CAUCHY, AUGUSTIN LOUIS. 



CAVAIGNAC, GENERAL. 



126 



than all tho rest of the poem, being a narrative of the desertion of 

 Ariadne by Theseus on the shores of Naxos, and having no reference ' 

 to or connection with the main story, into which it is introduced as a 

 description of the embroidery on the garment of Thetis. To this 

 criticism, which applies to the plan and not to the execution of the 

 poem, it may be observed that what editors and commentators have 

 thought fit to call the ' Epithalamium of Peleus and Thetis," is possi- 

 bly only part of a longer and unfinished work, intended by the author 

 to bear a different designation, or it is only the fragment of the entire 

 work which has come down to us. However that may be, the suffer- 

 ings of Ariadne, and her desertion of her father's house, form a fine 

 contrast with the chaste loves and the happy marriage of the parents 

 of Achilles, and her story may have been selected by the poet with a 

 view to produce that effect. 



The poems of Catullus are said to have been unknown to the 

 moderns till the beginning of tho 15th century, and that it was only 

 about 1425 that a copy, found in a granary, was first sent to the 

 native city of the author. The following are the most esteemed 

 editions of Catullus : Vossius, Lond. 1684, and Utr. 1691 ; Vulpius, 

 Patav. 1737; the 'Variorum* of Grsevius, with Tibullus and Proper- 

 tius, Utr. 1680 ; Mattaire's in 1715 ; in the ' Corpus Poetarum,' Lond. 

 1713; and Doering, Leipzig, 1788 and 1792, and Altona, 1834 ; and 

 Lachman, Berlin, 1829. The poems of Catullus have been translated 

 into English by Dr. Nott, 2 vols. 8vo, 1795, and by the Hon. George 

 Lamb, 2 vols. 12mo, 1821. 



(Catullus, Suetonius, Vulpius, Bayle, and the different commentators 

 and editors of Catullus.) 



CAUCHY, AUGUSTIN LOUIS, mathematician, was born at Paris, 

 21st of August, 1789. His father, Louis Francois, was a poet, and 

 became archiviate of the Chamber of Peers. The son was carefully and 

 religiously educated. In 1804, while at the ficoles Centrales, he was 

 crowned by the Institute as the pupil who had carried off moat prizes, 

 among which was the lirst in Latin poetry. In the following year he 

 entered the Ecole Polytechuique as second scholar, and in 1806, when 

 only in his seventeenth year, his solution of a difficult problem was 

 printed in the ' Corre.-pondance ' of the school. 



From the Ecole Polytechnique, where he rose to the first place, 

 M. Cauchy entered that of the Fonts et Chaussces, maintaining the 

 same position. He was afterwards appointed engineer of the works 

 for the port of Cherbourg ; and from this date commences his long 

 series of mathematical researches in questions previously unsolved. 



, priori le nomhre ues racines ruelles nog; 

 degrd quelconque,' which was followed by papers on the properties of 

 integrals, taking up questions started by Cluiraut. In 1815 he received 

 the grand mathematical and physical prize of the Institute for his 

 paper ' Sur hi Thdorie des Ondes,' which became the basis of a theory 

 of light 



In 1816 Caucby was elected a member of the Academy of Sciences, 

 and was appointed professor of mechanics in the Ecolc 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: 'Courg d' Analyse,' 1821; 'Lecons sur le Calcul diffdreu- 

 tiel,' 1826; 'Lecons sur lea Applications du Calcul infinitesimal a la 

 Geometric,' 2 vols. 4to, 1826-28. At the same time he continued his 

 valuable series of papers for the Academy, among which are ' Sur les 

 Intdgrales ddGnics entre les Limites Imaginaires,' 1825; 'Sur 1' Appli- 

 cation du Calcul des Residus a la solution des Problemes de Physique 

 Matbdmatique,' 1827 ; ' Sur la Resolution d'fiquatious numdriques, et 

 ur la Throne de 1' Elimination,' 1829 ; 'Sur la Thdorie des Nombres,' 

 and others. The last was presented in May 1880. The revolution 

 which followed deprived M. Cauchy of hii 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 Due de Bordeaux, who then resided at Prague ; and he cheerfully 

 devoted himself to the task. While thus engaged lie resumed in 1835 

 the publication of his ' Exercises de Mathdmatiques," which had been 

 for some years interrupted. In 1836 he published his ' Mdinoire sur 

 la 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 superior class of professors in the interests of legitimacy. 

 Ho 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 allegiance. 



