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What did "algebra" mean before the development of the algebraic theories ofthe 20th century ? This paper stresses the identities taken by the algebraicpractices developped during the century long discussion around the equationaround the equation of secular inequalities (1766- 1874). In 1874, a strongcontroversy on the theory of bilinear and quadratic forms opposed CamilleJordan and Leopold Kronecker. The arithmetical ideal of Kronecker facedJordan's claim for the simplicity of his algebraic canonical form. As thecontroversy combined mathematical and historical arguments, it gave rise to thewriting of a history of the methods used by Lagrange, Laplace and Weierstrassin a century long mathematical discussion around the "equation of secularinequalities".

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)