Étienne Bézout : Analyse algébrique au siècle des Lumières

Liliane Alfonsi (1, 2)

1 IMJ - Institut de Mathématiques de Jussieu
2 GHDSO - Groupe d'histoire et diffusion des sciences d'Orsay

The topic of this paper is, on the one hand to introduce algebraic analysis results of Étienne Bézout (1730- 1783) not as we know them today but as he found them in his time, and on the other hand to emphasize his innovating viewpoints. We will be concerned with Bezout special way of reducing elimination for any degree systems to finding conditions for linear systems solutions, with his typical use of indeterminate coefficients that he doesn't compute but looks only for existence and number, with his idea to work on set of polynomials products sums, and with a very personal method to found two equations resultant.

Mots clés: Sylvester; Algebraic analysis; algebraic equations; algebraic geometry; Bezoutiant; elimination; determinant; indeterminate coefficients; linearity; Bézout; Cramer; Euler; Sylvester.

Domaines: Histoire et perspectives sur les mathématiques [math.HO]

Liliane Alfonsi. Étienne Bézout : Analyse algébrique au siècle des Lumières. Revue d'Histoire des Mathématiques, 2009, 14 (2008) (2), p. 211-287. ⟨hal-00425053⟩