CAUCHY, AUGUSTIN LOUIS, BARON French mathematician, was born in Paris, on Aug. 21, 1789, and died at Sceaux (Seine) on May 23, 1857. He studied at the Ecole Polytechnique and the Ecole des Ponts et Chaussees, and practised for some time as an engineer. His health failed in 1813, and his father's friends, Lagrange and Laplace, persuaded him to devote himself entirely to mathematics. From 1816 onwards he held three professorships in Paris, which he lost at the revolution of 183o, on declining to swear allegiance to Louis Philippe. A chair of mathematical physics was created for him at the University of Turin. He spent some time travelling with the duke of Bordeaux, grandson of Charles X., and in 1838 returned to France, resuming his chair at the Ecole Polytechnique.
The genius of Cauchy was promised in his simple solution of the problem of Apollonius; i.e., to describe a circle touching three given circles, which he discovered in 1805, and in his generalization of Euler's theorem on polyhedra in 1811, etc. More important is his memoir on wave-propagation which obtained the grand prix of the Institut in 1816. His greatest contributions to mathematical science characterized by the clear and rigorous methods which he introduced and are mainly embodied in his three great treatises, Cours d'analyse de l'Ecole Polytechnique (1821) ; Le Calcul in initesimal (1823) ; Lecons sur les applications du calcul in finitesimal a la geometrie (1826-28). He clarified the principles of the calculus by developing them with the aid of limits and con tinuity, and was the first to prove Taylor's theorem rigorously, establishing his well-known form of the remainder. In mechanics, he made many researches, substituting the notion of the continuity of geometrical displacements for the principle of the continuity of matter. In optics, he developed the wave theory, and his name is associated with the simple dispersion formula. In elasticity, he originated the theory of stress, and his results are nearly as valu able as those of S. D. Poisson. His collected works, .uvres com pletes d'Augustin Cauchy, have been published in 27 volumes. See C. A. Valson, Le Baron Augustin Cauchy: sa vie et ses travaux (i868).