Eighth preliminary edition
the first edition. This edition only contained material on whole numbers. In 1552
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- SOME OTHER RECURRING REFERENCES
| 1543 the first edition. This edition only contained material on whole numbers.
In 1552, Recorde added a Second Part dealing with fractions, so the earlier material will be called the First Part. At some stage, John Dee augmented it, but it appears he simply made some revisions and additions to the existing text without adding new topics. The Dee material was added in 1590 (Smith) or 1573 (De Morgan). In 1582, John Mellis added a Third Part, mostly on rules of calculation, published by J. Harison & H. Bynneman, London. By 1640, the title was changed to: Record's Arithmetick, or, The Ground of Arts; Teaching The perfect Work and Practice of ARITHMETICK, both in whole Numbers and Fractions, after a more easie and exact form then in former time hath been set forth. Afterwards augmented by Mr. JOHN DEE. And since enlarged with a third part of RULES of PRACTICE, abridged into a briefer method then hitherto ..., by JOHN MELLIS. By 1648, more material was added by Robert Hartwell. I have a 1668 edition which has a little more material by Thomas Willsford, but these latter two extensions are of no interest to us. It is clear that the text was increased by accretion, with only minor revisions of Recorde's text, which is generally preserved in gothic (= black-letter) type, and this is indicated by Smith. So the presence of a problem in Part One or Part Two or Part Three of the 1668 ed almost certainly indicates its presence in the first version of these parts. This is certainly true for Part One, as I have the facsimile to compare, and it is confirmed by brief examination of a 1582 ed, though at the time, I was looking at Part Three and did not know of the material in Part Two. I will cite the pages from my 1662 ed and the side notes which are titles of the problems, and pages of any earlier editions that I have seen. Riccardi. Pietro Riccardi. Biblioteca Matematica Italiana dalla Origine della Stampa ai Primi Anni del Secolo XIX. G. G. Görlich, Milan, 1952, 2 vols. This work appeared in several parts and supplements in the late 19C and early 20C, mostly published by the Società Tipografica Modense, Modena, 1878-1893. For details, see in Section 3.B. Riddle, Edward (1788-1854). See: Ozanam Riddle. The Riddler. See under Boy's Own Book. Riese. Coss. 1524. Adam Riese (c1489-1559). Die Coss. German MS of 1524 found at Marienberg in 1855. Described and abstracted in Programm der Progymnasial und Realschulanstalt zu Annaberg 1860. Reprinted in 1892. My reference to this comes from Johannes Lehmann; Rechnen und Raten; Volk und Wissen, Berlin (DDR), 1987, pp. 7 14, esp. p. 13. I have since seen the Glaisher paper, op. cit. in 7.G.1 under Widman, esp. p. 37. Glaisher and Lehmann cite: Bruno Berlet; Adam Riese, sein Leben und seine Art zu rechnen; Die Coss von Adam Riese; Leipzig & Frankfurt, 1892. Glaisher notes that this was a pamphlet. BLLD provided a copy from Biblioth. Regia Berolinen. G., but it was lacking a title page. It seems to have the title: Zur Feier des vierhundertsten Geburtsjahres von Adam Riese. It was printed by Königl. Universitätsdruckerei von H. Stürtz in Würzburg. The Vorwort is dated 1892, but only signed 'Der Verfasser' and his name does not appear anywhere except on the spine of the library's cover. The booklet has two parts. Adam Riese, sein Leben, seine Rechenbücher und seine Art zu rechnen (from the Programm for 1855), pp. 1 26. This is a discussion of Riese's Rechnung, but it also mentions some material from his 'grosse Rechenbuch' titled Rechenung nach der lenge, auf den Linihen und Feder, written in 1525 but not published until 1550. Glaisher, loc. cit., p. 43, says he sees no authority for the date of 1525 and assumes it was written c1550. (I have recently obtained a 1976 reprint of this work, ??NYR) Die Coss von Adam Riese (with Abdruck der Coss) (from the Programm for 1860), pp. 27 62. This gives many numbered problems -- I will cite the problem number and pages from this. There is a recent facsimile of the MS which I have just received -- ??NYR. Riese. Rechnung. 1522. Adam Riese (c1489-1559). Rechnung auff der Linien unnd Federn ... Erfurt, 1522. I have two reprinted editions. See Rara 138-143. Christian Egenolph, Frankfurt, 1544. (Riese's text is dated 1525. There is a supplement on gauging by Erhard Helm, dated 1544.) Facsimile by Th. Schäfer, Hannover, 1978. Christian Egenolff's Erben, Frankfurt, 1574. (Riese's text is dated 1525 and appears to be the same text as above, but reset. The Supplement has further material.) Facsimile by Th. Schäfer, Hannover, 1987. Ripley's Puzzles and Games. 1966. Ripley's Believe It or Not! Puzzles and Games. Essandess Special Edition (Simon & Schuster), New York, 1966. Much of the material occurred in the various Ripley's Believe it or Not! books. Most of the material is well known, but there are a number of unusual variations and some interesting incomplete assertions and mistakes! RM. (François-) Édouard (-Anatole) Lucas (1842-1891). Récréations mathématiques. (Gauthier Villars, Paris, 4 vols, 1882, 1883, 1893, 1894, 2nd eds. of vol. 1, 1891, vol. 2, 1893) = Blanchard, Paris, (1960), 1975 1977, using 2nd ed. of vol. 1 and 1st ed. of vol. 2 (however, there seem to be very few differences in the editions). I will cite the Blanchard reprint volumes as RM1, etc. (Dates are as given in Harkin, op. cit. in 1 below, and on the books, but I have seen other dates cited.) Lucas; L'Arithmétique Amusante, 1895, Note IV, pp. 210-260 gives various fragments of material for further volumes which were found after Lucas's untimely death. His draft Tables of Contents for volumes 5 and 6 are given on p. 210, but no material exists for most of the chapters. RMM. Recreational Mathematics Magazine. Nos. 1 - 14 (Feb 1961 - Jan/Feb 1964). Quite a bit of the material in this was abstracted and sometimes extended in: Joseph S. Madachy; Mathematics on Vacation; Scribner's, NY, 1966; somewhat corrected as: Madachy's Mathematical Recreations; Dover, 1979. Rocha. Libro Dabaco. 1541. SEE: Tagliente. Libro de Abaco. (1515). 1541. Rohrbough. Lynn Rohrbough edited a series of 20 booklets, called Handy Series, Kits A-J and M V, for Cooperative Recreation Service, Delaware, Ohio, during at least 1925-1941. Most of these were reprinted and revised several times. Two of these are of especial interest to us and are listed below. Several others are cited a few times. Rohrbough. Brain Resters and Testers. c1935. Lynn Rohrbough, ed. Brain Resters and Testers. Handy Series, Kit M, Cooperative Recreation Service, Delaware, Ohio, nd [c1935]. Rohrbough. Puzzle Craft. 1932. Lynn Rohrbough, ed. Puzzle Craft Plans for Making and Solving 40 Puzzles in Wire, Wood and String. Handy Series, Kit U, Cooperative Recreation Service, Delaware, Ohio, (1930), 1932. I have another version of this, unfortunately undated, but apparently later, so I have dated it as 1940s? Jerry Slocum located this by tracking down Rohrbough's successors. The 1932 version has 39 puzzles in its index, but 4 more that were not indexed and some Notes which are listed in the index of this version, making 44 items in all. 13 items are omitted and replaced by 5 in the present version, giving 36 indexed items. The outside of the back cover of the 1932 version shows a number of puzzles, including several not described in either version of the booklet. Rudin. 1936. Jacob Philip Rudin. So You Like Puzzles! Frederick A. Stokes Co., NY, 1936.
