From Cardano's Great Art to Lagrange's Reflections: Filling a Gap in the History of AlgebraEuropean Mathematical Society, 2011 - 224 pagine This book is an exploration of a claim made by Lagrange in the autumn of 1771 as he embarked upon his lengthy ``Reflexions sur la resolution algebrique des equations'': that there had been few advances in the algebraic solution of equations since the time of Cardano in the mid sixteenth century. That opinion has been shared by many later historians. The present study attempts to redress that view and to examine the intertwined developments in the theory of equations from Cardano to Lagrange. A similar historical exploration led Lagrange himself to insights that were to transform the entire nature and scope of algebra. Progress was not confined to any one country: at different times mathematicians in Italy, France, the Netherlands, England, Scotland, Russia, and Germany contributed to the discussion and to a gradual deepening of understanding. In particular, the national Academies of Berlin, St. Petersburg, and Paris in the eighteenth century were crucial in supporting informed mathematical communities and encouraging the wider dissemination of key ideas. This study therefore truly highlights the existence of a European mathematical heritage. The book is written in three parts. Part I offers an overview of the period from Cardano to Newton (1545 to 1707) and is arranged chronologically. Part II covers the period from Newton to Lagrange (1707 to 1771) and treats the material according to key themes. Part III is a brief account of the aftermath of the discoveries made in the 1770s. The book attempts throughout to capture the reality of mathematical discovery by inviting the reader to follow in the footsteps of the authors themselves, with as few changes as possible to the original notation and style of presentation. |
Parole e frasi comuni
Academy aequationum Arithmetica universalis Bezout calculations Campbell Cardano Cauchy century Chapter claimed coefficients Collins Cramer cube roots cubic and quartic cubic equation degré degree equations Descartes Dulaurens elimination equation equation of degree équations equations of higher Euler Euler and Bezout example factors Frans van Schooten function further give Gregory Harriot higher degree Hudde ideas imaginary roots John Wallis Lagrange Lagrange's later Leibniz Maclaurin magna mathematics Mémoires method Moivre multiplied negative roots Newton Newton's rule nombre notation nth roots number of positive original equation paper Paris permutations polynomial positive roots problem proof published quadratic equation quantities quartic equations quintic racines real roots resolvent Ruffini rule of signs solution solving equations square substitution sums of radicals Suppose term theorem theory of equations transformation Tschirnhaus unknown valeurs values Vandermonde Viète Viète's Wallis Waring write wrote