L'identit\'e alg\'ebrique d'une pratique port\'ee par la discussion sur l'\'equation \`a l'aide de laquelle on d\'etermine les in\'egalit\'es s\'eculaires des plan\`etes (1766-1874)

TL;DR

This paper explores the historical algebraic practices related to the equation of secular inequalities (1766-1874), highlighting identities and debates that shaped early algebraic understanding before modern theories.

Contribution

It analyzes the identities and practices in algebra used during the 18th and 19th centuries, especially in the context of the secular inequalities controversy.

Findings

Identifies key algebraic identities used in historical practices.

Highlights the debate between Jordan and Kronecker on algebraic forms.

Connects mathematical controversies to the development of algebraic concepts.

Abstract

What did "algebra" mean before the development of the algebraic theories of the 20th century ? This paper stresses the identities taken by the algebraic practices developped during the century long discussion around the equation around the equation of secular inequalities (1766- 1874). In 1874, a strong controversy on the theory of bilinear and quadratic forms opposed Camille Jordan and Leopold Kronecker. The arithmetical ideal of Kronecker faced Jordan's claim for the simplicity of his algebraic canonical form. As the controversy combined mathematical and historical arguments, it gave rise to the writing of a history of the methods used by Lagrange, Laplace and Weierstrass in a century long mathematical discussion around the "equation of secular inequalities".