Sanford. 1930. Vera Sanford. A Short History of Mathematics. Houghton Mifflin, Boston, 1930 & 1958. See also: H&S. Santi. 1952. Aldo Santi. Bibliografia della Enigmistica. Sansoni Antiquariato, Florence, 1952. 2541 entries, often citing several editions and versions, arranged chronologically from 1479 onward. My thanks to Dario Uri for providing this. I will site item numbers. I have only entered part of the information so far. de Savigny. Livre des Écoliers. 1846. M. l'Abbé de Savigny. Le Livre des Écoliers Illustré de 400 vignettes. Jeux. -- Récréations. Exercises. -- Arts utiles et d'agrément. Amusements de la science. Gustave Havard, Paris, nd [dealer has written in 1846], HB. [This is almost entirely the same as Boy's Own Book, 1843 (Paris). Each has a few sections the other does not. de Savigny's illustrations seem to have been copied by a new hand, generally simplifying a little. Many of the copies have been done in reverse and this leads to one erroneous chessboard. However, there is one diagram in Boy's Own Book, 1843 (Paris), which looks like it was badly copied, so it is possible that both these books are based on an earlier book.] Schaaf. 1955-1978. William L. Schaaf. A Bibliography of Recreational Mathematics. Vol. 1, (1955, 1958, 1963); 4th ed., 1970. Vol. 2, 1970. Vol. 3, 1973. Vol. 4, 1978. National Council of Teachers of Mathematics, Washington, DC. See Schaaf & Singmaster in Section 3.B for a Supplement to these. Schott. 1674. Gaspare Schott. Cursus Mathematicus. Joannis Arnoldi Cholini, Frankfurt, 1674. The material of interest is in Liber II, Caput VI: De Arithmetica Divinatoria, pp. 57-60, and in Liber XXVI: Algebra, Pars III: De Exercitatione Algebraicam, Caput I, II, IV, VI, pp. 551-563, and Pars V: Exercitationes Algebraicae, pp. 570-571. Schwenter. 1636. Daniel Schwenter (1585-1636). Deliciæ Physico Mathematicae. Oder Mathemat und Philosophische Erquickstunden, Darinnen Sechshundert Drey und Sechsig, Schöne, Liebliche und Annehmliche Kunststücklein, Auffgaben und Fragen, auf; der Rechenkunst, Landtmessen, Perspectiv, Naturkündigung und andern Wissenschafften genomēn, begriffen seindt, Wiesolche uf der andern seiten dieses blats ordentlich nacheinander verzeichnet worden: Allen Kunstliebenden zu Ehren, Nutz, Ergössung des Gemüths und sonderbahren Wolgefallen am tag gegeben Durch M. Danielem Schwenterum. Jeremiæ Dümlers, Nuremberg, 1636. [Note: the text is in elaborate Gothic type with additional curlicues so that it is not always easy to tell what letter is intended!] Probably edited for the press by Georg Philip Harsdörffer. Extended to three volumes by Harsdörffer in 1651 & 1653, with vol. 1 being a reprint of the 1636 vol. Vol. 2 & 3 have titles as follows. Delitiæ Mathematicæ et Physicæ Der Mathematischen und Philosophischen Erquickstunden Zweiter Theil: Bestehend in Fünffhundert nutzlichen und lustigen Kunstfragen / nachsinnigen Aufgaben / und derselben grundrichtigen Erklärungen / Auss Athanasio Kirchero Petro Bettino, Marion Mersennio, Renato des Cartes, Orontio Fineo, Marino Gethaldo, Cornelio Drebbelio, Alexandron Tassoni, Sanctorio Sanctorii, Marco Marco, und vielen anderen Mathematicis und Physicis zusammen getragen durch Georg Philip Harsdörffern. Jeremia Dümlern, Nürnberg, 1651. Delitiæ Philosophicæ et Mathematicæ Der Philosophischen und Mathematischen Erquickstunden / Dritter Theil: Bestehend in Fünffhundert nutzlichen und lustigen Kunstfragen / und derselben gründlichen Erklärung: Mit vielen nothwendigen Figuren / so wol in Kupffer als Holz / gezieret. Und Aus allen neuen berühmten Philosophis und Mathematicis, mit grossem Fleiss zusammen getragen. Durch Georg Philip Harsdörffern. Wolffgang dess Jüngern und Joh. Andreas Endtern, Nürnberg, 1653. This 3 vol. version was reprinted in 1677 and 1692. Modern facsimile of the 3 vol. version edited by Jörg Jochen Berns, Keip Verlag, Frankfurt Am Main, 1991, HB. See also MUS II 325-326. Schott described this as a German translation of van Etten/Leurechon, but this is quite wrong. V&T, p. 152, say it is 'partially derived from' van Etten/Leurechon. C&B list just the 1636, under Schwenterum. P. 549 of vol. 1 is misprinted 249 which indicates that it was the first issue of the 1st ed. I have not yet entered all the items from this. The Secret Out. 1859. The Secret Out; or, One Thousand Tricks with Cards, And Other Recreations. Illustrated with over three hundred engravings. And containing Clear and comprehensive explanations how to perform with ease, all the curious card deceptions, and slight of hand tricks extant. With an endless variety of entertaining experiments in drawing room or white magic, including the celebrated science of second sight. Together with a choice collection of intricate and puzzling questions, amusements in chance, natural magic, etc., etc., etc. By the Author of "The Sociable, or, One Thousand and One Home Amusements," "The Magician's Own Book," etc, etc. Dick & Fitzgerald, NY, 1859. [Toole Stott 191, listing all versions under Cremer. C&B, under Frikell, have New York, 1859. H. A. Smith dates this as 1869.] The Secret Out (UK). c1860. The Secret Out or, One Thousand Tricks in Drawing-room or White Magic, with an Endless Variety of Entertaining Experiments. By the author of "The Magician's Own Book." Translated and edited by W. H. Cremer, Junr. With three hundred illustrations. I have seen several editions. [Toole Stott lists all versions under Cremer.] C&W (based on the John Camden Hotten, London, 1871?) (with ads from Sep 1886 at back and inscription dated 12 Oct 1887 on flyleaf). [NUC; Toole Stott 192; C&B, under Cremer, have London & New York, 1871, and under Frikell, have London, 1870.] C&W, nd [1871? -- NUC lists several dates; Toole Stott 1013 is 1870; Christopher 242 is 1878?]. John Grant, Edinburgh, nd [1872 -- Toole Stott 1014, no ads]. All these copies have identical green covers with five magic tricks on the cover. [Toole Stott 192 discusses the authorship, saying that Wiljalba (or Gustave) Frikell is named on the TP of some editions, but that most of the tricks are taken from the US ed of The Magician's Own Book. In the US ed, The Author acknowledges his indebtedness to The Sociable and The Magician's Own Book 'and many other works of similar character and value', but claims 'that the greater portion of it [i.e. the book] is entirely original.' In the Preliminary to the UK ed he says he is indebted to '"Le Magicien des Salons," revised by references to Decremps, Servière, Leopold, Besson, Kircher, Hildebrandt, Ozanam, &c., &c.' though an 1874 ad by C&W indicates that it is translated from Le Magicien des Salons. (This may be Le Magicien de Société, Delarue, Paris, c1860, but see Rulfs, below.) The back of the TP of Bellew's The Art of Amusing, Hotten, 1866?, says The Secret Out is a companion volume, just issued, by Hermann Frikell. BMC & Toole Stott say it is also attributed to Henry L. Williams. Toole Stott 481 cites a 1910 letter from