“ 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 valuable as those of S. D. Poisson. His collected works, Œuvres complètes d’Augustin Cauchy, have been published in 27 volumes. ”

“ He obtained an appointment at the École Polytechnique, which, however, he relinquished in 1830 on the accession of Louis Philippe, finding it impossible to take the necessary oaths. A short sojourn at Freiburg in Switzerland was followed by his appointment in 1831 to the newly-created chair of mathematical physics at the university of Turin. In 1833 the deposed king Charles X. summoned him to be tutor to his grandson, the duke of Bordeaux, an appointment which enabled Cauchy to travel and thereby become acquainted with the favourable impression which his investigations had made. ”

“ He clarified the principles of the calculus by developing them with the aid of limits and continuity, and was the first to prove Taylor’s theorem rigorously, establishing his well-known form of the remainder. ”