Introduction en l’art analytic. ou Nouuelle algebre de François Viete. [bound with:] Les cinq livres des Zetetiques de Francois Viette. [with:] Examen de la Traduction faicte par Anthoine Vasset, des cinq Livres des Zetetiques de M. Viette.

Paris: J. Jacquin, 1629/1630.

Very rare first edition of the first French translation and exposition of Viète’s In artem analyticum isagoge (Tours, 1591), the earliest work on symbolic algebra, here bound with a first edition of Vaulezard’s translation of Viète’s Zeteticorum libri quinque (Tours, 1593), which gives examples of the application of his ‘analytic art’ to problems from Diophantus’ Arithmetica. The third work is a scathing criticism of a slightly later translation of the Isagoge by Antoine Vasset, a response to criticisms Vasset had made of Vaulezard’s translation in his own work.

“The most important of Viète‘s many works on algebra... [In artem analyticem isagoge] also introduced the use of letters both for known quantities, which were denoted by the consonants B, C, D, and so on, and for unknown quantities, which were denoted by the vowels. Furthermore, in using A to denote the unknown quantity x, Viète sometimes employed A quadratus, A cubus ... to represent x2, x3, ... This innovation, considered one of the most significant advances in the history of mathematics, prepared the way for the development of algebra” (DSB XIV 19).

Perhaps the most important part of the work is chapter 4, in which “he presents a mode of calculation carried out completely in terms of ‘species’ of numbers and calls it logistice speciosa – in contrast with calculation using determinate numbers, which is logistice numerosa. Of significance for the formation of the concepts of modern mathematics, Viète devotes the logistice speciosa to pure algebra, understood as the most comprehensive possible analytic art, applicable indifferently to numbers and to geometric magnitudes.”

“In 1593 Viète published Zeteticorum libri quinque, which he very probably had completed in 1591. In it he offered a sample of logistice speciosa and contrasted it directly with Diophantus’ Arithmetica which, in his opinion, remained too much within the limits of logistice numerosa. In order to stress the parallelism of the two works, Viète ended the fifth book of his Zetetics with the same problem that concludes the fifth book of Diophantus’ Arithmetica. In other parts of the book he takes series of problems from the Diophantus work” (ibid. 19-20).

Vaulezard dedicates the Zetetics to Jean Beaugrand, who had close ties, both personally and intellectually, to Fermat and probably introduced him to Viete’s analytic art. In 1631 Beaugrand edited a duodecimo edition of the Isagoge. Apart from their inclusion in Viète’s Opera Mathematica (1646), neither of the works were published again in any language until the twentieth century.

The first edition of In artem analyticem isagoge is among the rarest of the important works in the history of mathematics. The present works are almost as rare on the market, and are in fact even rarer than the Isagoge in institutional collections. There is no copy of any of the three offered works on COPAC (which lists five copies of the Isagoge), and there are five copies of L’art analytique and six of the other two works on OCLC (which lists a dozen or so copies of the Isagoge).

OCLC: L’art analytique and Zetetiques (Brown, Harvard, Michigan, NYPL in US), Examen (Brown and Harvard only in US).

8vo (170 x 107 mm), contemporary limp vellum with coat of arms to front and rear boards, pp [1-8] 9-79; [2], 2, 8; [8], 9-66, 69-217, [3], quire I being one leaf ending on p. 66 with word FIN, text starting anew on K1, engraved figures in text as far as p.132, thereafter woodcut figures. Some gatherings browned, a few small water staines in the margin, contemporary ex-libris inscription to to title, in all a fine and untouched copy. Preserved in a custom half morocco clam shell box.

Item #3128

Price: $35,000.00