Harris B. Dick, of the publishers Dick & Fitzgerald, who thinks their version of The Secret Out "was a reprint of an English book by W. H. Cremer" -- but there seems to be no record of a UK ed before the US one. NUC says an 1871 ed. gives author as Gustave Frikell. Christopher 240-242 are two copies from Dick & Fitzgerald, c1859, and a C&W, 1878? He repeats most of the above comments from Toole Stott and 242 cites the Rulfs article mentioned under Magician's Own Book, above. Rulfs says The Secret Out is largely taken, illustrations and all, from Blismon de Douai's Manuel du Magicien (1849) and Richard & Delion's Magicien des salons ou le diable couleur de rose (1857 and earlier). H. A. Smith [op. cit. under Magician's Own Book] says the first US ed is 1869 (this must be a misprint or misreading -- though the date is a little hard to read in my copy, it is clearly 1859) and the UK eds are basically a condensed version with a few additions. He suggests the book is taken from DeLion. He doubts whether Cremer ever wrote anything. C&B, under Gustave Frikell, say it is a translation of Richard & Delion. C&B, under Herrman Frikell, list London, 1870. C&B, under Secret, list New York, nd. C&B also list it under Williams, as London, 1871.] [Toole Stott 1056 is [Frikell, Wiljalba]; Parlor Tricks with Cards, ...; By the Author of Book of Riddles and 500 Home Amusements, etc.; Dick & Fitzgerald, 1860?; which is described as "abridged from The Secret Out. Toole Stott 547 and 1142 are two versions of 1863, but without the description of the author and hence listed anonymously.] The US and UK editions are fairly different. The US ed has 382 sections, of which 157 (41%) are used in the UK ed. The UK ed has 323 sections, so 51% of it is taken from the US ed. The US ed seems like a magic book, with chapters on Scientific Amusements and Miscellaneous Tricks. The UK ed has much less magic and tricks, adding other general tricks and a lot more scientific tricks. The illustrations for the common sections are not quite identical -- one was probably copied from the other. The amount taken from The Magician's Own Book and The Sociable is fairly small, perhaps 10% from each, in either edition. Shortz. Will Shortz's library or his catalogues thereof, called "Puzzleana". The most recent I have is: May 1992, 88pp with 1175 entries in 26 categories, with indexes of authors and anonymous titles. Some entries cover multiple items. In Jan 1995, he produced a 19pp Supplement extending to a total of 1451 entries. SIHGM. 1939-1941. Ivor Bulmer Thomas. Selections Illustrating the History of Greek Mathematics. Loeb Classical Library, 1939 1941, 2 vols. I will give volume and pages as in SIHGM I 308 309. Simpson. Algebra. 1745. Thomas Simpson (1710-1761). A Treatise of Algebra; Wherein the Fundamental Principles Are fully and clearly demonstrated, and applied to the Solution of a great Variety of Problems. To which is added, The Construction of a great Number of Geometrical Problems; with the Method of resolving the same Numerically. John Nourse, London, 1745. I also have the 7th ed., with the slightly different title: A Treatise of Algebra. Wherein the Principles Are Demonstrated, And Applied In many useful and interesting Enquiries, and in the Resolution of a great Variety of Problems of different Kinds. To which is added, The Geometrical Construction of a great Number of Linear and Plane Problems; with the Method of resolving the same Numerically. The Seventh Edition, carefully Revised. F. Wingrave, Successor to Mr. Nourse, London, 1800. I have now seen a 6th ed., F. Wingrave, 1790 and it appears identical to the 7th ed. Both have an Author's Preface to the Second Edition. I will give the 1745 details with the 1790/1800 details in parenthesis like (1790: ...). SLAHP. 1928. Sam Loyd Jr. (1873-1934) Sam Loyd and His Puzzles. An Autobiographical Review. Barse & Co., NY, 1928. (This contains somewhat more original material than I expected, but he claims that he devised a lot of his father's puzzles given in the Cyclopedia, OPM, and even earlier.) Slocum. Compendium. 1977. Jerry (= G. K.) Slocum. Compendium of Mechanical Puzzles from Catalogues. Published by the author, Beverly Hills, 1977, 57pp. This is a compendium of illustrations and descriptions from 30 catalogues. The earliest ones are Bestelmeier, 1793, 1807 (Jacoby edition); The Youth's Companion, 1875; Montgomery Ward, 1886, 1889, 1903, 1930; Peck & Snyder, 1886; Joseph Bland, c1890. Others of some interest are: Gamage's, 1913, c1915, c1928; Johnson Smith, 1919, 1935, 1937, 1938, 1942. Slocum & Gebhardt -- see under Catel. SM. Scripta Mathematica. Smith, David Eugene (1860 1944). See: Rara and the following four items. Smith. History. 1923. David Eugene Smith. History of Mathematics. Two vols. (Ginn, NY, 1923) = Dover, 1958. Smith. Number Stories. 1919. David Eugene Smith. Number Stories of Long Ago. NCTM, (1919), reprinted 1968? Chaps. IX and X. Smith. Source Book. 1929. David Eugene Smith. A Source Book in Mathematics. Two vols. (1929) = Dover, 1959. Smith & Mikami. 1914. David Eugene Smith & Yoshio Mikami. A History of Japanese Mathematics. Open Court, Chicago, 1914. The Sociable. 1858. The Sociable; or, One Thousand and One Home Amusements. Containing Acting Proverbs; Dramatic Charades; Acting Charades, or Drawing-room Pantomimes; Musical Burlesques; Tableaux Vivants; Parlor Games; Games of Action; Forfeits; Science in Sport, and Parlor Magic; and a Choice Collection of Curious Mental and Mechanical Puzzles; &c,&c. Illustrated with nearly three hundred engravings and diagrams, the whole being a fund of never-ending entertainment. By the author of "The Magician's Own Book." (Dick & Fitzgerald, NY, 1858 [Toole Stott 640 lists this as anonymous; C&B list it under the title, with no author]); G. G. Evans, Philadelphia, nd, but the back of the title gives ©1858 by Dick & Fitzgerald, NY, so this copy seems to be a reprint of the 1858 book. Cf. Book of 500 Puzzles for discussion of possible authorship. The Preface here says that most of the Parlor Theatricals are by Frank Cahill and George Arnold -- Toole Stott opines that this reference led Harry Price to ascribe this and the related books to these authors. My thanks to Jerry Slocum for providing a copy of this. The entire section Puzzles and Curious Paradoxes, pp. 285-318, is identical to the same section in Book of 500 Puzzles, pp. 3-36. Rulfs (see under Status of the Project in the Introduction) says this draws on the same sources as Magician's Own Book, with more taken from Endless Amusement and Parlour Magic. See also: Book of 500 Puzzles; Boy's Own Conjuring Book; Illustrated Boy's Own Treasury; Indoor and Outdoor; Landells: Boy's Own Toy-Maker; The Secret Out; Hanky Panky. SP. Prefixed by ?? is a flag to check spelling. "The Sphinx". See: Lemon. Sridhara. c900. Śrīdharācārya. Patiganita (= Pâţîgaņita [NOTE: ţ, ņ denote t, n with underdot.]). c900. Transcribed and translated by Kripa Shankar Shukla. Lucknow Univ., Lucknow, 1959. The text is divided into verses and examples, separately numbered by the editor. I will cite verse (v.) and example (ex.) and the page of the English text. The editor has appended answers on pp. 93 96, some of which were given by an unknown commentator. (I have seen this dated 8C, which would put it before Mahavira -- ??) SSM. School Science and Mathematics. Struik. Source Book. 1969. D. J. Struik (1894- ), ed. A Source Book in Mathematics 1200 1800. Harvard Univ. Press, 1969. Sullivan. Unusual. 