Cauchy'ii diligence appears to have increased with his years. The 

 number and nature of his communications to the Academy may best 

 be judged of by reference to the ' C'omptes Rendus;' at one time they 

 became HO multiplied that their publication overstrained the Academy's 

 funds. Concurrently he wrote papers which appeared in other scien- 

 tific periodicals, chiefly in Liouville's 'Journal de Mathdmatiques," 



among which his ' Note sur le ddveloppemeut des fonctions en series 

 ordonndes suivaut les puissances ascendantes des Variables,' published 

 in 1846, is especially remarkable. 



In 1S43 a professorship of mathematical astronomy having been 

 created at the Faculty of Sciences of Paris, M. 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 'Resumds 

 Aualytiques,' 4to. In 1836 appeared 'Sur la Thdorie de la Lumiere,' 

 8vo ; ' Sur la Mdcanique celeste," &c., 8vo, in 1831 and a largo 

 number of others in the 'Mdmpires ' of the Academy, in the ' Annales 

 de Mathdmatiques,' 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. lu 1834 one of his poems ' Charles 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. 



* CAVAIGNAC, GENERAL LOUIS EUGENE, son of Jeau-Baptisto 

 Cavaiguac, member of the Convention and of the council of the Five 

 Hundred, and brother of the late Godefroy Cavaiguac, repeatedly 

 prosecuted by Louis Philippe, was born at Paris on the 15th of 

 December 1802. In 1820, at the age of eighteen, he entered the Kcole 

 Polytechnique. In the years 1828-29 he served in the second regiment 

 of Engineers as captain, and took an active part in the campaigns of 

 the Morea. Like most of the sons of the noted republicans of the 

 Great Revolution, he adopted early in life the principles of his father ; 

 he was consequently one of the first to adhere to the revolution of 

 July, in 1830. But the free expression of his opinions having given 

 offence to his superiors, he was sent in 1832 to join the army in Africa. 

 Even there he could not control or conceal his republican opinions ; 

 but the brilliant courage he displayed, and the services he rendered, 

 drew upon him the notice and the esteem of his commanding officers. 

 Ho was employed in the expeditions of Hedeyah, Bouffard, and 

 Chirchell ; and in the several battles and skirmishes of Ouara, Col 

 de Moozaia, &c., he gave proofs of that aptitude for war, which bespoke 

 the future general. But it was especially in the expedition against 

 Tlemseu that he proved his capacity, and evinced his valour. 



After the capture of Tlemsen, in January 1836, Marshal Clausel 

 formed a battalion of volunteers to garrison the citadel of that town ; 

 and gave the command of the place to Captain Cavaignac. In this 

 isolated position, he maintained himself with great honour. Although 

 frequently attacked by the Arabs, and blockaded by Abd-el-Kader, 

 he held out, teaching his troops, both by his example and intrepidity, 

 to endure the severest privations without a murmur. It was not 

 however till May 1837 that he received further promotion. Shortly 

 after the taking of Cuii stun tine, Cavaignac was transferred to tbi 

 Zouaves ; after which he had a battalion in the infantry of the hue. 

 In 1839 he published a work of considerable value, entitled 'De la 

 Rdgence d'Alger." 



Although his health and constitution were at all times delicate, 

 Cavaiguac sustained with unfaltering resignation the trials and fatigues 

 of a camp life ; being remarked as constantly the first to meet tho 

 enemy, and the last to retire to his tent. At the same time his 

 qualifications for providing resources and administering them when 

 found, were of a high order. Having returned to the corps of Zouaves, 

 as lieutenant-colonel, on the 21st of June 1840, he was created colonel 

 the following year ; but a short time before the battle of Isly, he 

 joined the 32nd of the line. It was in the capacity of commander of 

 the van-guard, in this memorable action, that he so ably supported 

 General Bugeaud against the army of Marocco. For hia behaviour in 

 this battle he was made mardchal de camp on the 16th of September 

 1844. After suppressing several revolts among the tribes on tho 

 western frontier in 1845, he invaded Marocco in February 1846, at 

 the head of 6000 men, driving before him the redoubtable Emir 

 Abd-el-Kader. 



In 1847 he succeeded Lamoriciore in the government of Oran, 

 and on the 24th of February 1848, he received his appointment as 

 governor-general of Algeria, by a decree from the Provisional Govern- 

 ment. Two months after this, Lamartiue, having foreseen the im- 

 pending dangers by which France was threatened, invited Cavaignao 

 to the capital. His great ability, and his decision in quelling the 

 insurrection of June, established his character both as a citizen and as 

 a soldier. It was by far the most serious revolt which had occurred 

 since 1789. Cavaiguac met the threatened danger with promptitude. 

 A force of 75,000 regulars and nearly 200,000 National Guards was 



