D'ALEMBERT, JEAN LE ROND. - D'ALEMBERT'S THEOREM - THE FUNDAMENTAL THEOREM OF ALGEBRA.

Recherches sur le Calcul Intégral. Premier - (Seconde) Partie. (+) Suite des Recherches sur le Calcul Intégral. (= Troisieme Partie). (+) Additons aux Recherches sur le Calcul Integral. (+) Errata pour les Mémoires, imprimés dans les Volumes de 1746, 1747, & 1748. (All three Memoires).

Berlin, Haude et Spener, 1848-52. 4to. No wrappers as extracted from "Mémoires de l'Academie Royale des Sciences et Belles-Lettres", tome II (1846), tome IV, tome VI a. tome VI. Pp. 182-224, pp. 249-291, pp. (361-) 378, pp. 413-416 and 1 folded engraved plate.

First apperance of d'Alembert's 3 importent papers on the Calculus of Integration, a branch of mathematical science which is greatly indepted to him. He here gives the proof of THE FUNDAMENTAL THEOREM OF ALGEBRA, called d'Alembert's theorem, and later corrected by Gauss (1799).

The theorem is based on these three assumptions:
Every polynomial with real coefficients which is of odd order has a real root. (This is a corollary of the intermediate value theorem.
Every second order polynomial with complex coefficients has two complex roots.
For every polynomial p with real coefficients, there exists a field E in which the polynomial may be factored into linear terms.

Also with an importent paper by Leonhard Euler "Mémoire sur l'Effet de la Propagation successive de la Lumiere dans l'Apparition tant des Planetes que des Cometes" (Memoir on the effect of the successive propogation of light in the appeareance of both comets and planets). Pp. 141-181 and 2 folded engraved plates. - The paper is founded on Euler's theory of light as waves and not as particles. It is from the same year as his fundamental work on light as waves: "Nova Theoria" - Enestroem E 104.

Order-nr.: 46603