1943 & 1947. Orville A. Sullivan. Problems involving unusual situations. SM 9 (1943) 114 118 & 13 (1947) 102 104. (Previously listed in Section 2 below.) Suter. 1900-1902. Heinrich Suter. Die Mathematiker und Astronomen der Araber und Ihre Werke. (AGM 10 (1900) & 14 (1902)); reprinted by APA -- Academic Publishers Associated, Amsterdam, 1981. See also: H. P. J. Renaud; Additions et corrections à Suter "Die Mathematiker und Astronomen der Araber"; Isis 18 (1932) 166-183. S&B. 1986. Jerry (= G. K.) Slocum & Jack Botermans. Puzzles Old & New -- How to Make and Solve Them. Univ. of Washington Press, Seattle, 1986. Slocum had produced a detailed index for this and has extended it to a joint index with New Book of Puzzles. Tabari. Miftāh al-mu‘āmalāt. c1075. Mohammed ibn Ayyūb Ţabarī [NOTE: Ţ denotes a T with a underdot.]. Miftāh al-mu‘āmalāt. c1075. Ed. by Mohammed [the h should have an underdot] Amin Riyāhi [the h should have an underdot], Teheran, 1970. ??NYS -- frequently cited and sometimes quoted by Tropfke and others. Tagliente. Libro de Abaco. (1515). 1541. Girolamo [& Giannantonio] Tagliente. Libro de abaco che insegnia a fare ogni raxone marcadantile & apertegare le terre con larte di la giometria & altre nobilissime raxone straordinarie cō la tarifa come raspondeno li pexi & monete de molte terre del mondo con la inclita citta de. Venetia. El qual Libro se chiama Texauro universale ...; Venice, 1515. See Rara 114-116, 495, 511 512, which seems to confuse this with another work whose title starts: Opera che insegna .... Riccardi lists 27 editions of this and three editions of the other work. He says Boncompagni has studied this work and found that Giovanni Rocha made some corrections and that several editions have only his name, so it is sometimes catalogued under Rocha -- cf below. Smith mentions 25 editions under Tagliente and says Riccardi mentions 11 others. Van Egmond's Catalog 334-344 lists 31 editions to 1586. It is clear that this was a major book of its time. I have briefly looked at a few examples and they seem to have the same material, though the woodcuts were often changed. I have examined: Giovanne Rocha; Libro Dabaco che insegna a fare ogni ragione mercadãtile: & a ptegare le terre cõ larte di la geometria: & altre nobilissime ragione straordinarie cõ la Tariffa come respõdeno li pesi & mone de molte terre del mõdo con la inclita di Vinegia. El qual Libro se chiama Thesauro universale. Venturino Rossinello, Venice, 1541. Smith, Rara, p. 529, only records a 1550 ed. printed by Giovanni Padovano in Venice. The Crawford Collection has 1544 & 1550. Not under Rocha in Riccardi. I found this in the Turner Collection at Keele as A4.32, but it is not under Rocha in Hill's Catalogue (listed in 3.B), but is under Tagliente. It has nice woodcut(?) illustrations in the text -- see Rara 512 for an example. Having first found this book on the shelf at the Turner Collection, I originally thought it was by Rocha and hence an extraordinarily rare book. I am grateful to Bill Kalush for identifying this as a version of Tagliente and for pointing out its importance. Cf Van Egmond's Catalogue 338, item 15. Tartaglia, Nicolo (or Niccolò) (c1506-1559). See: General Trattato. Thomas, Ivor B. See: SIHGM. Tissandier. Récréations Scientifiques. 1880. Gaston Tissandier. Les Récréations Scientifiques ou L'Enseignement par les Jeux. G. Masson, Paris, (1880); 2nd ed., 1881; 3rd ed., 1883; (4th ed., 1884); 5th ed., 1888; (6th ed., 1893; 7th ed., 1894.) I have seen 3rd ed., 1883, and I have 2nd ed., 1881, & 5th ed., 1888. Tissandier was editor of La Nature and the articles often have fine illustrations by L. Poyet and others, frequently copied elsewhere. See Tom Tit for more of Poyet's work. I have seen the date of the first two editions as 1881 & 1882, but the Avertissement of the 2nd ed. says the 1st ed. was Nov 1880 and the Avertissement is dated Apr 1881. [C&B only list 1881.] Tissandier. Popular Scientific Recreations. 1881. Translation and enlargement of the above. Ward Lock, London, ([1881, 1882]); New enlarged ed., nd [1890, 1891]. [Not clear which French edition the translation is based on. The new enlarged ed. contains a Supplement on pp. 775 876 which includes material which is in the 5th French ed. of 1888, but not in the 3rd French ed. of 1883, so it seems the the main text is c1885 and the supplement is c1890. C&B list a London edition, nd, 780pp.] The index refers to a puzzle of knots and cords on p. 775 which is not present. Most of the Supplement appeared as a series of Scientific Amusements in (Beeton's) Boy's Own Magazine from 1889 -- I have vol. 3 (1889) which has the first 10 articles, comprising 62 pages and 67 problems. Some of the material appeared in: Marvels of Invention and Scientific Puzzles. Being A Popular Account of Many Useful and Interesting Inventions and Discoveries. Ward, Lock, & Co., nd [c1890]. My copy has no authors listed, but Jerry Slocum has a copy with Tissandier and Firth on the TP, though it is difficult to see what Firth could have done to warrant his inclusion. This consists of Chapters 56-60, pp. 726-774, and Chap. 32, pp. 448-465, of Popular Scientific Recreations, set on smaller pages, plus a few extra items: An economical mouse-trap (pp. 57-58); Flying bridges (pp. 64-66); Performing fleas (pp. 77-79); Knots and cords and A Curious Toy (pp. 83-85). This last must be what was on pp. 775-776 of the earlier edition of Popular Scientific Recreations and the other material seems to have come from some edition of that work or from the articles in (Beeton's) Boy's Own Magazine. I won't bother to cite this version. Tom Tit. 1890-1893? Arthur Good [= "Tom Tit"]. La Science Amusante. 3 vols., Larousse, Paris, 1890, 1892, 1893? [I have seen the dates given as 1889, 1891, 1893, but the Introductions are dated as I have given, the last being Dec 1893.] The material originally appeared in the magazine L'Illustration with classic engravings by Poyet which have been often reproduced, e.g. in: Beeton's Boy's Own Magazine; The Boy's Own Paper; Kolumbus Eier (1890, 1976) -- translated as: Columbus' Egg (1978). Arthur Good's name is clearly English and I have wondered if the articles were written originally in French or if they were translated from his English. I have the three volume set and five one volume selections/adaptations. I will give references to these by the initials shown below.
