General theory of algebraic equations - Bézout, Etienne (Princeton University Press, 2006)
Cover; Title Page; Table of Contents; Translator's Foreword; Dedication from the 1779 edition; Preface to the 1779 edition; Introduction: Theory of differences and sums of quantities; Definitions and preliminary notions; About the way to determine the differences of quantities; A general and fundamental remark; Reductions that may apply to the general rule to differentiate quantities when several differentiations must be made.; Remarks about the differences of decreasing quantities
This book provides the first English translation of Bezout's masterpiece, the General Theory of Algebraic Equations. It follows, by almost two hundred years, the English translation of his famous mathematics textbooks. Here, Bézout presents his approach to solving systems of polynomial equations in several variables and in great detail. He introduces the revolutionary notion of the "polynomial multiplier," which greatly simplifies the problem of variable elimination by reducing it to a system of linear equations. The major result presented in this work, now known as "Bézout's theorem," is stat