# Arithmeticorum libri sex, et de numeris multangulis liber unus. Nunc primum Graece & Latine editi, atque commentariis illustrati. Auctore C. G. Bacheto.

Paris: H. Drouart, 1621. First edition.

Editio princeps of “the first systematic treatise on algebra” (David Eugene Smith, Rara Arithmetica). First printing of the Greek text, accompanied by Xylander’s Latin translation (1575) and Bachet’s commentary. “The most famous edition of the Arithemtic was that of Bachet de Mézeriac (1621). Bachet glimpsed the possibility of general principles behind the special problems of the Arithmetic and, in his commentary on the book, alerted his contemporaries to the challenge of properly understanding Diophantus and carrying his ideas further. It was Fermat who took up this challenge and made the first significant advances in number theory since the classical era.” (John Stillwell, Mathematics and Its History, p.51). Fermat’s son published in 1670 the second edition of this work adding his father’s notes and an essay by Fermat’s correspondent Jacques de Billy.

“Although entitled an arithmetic this is really a treatise on algebra, the first systematic one ever written. It contains, however, a good deal of matter upon Greek theory of numbers, notably the ‘Clavdii Gasparis Bacheti Sebusiani, in Diophantvm, Liber Primus,’ ‘Liber Secundus,’ and ‘Liber Tertius.’ A certain amount of this work also enters into the treatise itself, but this is generally algebraic in character, the standard problem requiring the finding of a number satisfying given conditions. This leads to numerous indeterminate (Diophantine) equations.” (Smith, Rara Arithmetica, p.348). “One of Diophantus’ major steps is the introduction of symbolism into algebra … Diophantus called the unknown ‘the number of the problem,’ For our x2 Diophantus used ΔY, the Δ being the first letter of ‘dynamis’ (power) … The appearance of such symbolism is of course remarkable but the use of powers higher than three is even more extraordinary. The classical Greeks could not and would not consider a product of more than three factors because such a product had no geometrical significance. On a purely arithmetic basis, however, such products do have a meaning; and this is precisely the basis Diophantus adopts.” (Kline, Mathematical Thought from Ancient to Modern Times, p.138-44). “Although many of the problem-solving methods we now know as algebra are very ancient, the explicit statement of the notion of an equation, that is, the equivalence of two formally different expressions for the same unknown quantity, was first formulated by Diophantus of Alexandria in the second or third century CE. As Bashmakova and Smirnova note [The Beginnings and Evolution of Algebra], ‘Diophantus was the first to deduce that it was possible to formulate the conditions of a problem as equations or systems of equations; as a matter of fact, before Diophantus, there were no equations at all, either determinate or indeterminate. Problems were studied that we can now reduce to equations, but nothing more than that’.” (Landmark Writings in Western Mathematics, p. 391).

Honeyman 891.

Folio: 338 x 217 mm. Contemporary calf with raised bands, old repair to front board, richly gilt spine, red sprinkled edges, very light waterstain to the upper right corner, and slight browning throughout, alltogether a very genuine, attractive copy in a nice binding, with wide margins. Title printed in red and black, woodcut vignette, old owners signature scraped from the lower right corner og title. There are two imprints of this edition; one by Drouart and one by Cramoisy, which are identical besides the title vignette (no priority established). Pp. (6), 32, 451, (1:blank), 58, (2:errata).

[Item #2441]
Price: €11,000.00
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