[I have also seen an Italian translation. There was a US ed., trans. by Camden Curwen & Robert Waters; Magical Experiments or Science in Play; (© Worthington, 1892); David McKay, Philadelphia, 1894, 329 pp. [Christopher 398.]] Todhunter. Algebra, 5th ed. 1870. Isaac Todhunter (1820-1884). Algebra For the Use of Colleges and Schools. With Numerous Examples. Macmillan, (1858; 5th ed, 1870); new edition, 1879, HB. [1st ed was 1858; 2nd, 1861; 5th, 1870. The Preface in my 1879 copy is dated 1870 and says the work has been carefully revised, with two chapters and 300 miscellaneous examples added, so it was quite different than previous editions and I will date citations as 1870.] Tonstall. De Arte Supputandi. 1522. Cuthbert Tonstall [often spelled Tunstall] (c1474-1559). De Arte Supputandi Libri Quatuor. ([With Quattuor] Richard Pynson, London, 1522 -- the first arithmetic printed in England, with TP engraved by Holbein.) I have seen: Robert Stephan, Paris, 1538. Though the TP and pagination are different, Smith, Rara, gives no indication that the 1538 text is any different than the 1522, so I will cite this as 1522. Most citations are to Book III, whose problems are numbered. See Rara 132-136. Toole Stott. 1976-1978. Raymond Toole Stott. A Bibliography of English Conjuring 1581 1876. 2 vols., published by the author, Derby, 1976, 1978; distributed by Harpur & Sons, Derby. 1414 entries. References are to the item number. TP Title Page. Tropfke. 1980. Johannes Tropfke, revised by Kurt Vogel, Karin Reich and Helmuth Gericke. Geschichte der Elementarmathematik. 4th ed., Vol. 1: Arithmetik und Algebra. De Gruyter, Berlin, 1980. (Prof. Folkerts says (1994) that vol. 2 is being edited.) [The 1st ed. was De Gruyter?, Leipzig, 1902, 2 vols. 2nd ed., De Gruyter, Berlin & Leipzig, 1921-1924, 7 vols. 3rd ed., De Gruyter, Berlin & Leipzig, 1930-1940, vols. 1-4 (the MSS of the remaining volumes were destroyed in 1945).] Tunstall, Cuthbert -- see: Tonstall, Cuthbert. Turner. The Turner Collection, formerly at University of Keele. Sadly this collection was secretly sold by the University in 1998 and has now been dispersed. A useful catalogue was prepared: Susan Hill; Catalogue of the Turner Collection of the History of Mathematics Held in the Library of the University of Keele; University Library, Keele, 1982.
Uncle George. See: Parlour Pastime. Unger. Arithmetische Unterhaltungen. 1832. Ephraim Salomon Unger. Arithmetische Unterhaltungen, bestehend in einer systematisch geordneten Sammlung von mehr als 900 algebraischen Aufgaben, verbunden mit einer Anleitung, diese Aufgaben mittelst der einfachsten Regeln der Arithmetick zu lösen. (Erfurt, 1832, 4 + 253 pp., ??NYS); 2nd ed., Keysersche Buchhandlung, Erfurt, 1838, 10 + 268pp. MUS 166 only mentions the 1838 ed. but a copy of the 1st ed. was advertised by Sändig in Jun 1997. I haven't seen any other reference to this work. In general, this book believes in beating problems to death -- each type of problem is done several times. E.g. there are 10 problems of the Chinese Remainder Theorem with two moduli. Hence I will generally not describe all the problems. van Etten. See: Etten, above. Van Egmond's Catalog. Warren Van Egmond. Practical Mathematics in the Italian Renaissance: A Catalog of Italian Abbacus Manuscripts and Printed Books to 1600. Supp. to Annali dell'Istituto e Museo di Storia della Scienza (1980), fasc. 1. = Istituto e Museo di Storia della Scienza, Monografia N. 4. Florence, 1980. I have consulted this for (almost?) all MSS cited in these Sources and have made a number of changes of dates and even authorship based on it. Like any such catalog, there are some omissions and errors, but it is by far the most authoritative listing of the material and I have adopted his dates and attributions -- cf Benedetto da Firenze, P. M. Calandri, dell'Abbaco, pseudo-dell'Abbaco. Vinot. 1860. Joseph Vinot. Récréations Mathématiques Nouveau Recueil de Questions Curieuses et Utiles Extraites des Auteurs Anciens et Modernes. Larousse & Boyer, Paris, 1860, (3rd ed., Larousse, Paris, 1893; 1898; 1902; 6th ed., nd [1911]). I have found no difference between the 1st and 6th eds -- indeed I have found a simple typographical error repeated. Vogel, Kurt (1888-1985). See: AR; BR; Chiu Chang Suan Ching; Columbia Algorism; Tropfke; items in 7.K under al Khwârizmî; items in 7.P.7 and 7.R.2 under Fibonacci. Vyse. Tutor's Guide. 1771? Charles Vyse (fl. 1770-1815). The Tutor's Guide, being a Complete System of Arithmetic; with Various Branches in the Mathematics. In Six Parts, .... To which is added, An Appendix, Containing Different Forms of Acquittances, Bills of Exchange, &c. &c. The whole being designed for the Use of Schools, .... The Eighth Edition, corrected and improved, with Additions. G. G. J. and J. Robinson, London, 1793, HB. 12 + 324 pp. [1st ed. was 1770 or 1771; 2nd ed., 1772; 4th ed., 1779; 6th ed., 1785; 1790; 8th ed., 1793; 1799; 12th ed., 1804; 13th ed., 1807; 14th ed., 1810; 15th ed., 1815; 1817; 16th ed., 1821.] Since books of this nature rarely had major changes, I will date this as 1771? until I see further editions. Charles Vyse (fl. 1770-1815). The Tutor's Guide, being a Complete System of Arithmetic; with Various Branches in the Mathematics. In Six Parts, .... To which is added, An Appendix, Containing Different Forms of Acquittances, Bills of Exchange, &c. &c. The whole being designed for the Use of Schools, .... 