Viète François. The Analytic Art: Nine Studies in Algebra, Geometry and Trigonometry from the Opus Restitutae

Dover Publications, 2006. — 455 p. — (Dover Books on Mathematics). — ISBN 9780873382823, 087338282X.This historic work consists of several treatises that developed the first consistent, coherent, and systematic conception of algebraic equations. Originally published in 1591, it pioneered the notion of using symbols of one kind (vowels) for unknowns and of another kind (consonants) for known quantities.
Francois Viète (1540-1603), a lawyer at the court of King Henry II in Tours and Paris, wrote several treatises that are known collectively as The Analytic Art. His novel approach to the study of algebra developed the earliest articulated theory of equations, allowing not only flexibility and generality in solving linear and quadratic equations, but also something completely new — a clear analysis of the relationship between the forms of the solutions and the values of the coefficients of the original equation. Viète regarded his contribution as developing a «systematic way of thinking» leading to general solutions, rather than just a «bag of tricks» to solve specific problems. These essays demonstrate his method of applying his own ideas to existing usage in ways that led to clear formulation and solution of equations.Translator's Introduction.
Introduction to the Analytic Art.
Preliminary Notes on Symbolic Logistic.
Five Books of Zetetica.
Two Treatises on the Understanding.
and Amendment of Equations.
On the Numerical Resolution of Powers by Exegetics.
A Canonical Survey of Geometric Constructions.
A Supplement to Geometry.
Universal Theorems on the Analysis of Angular Sections.