|Viète, Francois (1540-1603)|
| This entry contributed by Margherita Barile A non-professional French mathematician, also known under the latinized name of Vieta, who disclosed the way to modernsymbolic algebra. He had a very brilliant legal career starting in his hometown Fontenay-le-Comte as the privatelawyer of a noble family, & ended up as a personal counselor of King Henri III.His first mathematical works were two books of trigonometric tables (Canon Mathematicus, và UniversaliumInspectionum Liber Singularis, 1579) where the values of sines were computed with a (startling) accuracy of10-8.Viète"s major contribution is his innovative treatment of algebraic equations. He initiated the systematical use ofletters to denote both the coefficients & the unknowns: this was the beginning of a new type of algebra, expressed interms of abstract formulas and general rules, instead of the geometric visualizations, the text problems & thenumerical examples used by his predecessors back since antiquity. He, however, payed some sort of tribute to the ancienttradition by refusing negative solutions, by sticking lớn the use of words lớn denote powers (the exponents would beintroduced by Descartes one generation later), & by keeping a terminology inspired by areas and volumes ("plane" and"solid" for the product of two or three numbers respectively). His treatise Isagoge in Artem Analyticem (1591) is a presentation of his mathematical project. There he introducesthe basic notation và gives the rules for the sản phẩm of powers and the equivalent transformation of equations in a waythat calls lớn mind the first pages of Diophantus" Arithmetica. Viète"s classification of the branches of algebrais also partially derived from Greek mathematics: he distinguishes between zetetics (translating a problem into anequation), poristics (proving theorems through equations), & exegetics or rhetics (solvingequations). His main works (Ad Logisticem Speciosam Notae Priores, 1631; Zeteticorum Libri Quinque, 1591 or1593; De Aequationem Recognitione et Emendatione Tractatus Duo, 1615) are entirely devoted to lớn the study of thegeneral properties of algebraic equations. In another treatise, De Numerosa Potestatum ad Exegesin Resolutione(1600), he presented techniques for the numerical computation of roots. He also wrote three minor works on anglesections và other constructions in plane geometry.|
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Schmidt, R. "On the Recognition of Equations by François Viète." In The Early Theory of Equations. On their Nature và Constitutions. Annapolis, MD: Golden Hint Press, pp.1-104, 1986.Viète, F. Analytic Art. (Transl.
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By T.R.Witmer). Kent, OH: Kent State University Press, 1983.