10th ed., ed. by J. Warburton. S. Hamilton for G. G. and J. Robinson, London, 1799. 12 + 335 pp. [Dedication removed; Preface by the Editor and references to the Key added. Though the text is reset with one or two more lines per page, the text seems to be preserved, though the editor has added substantial footnotes in places.] The Key to the Tutor's Guide; or the Arithmetician's Repository: containing Solutions to the Questions, &c. in the Tutor's Guide, with references to the pages where they stand. To which are added Some Useful Rules, &c. Likewise An Appendix; showing the Combination of Quantities; The different Ways they may be varied; with the method of filling the magic squares, &c. .... Eighth edition; Carefully revised, corrected, and augmented. G. & J. Robinson, London, 1802. 8 + 370 pp + 2pp publisher's ads. [1st ed., 1773; 3rd ed., 1779; 4th ed., 1785; 7th ed., 1799; 8th ed., 1802; 9th ed., 1807; 11th ed., 1818.] Despite the claim in the title of the Key, the references to the answers are in the text of the 10th ed at the beginning of each set of exercises. There is no mention of the Key in the 8th ed of the book. I have the 8th and 9th eds. of the Key and have not seen any difference between them -- indeed I have found a common misprint -- and they give the answers to the 10th ed. of the book, on the pages cited in the book, so I assume they are essentially identical to the 7th ed. of the Key. V&T, 1952. Volkmann, Kurt & Tummers, Louis. Bibliographie de la Prestidigitation Tome I Allemagne et Autriche. Cercle Belge d'Illusionnisme, Bruxelles, 1952. With a 2 page list of Bibliographies of Conjuring. Walkingame. Tutor's Assistant. Francis Walkingame. The Tutor's Assistant; Being a Compendium of Arithmetic, and a Complete Question-Book. ... To which are added, A new and very short Method of extracting the Cube Root, and a General Table for the ready calculating the Interest .... The Fifteenth Edition. Printed for the Author, London (Great Russel-Street, Bloomsbury), 1777. [First ed. was 1751. There were about a hundred editions in all. See Wallis's article on this book in MG 47 (No. 361) (1963) 199-208.] The Tutor's Assistant. Being a Compendium of Arithmetic, and a Complete Question-Book. ... To which are added, A new and very short Method of extracting the Cube Root, and a General Table for the ready calculating the Interest .... The Twentieth Edition. Printed for the Author, London (Kensington), 1784. Appears to be identical to the 15th ed., except for resetting and some small changes, both corrections and errors, so I won't cite this separately. The Tutor's Assistant, being a Compendium of Arithmetic, and Complete Question-Book; ...; to which is added, A Compendium of Book-keeping, by Single Entry, by Isaac Fisher. Thomas Richardson, Derby; Simpkin, Marshall & Co., London, 1835. [The first Derby edition by Fisher was 1826.] The Tutor's Companion; or, Complete Practical Arithmetic. To which is added A Complete Course of Mental Arithmetic, ..., by Isaac Butler. Webb, Millington, and Co., London, 1860. The editions are pretty similar, but the interesting collection of problems at the end is much shortened in the 1835 ed. and a few are omitted in the 1860 ed. Consequently I will assume the problems date from 1751, unless they vary in some important way. I also have a Key to Walkingame from 1840, but it does not correlate with any of the editions I have! Wallis. The Wallis Collection of early English mathematics books. Gathered by Peter J. Wallis and left to the University of Newcastle upon Tyne in 1992. A typical catalogue entry is Wallis 227 CAR and there are special sections for Newtoniana and Record(e). Week End. 1932. Hubert Phillips. The Week End Problems Book. Nonesuch Press, London, 1932. Wehman. New Book of 200 Puzzles. 1908. Wehman Bros.' New Book of 200 Puzzles. Wehman Bros., 126 Park Row, NY, 1908. Largely copied from various 19C works: Boy's Own Book, Magician's Own Book, The Sociable, sometimes with typographical omissions. I only count 130 puzzles! There seems to have been a Johnson Smith reprint at some time. Wells. 1698. Edward Wells. Elementa Arithmeticæ Numerosæ et Speciosæ. In Usum Juventutis Academicæ. At the Sheldonian Theatre (i.e. OUP), Oxford, 1698. (My copy was previously in the Turner Collection, Turner D1.1.) All the material cited is in Appendix Posterior: Viz. Problemata sive Quæstiones ad exercendas Regulas Arithmeticæ. Western Puzzle Works. 1926. Western Puzzle Works, 979 Marshall Avenue, St. Paul, Minnesota. 1926 Puzzle Catalogue. Photocopy provided by Slocum. Unpaginated, 8pp. Williams. Home Entertainments. 1914. Archibald & F. M. Williams. Home Entertainments. The Hobby Books, ed. by Archibald Williams. Nelson, London, nd [1914 -- BMC]. Williams, Henry Llewellyn, Jr. (1842-??). Books by Frikell?, particularly Magician's Own Book, are often attributed to him. [C&B, under Williams, Henry Llewellyn ("W. Frikell") lists: Hanky Panky; Magician's Own Book, London & New York; (Magic No Mystery); The Secret Out and says to also see Cremer.] Williams, J. L. See: Boy's Own Book, 1843 (Paris) edition, which lists him as author. Wilson, Robin J. See: BLW. Wingate/Kersey. 