Catalogue (of books) to 1955. c1963).

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

BN(C). Bibliothèque National, Paris. (Catalogue, 1897-1981.)

Bodleian. The Bodleian Library, University of Oxford, or its catalogue.

Bonnycastle. Algebra. 1782

John Bonnycastle (??-1821). An Introduction to Algebra, with Notes and Observations; designed for the Use of Schools, and Other Places of Public Education. 1782. The first nine editions appeared "without any material alterations". In 1815, he produced a 10th ed., "an entire revision of the work" which "may be considered as a concise abridgment" of his two volume Treatise on Algebra, 1813, (2nd ed. in 1820). The 1815 ed. had an Appendix: On the application of Algebra to Geometry. I have a copy of the 7th ed., 1805, printed for J. Johnson, London, and it is identical to the 2nd ed. of 1788 except for a problem in the final section of Miscellaneous Questions. However, the 9th ed. of 1812 has page numbers advanced by 10 except toward the end of the book. I also have the 13th ed. of 1824, printed for J. Nunn and 11 other publishers, London, 1824. This version has an Addenda: A New Method of resolving Numerical Equations, by his son Charles Bonnycastle (1797-1840), but is otherwise identical to the 10th ed. of 1815. The earlier text was expanded by about 10% in 1815, so a number of problems only occur in later editions. I will cite these later problems as 1815 and will cite the earlier problems as 1782. [Halwas 36-38 gives some US editions.]
Book of 500 Puzzles. 1859.

The Book of 500 Curious Puzzles: Containing a Large Collection of Entertaining Paradoxes, Perplexing Deceptions in Numbers, and Amusing Tricks in Geometry. By the author of "The Sociable," "The Secret Out," "The Magician's Own Book," "Parlor Games," and " Parlor Theatricals," etc. Illustrated with a great Variety of Engravings. Dick & Fitzgerald, NY, 1859. Compiled from The Sociable (qv) and Magician's Own Book. Pp. 1-2 are the TP and its reverse. Pp. 3 36, are identical to pp. 285-318 of The Sociable; pp. 37-54 are identical to pp. 199-216 of Magician's Own Book and pp. 55-116 are identical to pp. 241-302 of Magician's Own Book. [Toole Stott 103 lists it as anonymous. NUC, under Frikell, says to see title. NUC, under Book, also has an 1882 ed, compiled by William B. Dick. Christopher 129. C&B lists it under Cremer.]

The authorship of this and the other books cited -- The Sociable, The Secret Out, The Magician's Own Book, Parlor Games, and Parlor Theatricals, etc. -- is confused. BMC & NUC generally assign them to George Arnold (1834-1865) or Wiljalba (or Gustave) Frikell (1818 (or 1816) - 1903), sometimes with Frikell as UK editor of Arnold's US version -- but several UK versions say they are translated and edited by W. H. Cremer Jr, and one even cites an earlier French book (though the given title may not exist!, but cf Manuel des Sorciers, 1825) -- see the discussion under Status of The Project, in the Introduction, above. The names of Frank Cahill, Henry Llewellyn Williams and Gustave Frikell (Jr.) are sometimes associated with versions of these as authors or coauthors. The Preface of The Sociable says that most of the Parlor Theatricals are by Frank Cahill and George Arnold -- this may indicate they had little to do with the parts that interest us. Toole Stott 640 opines that this reference led Harry Price to ascribe these books to these authors.

A publisher's ad in the back says: "The above five books are compiled from the "Sociable" and "Magician's Own."", referring to: The Parlor Magician [Toole Stott 543, 544]; Book of Riddles and Five Hundred Home Amusements [Toole Stott 107, 951]; Book of Fireside Games [possibly Toole Stott 300??]; Parlor Theatricals; The Book of 500 Curious Puzzles. However, [Toole Stott 951] is another version of The Book of Riddles and Five Hundred Home Amusements "by the author of "Fireside Games" [Toole Stott 300], "The Parlor Magic" [perhaps Toole Stott 543, 544], "Parlor Tricks with Cards" [Toole Stott 1056 lists this as by Frikell, "abridged from The Secret Out" (see also 547, 1142)], ..."; Dick & Fitzgerald, 1986 [sic, but must mean 1886??].

See Magician's Own Book for more about the authorship.

See also: Boy's Own Book, Boy's Own Conjuring Book, Illustrated Boy's Own Treasury, Indoor and Outdoor, Landells: Boy's Own Toy-Maker, The Secret Out, Hanky Panky, The Sociable.

Book of Merry Riddles. 1629?

The Book of Merry Riddles. London, 1629. [Santi 235.]

Several reprints. Also known as Prettie Riddles.

A Booke of Merry Riddles; Robert Bird, London, 1631. [Mark Bryant; Dictionary of Riddles; Routledge, 1990, p. 100.]

Booke of Merry Riddles; John Stafford & W. G., London, 1660.

Reprint of the 1629 in: J. O. Halliwell; The literature of the sixteenth and seventeenth centuries; London, 1851, pp. 67 102. [Santi 235.]

Reprint of the 1660 in: J. O. Halliwell; The Booke of Merry Riddles, together with proper questions, and witty proverbs, to make pleasant pastime. Now first reprinted from the unique edition printed at London in the year 1660. For the author, London, 1866. This was a printing of 25 copies. There is a copy at UCL and a MS note at the end says 15 copies were destroyed on 9 Apr 1866, signed: J. O. H., with Number 9 written below. [Santi 307.] I have seen this, but some of the riddles are quoted by other authors and I will date all items as 1629? until I examine other material.

Reprint of the 1629 in: Alois Brandl; Shakespeares Book of Merry Riddles und die anderen Räthselbücher seiner Zeit; Jahrbuch der deutschen Shakespeare-Gesellschaft 42 (1906) 1-64 (with the 1631 ed on pp. 53-63). ??NYR. [Santi 235 & 237.]

Borghi. Arithmetica. 1484.

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

The 3rd ed of 1491 had a title: Libro dabacho. From the 4th ed of 1501, the title was Libro de Abacho, so this is sometimes used as the title for the first editions also. Rara indicates that the printing was revised to 100 numbered ff by the 4th ed. of 1491. I have examined a 1509 ed. by Jacomo Pentio, Venice, ??NX. This has 100 numbered ff, but the last three ff contain additional material, though Rara doesn't mention this until the 11th ed of 1540. H&S discusses a problem and the folio in the 1540 ed is the same as in the 1509 ed. The locations of interest in the 1509 ed. are c18ff before the corresponding locations of the 1484. Van Egmond's Catalog 293-297 lists 13 Venetian editions from 1484 to 1567.