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CAVALCANTI. 364 CAVALIEKI. was banished, so shattered liis health that, though recalled soon after, he died in August of the same year. Of Cavalcanti's poems two excel- lent critical editions have recently appeared: one edited by Arnone (Florence, 1881), the other by Krcole (Leghorn, 1885). Consult also Bartoli, tiluiia dclla letteratura italiana, Vol. IV. (Flor- ence, 1881). CAVALCASELLE, ka-vaVka-selia, Gio- YA.N.xi Battista (1820-97). An Italian art- historian, born iu Legnago, and e<hicated at the Academy of Venice, and in Padua, Milan, and Munich. He joined the Revolution of 1848, and after the reverses of 1849 was compelled to go into exile in England. There he wrote with J. A. Crowe an imjjortant vork on The EarJy Flemish Faintcrs (1857, 2d ed. 1872). lie also wrote ith Crowe a five-volume Ilistoiy of Painting in Italy (1804-71), from which the life of Titian was detached for the fourth centenary of the artist, and published as Tiziano, la sua vita ed i suoi tempi (1877). He was subsequently in- spector of the National Museum in Florence, and director-general of fine arts in Rome. His other publications include a volume on Raphael (1884). CAVALIER, kav'a-ler' (OF. cavalier, Fr. chevalier, from It. cavaliere, Sp. caballero, Med. Lat. cabellarius, horseman, knight, from Lat. cuhallus, horse, from the Celtic or Welsh caffyl, horse, Gael, ccipi//?, mare) . A horse-soldier. In English history, a name applied to tlie adherents of King Charles I. as opposed to 'Roundheads' (q.v.), or friends of the Parliament. CAVALIER. In fortification, a defense-work constructed ou the tcrre-plcin. or level ground of a bastion. See Foktuicatiox. CAVALIER, ka'va'lya', Jean (c.1680-1740) . The famous chief of the Camisards (q.v.). He was a native of Lower Languedoc, the son of a peasant, and was first a shejtherd, and afterwards a baker. He was driven from liome by the pitiless persecution of Protestants that followed upon the revocation of the Edict of Xantes, and took refuge in Geneva. When the persecution imder Louis XIV. drove the Protestants of the Cevennes to revolt, Cavalier returned in 1702 to his own coun- try, where lie became one of the leaders of the in- surrection, which broke out in .July of that year. Roland was put in chief command, but Cavalier soon rose to be his equal, and, tbough untrained in arms, he displayed extraordinary skill as well as courage. Although the 'Children of God,' as the insurgents were called, numbered at the most not more tlian 3000 men, they coped successfully with the far greater forces of the King, and ^ere never entirely conquered. After several conflicts, Cava- lier changed the seat of war to Vivarais, and on February 10, 1703, defeated the royal troops at Ardfche. A few days later he was himself defeated, but was successful in subse- quent encounters, invaded the region of the plains, and even threatened Ninies. In April, 1704, be was defeated by JIarshal Montrevel, but retreated with two-thirds of his forces. Mien ^larshal Vilbus was sent against the Camisards, Roland remained obdurate, but Cavalier agreed to treat, and received a colonel's commission and a pension, while his father and other Protestant prisoners were liberated. As this treaty did not secure general liberty of conscience, Cavalier was denounced as a traitor, and was so disheart- ened by his treatment evcrj^vhere that he left France for Switzerland, and from there passed to Holland, where he married. He then entered the service of England, became the head of a regiment of French refugees, and served with the English forces in Spain in 1705. After his return to England lie was made a major-general and Governiir of Jersey, and finally Governor of the Isle of Wiglit. He died at Chelsea in 1740. Cavalier ]>ublished in 1726 his Memoirs of the Wars of Ihc Ccvennes. CAVALIERI, kil'vii-lya'rf, Boxavextura F'rancesco (159S-IC47). An Italian mathemati- cian and astronomer. He was educated at Pisa, and was a pupil of Castelli. In 1029 he was made professor at Bologna, where he died. His chief contribution to mathematics is the method of indivisibles, first conceived in 1G29 aiul pub- lislied in 1035. This method forms a connecting link between the Greek method of exhaustions and the methods of Newton and Leibnitz. The basal idea of the method consists in considering a line as composed of a series of points (or small line-segments of equal length), a surface as com- posed of a series of adjacent lines (or strips of area of equal width), and a solid as composed of a series of planes (or laminiB of equal thickness). In general, however, a summation of sudi ele- ments, if they are finite (no matter how small), only appro.ximates, but does not equal, the length, area, or volume of a given magnitude. E.g. consider a triangle as composed of a series of very narrow rectangles constructed on its base; the sum of such elements will differ the less from the area of the triangle, the smaller the width of the rectangles; but as long as that width remains a finite quantity, the dilTerenee in area will, evidently, likewise remain finite. Never theless, with the aid of limits, the method may be used to deter- mine the ratio of the area of a given figure to that of an- other figure whose area is known. In fact, it was tints actually employed for measuring areas and volumes for more than lialf a century before the introduction of the integral calculus. For example, it was tised to prove the proposition that two solids ly- ing between two ))aranel planes, and such that the tw-o sections made by any plane parallel to the given planes are equal, are themselves equal ; as, for example, S and S' in the ac- companying Fig. 1. Such solids are called Cavalieri bodies. This forms one of the best bases for proving that the vohinie of a sphere is J T r» for, .as may be seen from Fig. 2, the area of the ring CD is easily shown to lie IT (r* — or"), and this is also easily shown to be the area of the circle AB. Hence the sphere and Fia. L ..- ,^ a ■Tr rnxt 7? FIO. 2.