1678?. Edmund Wingate (1596-1656). Mr. Wingate's Arithmetick; Containing A Plain and Familiar Method For Attaining the Knowledge and Practice of Common Arithmetick. (1629.) The Seventh(?) Edition, very much Enlarged. First Composed by Edmund Wingate, late of Gray's-Inn, Esquire. Afterwards, upon Mr. Wingate's Request, Enlarged in his Life-time: Also since his Decease carefully Revised, and much Improved; ... By John Kersey, late Teacher of the Mathematicks. My copy is lacking the TP and pp. 345+, but it appears to be identical to The Tenth Edition; J. Philips, J. Taylor & J. Knapton, London, 1699 -- though reset, it has the same pagination throughout except for the Dedication. A Librarian's note suggests my earlier version is the 7th ed. of 1678. This would be the fourth and last of Kersey's versions. Kersey began editing from the second or third (1658) ed. and did four versions, the last in 1678. The material of interest is almost all in Chapter 10 of Kersey's Appendix: A Collection of subtil Questions to exercise all the parts of Vulgar Arithmetick; to which also are added various practical Questions about the mensuration of Superficial Figures and Solids, with the Gauging of Vessels, pp. 475-527, 75 questions. There are a few further items in Chapter 11: Sports and Pastimes, pp. 528-544, 7 problems. Chapter 11 is not clearly marked as being by Kersey in these copies, but is so marked in later editions and it is pretty clear that the entire Appendix is due to Kersey. At the end, he says he has taken the problems of Chap. 11 from Bachet's Problemes. I have seen a 14th ed. of 1720 which has the same text, reset and repaginated, with some supplementary material by George Shelley. I have also seen a 19th ed. of 1760 which has been considerably reorganized by James Dodson. The two chapters of puzzle problems have become Chapters XLIII and XLIV and the material has been changed, generally omitting some problems of interest and only adding two. Winning Ways. 1982. Elwyn R. Berlekamp, John H. Conway & Richard K. Guy. Winning Ways for Your Mathematical Plays: Vol. 1: Games in General; Vol. 2: Games in Particular. 2 vols, Academic Press, NY, 1982. Witgeest. Het Natuurlyk Tover-Boek. 1686. Simon Witgeest. Het Natuurlyk Tover-Boek, Of't Nieuw Speel-Toneel Der Konsten. Verhandelende over de agt hondert natuurlijke Tover-Konsten. so uyt de de Gogel-tas, als Kaartspelen, Mathematische Konsten, en meer andered diergelijke aerdigheden, die tot vermaek, en tijtkorting verstrecken. Mitsgaders een Tractaet van alderley Waterverwen, en verligteryen; Als oock Een verhandelinge van veelderley Blanketsels. Om verscheyde wel-ruykende Wateren, Poederen en Balsemen, als ook kostelijke beeydselen, om het Aensicht, Hals en Handen, wit en sagt te maecken, door Simon Witgeest. Jan ten Hoorn, Amsterdam, 1686. ??NYS -- some photocopies sent by Jerry Slocum. 'Boek' is 'Boeck' on the frontispiece and running heads. This is a much expanded and retitled 3rd edition of Witgeest's 1679 work. The new material is stated to already be in the 2nd ed. of 1682. [There were many later editions: 1695; 1698; Ten Hoorn, 1701; G. de Groot Keur, Amsterdam, 1725 (10th ed.), 1739; 1749; 1760; Amsterdam, 1773; 1815 [Christopher 1098-1099, C&B, HPL]. It was translated as: Naturliches Zauber-Buch (or Zauber=Buch) oder neuer Spiel-Platz der Künste; Hoffmanns sel Wittw. & Engelbert Streck, Nürnberg, 1702. There were later editions (all in Nürnberg?) of 1713 (in 1 or 2 vols); Hoffmann, Nürnberg, 1718; 1730; 1739; 1740; 1745; 1753; Johann Adam Stein, Nürnberg, 1755; 1760-1762; 1763; 1766; 1781; 1786; 1798 and a Lindau reprint of 1978 [Christopher 1092-1097, C&B, V&T], all apparently based on the 1682 Dutch ed.] Witgeest. Het Nieuw Toneel der Konsten. 1679. Simon Witgeest. Het Nieuw Toneel der Konsten, Bestaande uyt Sesderley Stukken: het eerste, handelt van alderley aardige Speeltjes en Klugjes: het tweede, van de Verligt-konst in 't Verwen en Schilderen: het derde, van het Etzen en Plaat-shijden: het vierde, van de Glas-konst: het vijfde, heest eenige aardige remedien tegen alderley Ziekten: het sesde, is van de Vuur-werken. Uyt verscheyde Autheuren by een vergadert, door S. Witgeest, Middel-borger. Jan ten Hoorn, Amsterdam, 1679; facsimile with epilogue by John Landwehr, A. W. Sijthoff's Uitgeversmaatschappij N. V., Leiden, 1967 (present from Bill Kalush). There were many later editions, but Nanco Bordewijk has examined these and discovered that the 3rd ed. of 1686 (I can't recall if he saw the 1682 ed.) was so extensively revised and extended as to constitute a new book, and it has the different title given in the previous entry. (Other sources indicate these revisions are already in the 2nd ed. of 1682.) Landwehr has written a bibliographical article on this book -- ??NYR. Wood. Oddities. Clement Wood. A Book of Mathematical Oddities. Little Blue Book 1210. Haldeman-Julius, Girard, Kansas, nd [1927].
Anonymous. The Young Man's Book of Amusement. Containing the Most Interesting and Instructive Experiments in Various Branches of Science. To Which is Added All the Popular Tricks and Changes in Cards; and the Art of Making Fire Works. William Milner, Halifax, 1844, HB. 2 + 384 pp + folding plate (originally a frontispiece). My copy has a number of annotations as though in preparation for another edition. [Hall BCB 322. Toole Stott 751. BCB 320-323 are 1839, 1840, 1844, 1848. Heyl 358-360 are 1846, 1846 (Milner & Sowerby ??), 1850. Toole Stott 749-752, 1216 are 1839, 1840, 1844, 1846, 1850. Christopher 1111-1113 are 1839, 1846, 1859 (Milner & Sowerby). All these are apparently the same except for the publisher's name change.] Young World. c1960. Young World Productions. Tricks and Teasers. 