## From Cardano's Great Art to Lagrange's Reflections: Filling a Gap in the History of AlgebraThis 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. |

### Wat mensen zeggen - Een review schrijven

We hebben geen reviews gevonden op de gebruikelijke plaatsen.

### Veelvoorkomende woorden en zinsdelen

Academy aequationum algebra argument Arithmetica universalis BBAW Bombelli calculations Campbell Cardano Cauchy century Chapter claimed coefficients Collins Cramer cube roots cubic and quartic cubic equation curves degré demonstrated Descartes Dulaurens elimination equation équation equation of degree equations of higher Euler and Bezout example factors Frans van Schooten function further gave geometric Girard give Gregory Harriot Hudde ideas imaginary roots Lagrange Lagrange's later Leibniz linear Maclaurin magna mathematical mathematicians Memoires method Moivre multiplied negative roots Newton Newton's rule number of positive original equation pairs paper permutations positive roots possible powers problem proof proposed equation published quadratic equation quantities quartic equations quintic racines real roots reduced resolvent roots of unity Ruffini rule of signs similar solution solving equations square substitution sums of radicals Suppose theorem theory of equations three-term equations transformation treatise Tschirnhaus unknown values Vandermonde Viete Viete's Wallis Waring write wrote