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 CAUBERT

457

CAUCHY

faro seems to have been a republic; as early as 1178 its coins appear, bearing the image of St. Trypho. Later on it passed successively under Byzantine and Servian rule, and in 1368 formed an alliance with Kins Louis of Hungary. Having sided with the Genoese against the Venetians, it was captured and burned by the latter (1378). In 1423 Cattaro volun- tarily submitted to Venice, though retaining a cer- tain autonomy. The long rule of Venice is reflected in the architecture of the town. During the Napo- leonic period it passed successively into the hands of the Austrian*, the French, the Russians, the French,

and the Montenegrins, who sacked it after the depart- ure of the French (1814). It then fell under Aus- trian rule, and is now a seaport of the Austro- Hungarian Monarchy, and the commercial outlet of Montenegro. Situated as it was, Cattaro must have received the Gospel at an early period, according to legend from St. Boimus. The list of bishops, how- ever, does not go farther back than 877. The Catho- lic population of the diocese is 13,363, the non- Catholic, 15,000. There are 19 parishes, 11 vicari- ates, .50 secular and 12 regular priests.

Faruti, lUur.mcr. (1800) VI, 421-518; Giurovich. Palrio- logia d- <; <r. di Botche di ( 'attaro (Venice,

1844); Valentinki.i.i, Hiblinth. Dalmaziana (1855), 242-53; Ann. pont. cath. (1907), 321.

U. Benigni.

Caubert, Jean. See Commune, Martyrs of the Paris.

Cauchy, Augusttn-Louis, French mathematician,

b. at Pari-;. Ill August, 1789; d. at Sceaux, 23 May. 1857. He owed his early training to his father, a man of much learning and literary taste, and. at the sug- gestion of La Grange, who early detected his talents and took a lively interest in him, he received a good classical education at the Eeole Centrale du Pan- in Paris. In ISD.'i he entered the Ecole Poly- technique, where he distinguished himself in mathe matics. Two years later he entered the Ecole des Ponts et Chaussees and, alter a brilliant course of study, he was appointed one of the engineers in charge of the extensive public works inaugurated by N^apoleon at Cherbourg. While here he devoted boa

leisure moments to mathematics. Several important memoirs from his pen, among them those relating to the theory of polyhedra, symmetrical functions, and particularly his proof of a theorem of Fermat which had bafHed mathematicians like Gauss and Euler, made him known to the scientific world and won him admittance into the Academy of Sciences. At about the same time the Grand Prix offered by the Academy was bestowed on him for his essays on the propagation of waves. After a sojourn of three

years at Cherbourg bis health began to fail, and he resigned his post to begin at the age of twenty-two his career of professor at the Ecole Polytechiiique. In 1818 he married Mile, de Bure, who, with two daughters, survived him.

Cauchy was a stanch adherent of the Bourbons and after the Revolution of 1830 followed Charles \ into exile. After a brief stay at Turin, where he oc- cupied the chair of mathematical physics created for him at the university, he was invited to become one of the tutors of the young Due de Bordeaux, grandson of Charles, at Prague. The old monarch conferred the title of baron upon him in recognition of his ser- vices. He returned to France in 1838, and was pro- posed by the Academy for a vacant chair at the Col- lege de France. His conscientious refusal to take the requisite oath on account of his devotion to the prince prevented his appointment. His nomination to the Bureau des Longitudes was declared void for the same reason. After the Revolution of 1848, how- ever, he received a professorship at the Sorbonne. Upon the establishment of the Second Empire the oath was reinstated, but an exception was made by Napoleon III in the cases of Cauchy and Arago, and he was thus free to continue his lectures. He spent tin' last years of his life at Sceaux, outside of Paris, devoting himself to his mathematical researches until the end.

Cauchy was an admirable type of the true Catholic savant. A great and indefatigable mathematician, he was at the same time a loyal and devoted son of the Church. He made public profession of his faith and found his greatest pleasure and recreation in works of zeal and charity. He was an active member of the Society of St, Vincent de Paul, and took a leading part in founding the " Ecoles d'< Irienl " in L856, and the "Association pour la liberie du dimanche". During the famine of 1816 in Ireland Cauchy made an appeal to the pope on behalf of the stricken people. He was on terms of intimate friendship with Pere de Ravignan, S. .1., the well-known preacher, and when, during the reign oi Louis-Philippe, the colleges of the Society of Jesus were attacked he wrote two me- moirs in their defence. Cauchy is best known for his achievements in the domain" of mathematics, to almost every branch of which he made numerous and important contributions. He was a prolific writer and, besides his larger works, he was the author of over seven hundred memoirs, papers, etc., published chiefly in the "Comptes Etendus". A complete edi- tion of his works has been issued by the French Gov- ernment under the auspices of tin- Academy of Sciences. Among his researches may be mentioned his development of the theory of series in which he established rides for investigating their convergency. To him is due the demonstration of the existence and number of real and imaginary roots of any equation, and he did much to bring determinant 3 into general use. In connexion with his work on definite integrals, his treatment of imaginary limits deserves special men- tion. He was the first to give a rigid proof of Taylor's theorem. The "Calculus of Residues" was his in- vention, and he made important n searches in the theory of functions. By hi 'inuity

of functions and the method of hunt- he placed the differential calculus on a logical basis. Cauchy was also a pioneer in extending the applications of n matics to physical i cially to molecular

mechanics, optics, and astronomy. In the theory of dispersion we have Ins well-known formula giving the refractive index in terms ,,f the wave length and three constants. Besides hi- qui irs, he

was the author of "Couts d 'analyse de I'Ecole royale polytechnique" (1821 : 'Resumi di lecom donnees tei 1 1 ii H pie sur les applications du calcul infinitesimal" (1823) : " Lecons sur les applica- tions du calcul infinitesimal a la gcomeirie" (1826,