Sur l'histoire des démonstrations analytiques du théorème fondamental de l'algèbre

The first proof of the fundamental theorem of algebra, proposed by D'Alembert in 1746 and practically unknown to this day, stimulated a series of “analytic” proofs which made essential use of the properties of polynomials as analytic functions and placed the theorem within complex analysis. One of the simplest and most widely known modern proofs is formed from the “analytic” proofs of Gauss, Argand, Legendre and Cauchy, which used and developed the ideas of D'Alembert.