Beschreibung
First edition, extremely rare, of the Ad logisticem speciosam notae priores, bound with the fifth edition of Viète's epoch-making In artem analyticem isagoge, the first work on symbolic algebra (Latin editions of the Isagoge were published in 1591 and 1624, and French in 1629 and 1630). The Isagoge is unfortunately lacking 3 leaves of text, but the other work is complete and published here for the first time. The original editions of Viète's works are all virtually unobtainable. "To the treatises of the Isagoge belong Ad logisticen speciosam notae priores and Ad logisticen speciosam notae posteriores, the latter now lost. The first was not published during his lifetime, because Viète believed that the manuscript was not yet suitable for publication. (It was published by Jean Beaugrand in 1631.) It represents a collection of elementary general algebraic formulas that correspond to the arithmetical propositions of the second and ninth books of Euclid's Elements, as well as some interesting propositions that combine algebra with geometry. In propositions 48-51 Viète derives the formulas for sin 2x; cos 2x; sin 3x; cos 3x; sin 4x; cos 4x; sin 5x; cos 5x expressed in terms of sin x and cos x by applying proposition 46 . . . He remarks that the coefficients are equal to those in the [binomial] expansion, . . . that the various terms must be 'homogeneous' and that the signs are alternately + and -" (DSB). The editor, Jean Beaugrand (ca. 1590-1640) "studied under Viète and became mathematician to Gaston of Orléans in 1630; in that year J. L. Vaulezard dedicated his 'Cinq livres des Zététiques de FR. Viette' to Beaugrand, who had already achieved a certain notoriety from having published Viète's In artem analyticam isagoge, with scholia and a mathematical compendium, in 1631. Some of the scholia were incorporated into Schooten's edition of [Viète's Opera Mathematica of] 1646" (DSB, under Beaugrand). Beaugrand was an early friend of Fermat and became his official Paris correspondent, before being replaced in that role by Carcavi. He also communicated some of Fermat's results to Castelli, Cavalieri and Galileo, all of whom seem to have been impressed by his mathematical ability. In France he became involved in several polemics: against Desargues, claiming that the main proposition of the Brouillon projet was nothing but a corollary to a proposition in Apollonius; and against Descartes, claiming that his Géométrie was plagiarized from Harriot, and that Viète's methods were in any case superior. OCLC lists BNF and Glasgow only for Ad logisticem speciosam notae priores. We know of no other copy having appeared in commerce. Two parts in one volume, 24mo (108 x 56mm), pp. [xii], 42 (lacking 5-10), 25-99, [1]; [ii], 86, 89-99, 200-233, [2], woodcut arms of France on title-pages, woodcut initials and headpieces, woodcut diagrams (title-page with short closed tear and 3 small holes without loss of text). Contemporary vellum, small gilt stamp on covers. Bestandsnummer des Verkäufers ABE-1677668868105
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