BARON AUGUSTIN

See also:

• LOUIS
• LOUIS (804–876)
• LOUIS (893–911)
• LOUIS, JOSEPH DOMINIQUE, BARON (1755-1837)
• LOUIS, or LEWIS (from the Frankish Chlodowich, Chlodwig, Latinized as Chlodowius, Lodhuwicus, Lodhuvicus, whence-in the Strassburg oath of 842-0. Fr. Lodhuwigs, then Chlovis, Loys and later Louis, whence Span. Luiz and—through the Angevin kings—Hungarian

LOUIS

See also:

• BARON AUGUSTIN LOUIS CAUCHY (1789-1857)

CAUCHY (1789-1857)  , French mathematician, was born at Paris on the 21st of August 1789, and died at Sceaux (Seine) on the 23rd of May 1857 . Having received his early education from his father Louis Francois Cauchy (176o-1848), who held several minor public appointments and counted Lagrange and Laplace among his friends, Cauchy entered Ecole Centrale du Pantheon in 1802, and proceeded to the Ecole Polytechnique in 18o5, and to the Ecole des Ponts et Chaussees in 1807 . Having adopted the profession of an engineer, he left Paris for Cherbourg in 181o, but returned in 1813 on account of his health, whereupon Lagrange and Laplace persuaded him to renounce engineering and to devote himself to mathematics . He obtained an appointment at the Ecole 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 . Charles created him a baron in return for his services . Returning to Paris in 1838, he refused a proffered chair at the College de France, but in 1848, the oath having been suspended, he resumed his post at the $tole Polytechnique, and when the oath was reinstituted after the coup d'etat of 1851, Cauchy and Arago were exempted from it . A profound mathematician, Cauchy exercised by his perspicuous and rigorous methods a great influence over his contemporaries and successors . His writings cover the entire range of mathematics and mathematical physics . Cauchy had two brothers: ALEXANDRE LAURENT (1792-1857), who became a president of a division of the court of appeal in 1847, and .a judge of the court of cassation in 1849; and EUGENE FRANCOIS (1802-1877), a publicist who also wrote several mathematical works . 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, his generalization of Euler's theorem on polyhedra in 1811, and in several other elegant problems .

More important is his memoir on

wave-propagation which obtained the Grand Prix of the Institut in 1816 . His greatest contributions to mathematical science are enveloped in the rigorous methods which he introduced . These are mainly embodied in his three great treatises, Cours d'analyse de l'Ecole Polytechnique (1821); Le Calcul infinitesimal (1823) ; Lecons sur les applications du'calcul infinitesimal d la geometrie (1826–1828) ; and also In his courses of mechanics (for the Ecole Polytechnique), higher algebra (for the Faculte de Sciences), and of mathematical physics (for the College de France) His treatises and contributions to scientific journals (tto the numbei of 789) contain investigations on the theory of series (where he developed with perspicuous skill the notion of convergency), on thr theory of numbers and complex quantities, the theory of groups and substitutions, the theory of functions, differential equations and determinants . 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 . 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, (Euvres completes d'Augustin Cauchy, have been published in 27 volumes . See C . A .

Valson, Le Baron Augustin Cauchy: sa

vie et ses travaux (Paris, 1868) .