303 Gags Games Tongue Twisters Problems Tricks. Young World Productions, London, nd [inscribed 1965 on first page, so probably c1960; BLC-Ø]. 536. H. E. Dudeney. 536 Puzzles and Curious Problems. Ed. by M. Gardner. Scribner's, NY, 1967. (This consists of almost all the puzzles from Modern Puzzles (MP) and Puzzles and Curious Problems (PCP).) [There is also a Fontana, London, 1970, edition in two volumes: Puzzles and Curious Problems (258 problems); More Puzzles and Curious Problems (261 problems).] ?? indicates uncertainty and points where further work needs to be done. BC, e.g. 330 is 330 BC and 5C is 5th century BC. Inequality or incongruence (mod m). (My word processor does not have an incongruence sign. I may change this in Word using an Arial character.) Ø Nothing, used after catalogues, etc., to indicate that I have looked in that catalogue and found no entry. E.g. BLC-Ø. SOME OTHER RECURRING REFERENCES Details of these items are given under the first reference in Sources. Later references often cite the first reference. I tend to make entries below when I use the item, but sometimes I have entered the entry long after the first usage of the item, and I haven't searched the text for other (perhaps entered long ago) appearances of these items. For: See Sections: Anon: Home Book ..., 1941 4.B.1, 4.B.3, 5.U, 6.AO, 6.BF.4, 7.B, 7.AT, 9.E.1 Anon: Treatise, 1850 7.H, 7.P.6, 7.S, 7.X, 10.A, 10.R Allen, 1991 5.B, 5.I.1, 5.N, 6.L, 7.E, 7.I, 7.P.1, 7.R.3, 7.AC.6, 7.AH, 7.AL, 9.B, 10.A.4 Always: More Puzzles to Puzzle You, 1967 6.BF.4, Always: Puzzles for Puzzlers, 1971 5.D.2, 5.D.5, 7.G.1, 7.AC.1, 9.J, 10.I, 10.K Always: Puzzles to Puzzle You, 1965 5.K.2, 5.W.1, 5.X.2, 7.AC.3, 7.AC.6, 7.AS, Always: Puzzling You Again, 1969 5.C, 6.BD, 7.AH, Ananias of Shirak, c640 7.E, 7.H, 10.A André, 1876 7.H, 7.H.1, 7.S.1, 7.S.2, 7.AF, 7.AF.2 August, 1939 5.X.1, 6.BE, 7.I, 7.X, 7.Z, 7.AL, 7.AN, 7.AT, 7.AV, 10.H Badcock, 1823 6.BH, 7.H.3, 7.P.5, 7.Q Bagley: Paradox Pie, 1944 6.BN, 7.Z, 7.AI, 7.AW, 10.F, 10.Q, 10.S Bagley: Puzzle Pie, 1944 5.D.5, 6.O, 6.P.1, 6.P.2, 6.R.1, 6.R.2, 6.Y, 6.AF, 6.AI, 7.AV, 10.L Bath, 1959 5.C, 7.G.1, 7.I, 7.P.5, 7.AC.3, 7.AC.6, 7.AM Bellew, 1866 5.E, 6.AO.1, 6.AQ Berloquin, 1981 5.N, 7.H.5, 7.N.3, 10.R Black, 1952 [1946?] 5.T, 6.F.2, 9.D, 9.F Bourdon, 1834 7.E.1, 7.H, 7.P.1, 7.S, 7.X, 7.AF.1, 7.AK, 10.A, 10.R Brandreth Puzzle Book [1895] 5.B, 5.B.1, 5.O, 6.AW.1, 6.AY.1, 7.B, 7.G.1 Bullen, 1789 7.G.1, 7.H, 7.H.5, 7.L.2.b, 7.S.1, 7.AF.1 Bullivant, 1910 5.S, 6.T, 6.AK [Chambers], 1866? 7.H, 7.L.2.a, 7.L.2.b, 7.Y, 7.AF.2 Chang Chhiu Chien -- see Zhang Qiujian Colenso, Algebra, 1849 7.P.1, 10.G Colenso, Arithmetic, 1853 7.H, 7.X, 10.G, 10.R Devi, 1976 5.D.1, 5.X.1, 7.E, 7.P.1, 7.AC.3, 7.AC.6, 7.AE, 10.A.3; 10.K Dresner, 1962 5.B.1, 5.C, 5.D.4, 5.K.1, 5.W Dudeney: World's best puzzles, 1908 2, 5.P.1, 5.S, 6.P.1, 6.S, 6.AI, 6.AO, 6.AW Elliott, 1872 6.V, 6.AQ, 6.AV, 6.AZ, 11.B, 11.C, 11.D Filipiak, 1942 5.H.1, 6.W.1, 6.W.2, 6.AK Fisher, 1968 6.E, 6.P.2, 7.M.4, 7.AI Fisher, 1973 1, 5.E, 7.S.2, 10.L Fourrey, Cur. Geom., 1907 6.S.1, 8.G (also 6.R.1) Fourrey, Rec. Arith., 1899 4.A.1, 5.B, 5.P.1, 5.U, 7.N.1 Fuss, 1843 5.F.1 Goldston, nd [1910?] 6.AK, 11.E Gomme, 1894/98 4.B.1, 5.R.5 (Also 4.A.3) Greenblatt, 1965 6.U.2, 6.AE, 7.AG Heald, 1941 7.Z, 10.E.3, 10.G, 10.0 Hooper, 1774 4.A.1, 5.AA, 6.F, 6.P.2, 7.B, 7.AO, 7.AZ Hutton, 1804 7.G.2, 7.H, 7.X, 7.AF.1, 7.AK, 10.A, 10.R Kamp, 1877 5.B, 5.D.1, 5.E, 5.R.7, 7.B, 7.L, 7.Q Kraitchik, MJ, 1930 4.A.2, 5.J, 7.E, 7.G.1, 7.H.3, 7.AR, 10.B, 10.P Kraitchik, MR, 1943 4.A.2, 5.J, 6.M, 7.H.2, 7.H.3, 9.D, 9.G, 10.P Laisant, 1906 6.P.1, 7.AR, 10.A.2, 10.B, 10.H, 10.I Larte de labbacho, 1478 See: Treviso Arithmetic. Von der Lasa, 1897 5.F.1, 7.B (Also 4.B.1, 4.B.5) Licks, 1917 5.A, 6.R.4, 6.AG, 7.P.3, 7.S.2, 7.AC, 7.AD Van der Linde, 1874 5.F.1, 7.N (Also 4.B.1, 4.B.5) Littlewood, 1953 5.C, 5.W, 6.J, 8.B, 9.C, 9.D Lucas, Théorie, 1891 5.L, 5.Z.5, 5.AB Madachy, 1966 5.O, 6.D, 6.X, 7.N.3, 7.N.4, 7.AC.3, 7.BB Meyer, 1965 7.I, 7.AC.4, 7.AH, 7.AR, 7.AX Milne, 1881 7.E, 7.H, 7.R, 7.X, 7.Y, 10.A, 10.A.3, 10.G, 10.R W. O. J. Moser, 1981 6.I, 6.T Nordmann, 1927 4.A.4, 5.G.1, 6.AR, 7.AC.3, 7.AR, 11.C, 11.E Papyrus Rhind, c 1650 7.C, 7.G.1, 7.L, 7.S.1 Phillips: Playtime Omnibus, 1933 6.AF, 7.S.2, 7.AC.1, 7.AD.1, 7.AE, 9.D Phillips: Question Time, 1937 5.U, 7.E, 7.AG, 9.G Ransom, 1955 6.M, 7.F, 7.X, 7.AC.2, 8.B, 10.A.1, 10.B, 10.I Smith: Origin, 1917 3A, 7.G.2, 7.H, 10.A Steinhaus: 1938,1950,1960,1969 5.C.1, 6.E, 6.G.1, 6.H, 6.AB Strutt, 1791?, 1801 4.B.1, 5.R.1, 5.R.5 (Also 4.A.3) Strutt-Cox, 1903 4.B.1, 5.R.1, 5.R.5 (Also 4.A.3) Trenchant, 1566 7.L.2.a, 7.S.1 (also 5.B, 5.D.1, 7.E, 7.S.1, 7.AF.1) Treviso Arithmetic, 1478 7.H, 7.K.1, 7.AL, 10.A Trigg: Quickies, 1967 5.Q, 6.AE, 6.AN, 7.N.3, 7.W Wagner, Rechenbuch, 1483 7.G.1, 7.G.2, 7.H, 7.AK, 10.A Wecker, (1582), 1660 7.L.3, 7.AO, 10.P, 11.I, 11.N A. C. White, 1913 1, 5.I.1, 6.T, 6.AK, 7.X, 11.E Widman(n), 1489 7.G.1, 7.H, 7.L.2, 7.P.1, 7.P.5, (7.AL) Williams & Savage, 1940 7.P.5, 7.X, 7.AC.2, 7.AM, 7.AP, 8.I, 10.E.2 Wolff, 1937 7.R.3, 7.S.2, 7.AC.1, 7.AE, 9.E, 9.E.1, 10.O Workman, 1902 7.H.1, 7.H.4, 7.J, 7.S.2, 7.AC.2, 10.G Wyatt, 1928 5.H.1, 6.V, 6.W.1, 6.W.2, 6.AI Mr. X, 1903, 1911 4.A.1, 5.B, 5.P.1, 5.S, 6.AF, 6.AU, 7.H.3, 7.I, 7.J, 7.M.4, 9.E, 9.J, 10.H Yang Hui, 1275 7.N, 7.P.1, 7.P.2, 10.A Zhang Qiujian, 468 7.E, 7.L, 7.P.1, 7.P.6, 10.AYüklə 0,59 Mb. Dostları ilə paylaş:
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