In artem analyticum isagoge: eiusdem, Ad logisticem speciosam notae priores. Francisci Vieta Fontenaeensis ; recensuit, scholiisq; illustravit I.D.B[eaugrand]. VIÈTE, François.
In artem analyticum isagoge: eiusdem, Ad logisticem speciosam notae priores. Francisci Vieta Fontenaeensis ; recensuit, scholiisq; illustravit I.D.B[eaugrand].
First printing of Viète’s Ad logisticem speciosam notae priores (one of his main works), together with the second edition of his In artem analyticum isagoge, "the earliest work on symbolic algebra [by] the greatest French mathematician of the sixteenth century" (PMM). The first edition of the Isagoge, published at Tours in 1591, is, together with the Lobachevsky, the rarest mathematical work in PMM, and this second edition is in fact rarer than the first in institutional collections [OCLC lists only copies in France and UK]."The ‘Introduction to the Art of Analysis’ is the earliest work on symbolic algebra. Viète’s greatest innovation in mathematics was the denoting of general or indefinite quantities by letters of the alphabet instead of abbreviations of words as used hitherto. Known quantities were represented by consonants, unknown ones by vowels; squares, cubes, etc., were not represented by new letters but by adding the words quadratus, cubus, etc. Viète also brought the + and – signs into general use. This algebraic symbolism made possible the development of analysis, with its complicated processes, a fundamental element in modern mathematics" (PMM). "This innovation, considered one of the most significant advances in the history of mathematics, prepared the way for the development of algebra" (DSB). "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: BNF and Glasgow only; COPAC adds Oxford, UCL and University of London Senate House (for comparison OCLC lists some 15 copies of the 1591 edition). PMM 103 (1591 edition). 12mo (108 x 57 mm), pp  99 [1:errata];  99, 200-233  [1:blank], although the pagination jumps from 99 to 200 the signatures are continuous (i.e., i2-i3), fine contemporary limp vellum with gilt decoration to front and rear boards, manuscript paper label to spine, two very small paper flaws to the first title, otherwise very fine and clean throughout. N° de réf. du libraire 2885