CAUCHY, AUGUSTIN LOUIS, mathematician, was born at Paris, 21st of August, 1789. His father, Louis Francois, was a poet, and became archiviste of the Chamber of Peers. The son was carefully and religiously educated. In 1804, while at the Scales Centrales, he was crowned by the Institute as the pupil who had carried off most prizes, among which was the first in Latin poetry. In the following year he entered the Peale Polytechnique as second scholar, and iu 1806, when only in his seventeenth year, his solution of a difficult problem was printed in the Correspondence' of the school.
From the Ecole Polytechnique, where be rose to the first place, 31. Cauchy entered that of the Ponta et Chaussdea, maintaining the same position. He was afterwards appointed engineer of the works for the port of Cherbourg; and from this data commences his long series of mathematical researches in questions previously unsolved. Among the first was his demonstration of Euclid's celebrated theorem on the polyedra. In 1813 ha published his 316thode pour d6terminer it prion le nombre des ravines rtelles n6gatives dune extraction d'un degrd quelconque,' which was followed by papers on the properties of integrals, taking up questions started by Clairaut. In 1815 he received the grand mathematical and physical prize of the Institute for his paper Sur in Thdorie des Ondes,' which became the basis of a theory of light.
In 1816 Cauchy was elected a member of the Academy of Sciences, and was appointed professor of mechanics in the Ecole Polytechnique, and in the same year he published his demonstration of Fermat's theorem of the polygonal numbers. His lectures had a most salutary influence on the educational results of the school, and the progress of his pupils was materially aided by the works which he successively published : ' Cours d'Analyee,' 1821; Lecona sur In Calcul diffdrens tiel,' 1826; Lecons sur les Applications du Calcul infinitesimal it la Gdometrie,' 2 vole. 9to, 1826-28. At the same time he continued his valuable series of papers for the Academy, among which are 'Sur les Ietdgrales ddfinics entre les Limites Imagmairee ' 1825; 'Sur rAppli cation du Calcul des Residua it la solution des Problemes de Physique Math6matique; 1827; Sur la Rdsolutiou d'Equations nunadriquee, et sur la Thdorie de rElimination; 1829 ; 'Sur la Thdorie des Nombres,' and others. The last was presented in May 1830. The revolution which followed deprived M. Cauchy of his public employment, as his loyalty to the Bourbon dynasty prevented his taking the oath of allegiance to the government of Louis Philippe. Under these circum stances he accepted the offers of the King of Sardinia, who invited him to deliver a course of physico-mathematical lectures at the univer sity of Turin. In 1832 the Royal Society of London elected Cauchy one of their fifty foreign members. In the following year he received an invitation from Charles X. to undertake the scientific education of the Duc de Bordeaux, who then resided at Prague ;' and he cheerfully devoted himself to the task. While thus engaged ho resumed in 1835
the publication of his ' Exercises de Math6matiques,' which had been for some years interrupted. In 1836 he published his 316moiro sur in Dispersion de la Lumiere.' In 1838, having terminated his work of instruction, he returned to Paris, and took part in a scheme for training a euperior class of professors in the interests of legitimacy. He was chosen a member of the Bureau des Longitudes in 1839, but the minister refused to sanction the choice, remembering the refusal to take the oath of allegianco.
Cauchy's diligence appears to have increased with his years. The number and nature of his communications to the Academy may beet be judged of by reference to the Comptes Rendus ;' at one time they became so multiplied that their publication overstrained the Academy's fonds. Concurrently he wrote papers which appeared in other scien tific periodicals, chiefly in Liouville's 'Journal de Math6matiques,' among which his Note sur le ddveloppement des fonctions en thins ordonnees suivant les puiseances aseendantes des Variables,' published in 1846, is especially remarkable.
In 1848 a professorship of mathematical astronomy having been created at the Faculty of Sciences of Paris, 31. Cauchy was ap pointed to the chair; but, as had happened eighteen years before, his refusal to take the oath required in 1852, again lost him his public employments. He has since continued his studies; adding every month to the number of his works. He has treated of the higher branches of algebra, the theory of numbers, the infinitesimal calculus, mechanics, astronomy, and physics, exploring indeed every branch of mathematical analysis. Of him it has been said that he has "thrown back the limits of the integral calculus ; and if showing a preference for abstract questions, he has on the other hand rendered important service to the elementary portions of science, by simplifying the theory of asymptotes, introducing the use of limits in all parts of geometry, and by giving an elegant demonstration of the fundamental theorem of the theory of equations." M. Cauchy is a member of several scientific societies. Besides the works above mentioned, he published at Turin his 'Rasura& Analytiques,' 4to. In 1836 appeared 'Sur la Thdorie de la Lurniere,' 8vo; 'Sur la 31deanique celeste,' &c., 8vo, iu 1831—and a largo number of others iu tho '3Iempires ' of the Academy, in the 'Annales de Mathdmatiquee; and other scientific journals. He has shown too, that he inherits his father's poetical ability and lively imagination, and relieves at times his severer studies by the composition of French and Latin poetry. In 1834 one of his poems ' Chance V. en Espagne ' was published, which has much merit, and exhibits the monarchical predilections and religious opinions which have actuated the whole life of the author.