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 CAVALIERI

468

CAVO

che e, quel che ha fatto, quel ohe vuole" (Rome, 1905); "Institutiones Iuris Publici Ecclesiastici" (Rome, 1906), in three volumes. S. Luzio.

Cavalieri, Bonaventura, Italian mathematician, b. at Milan in 1598; d. at Bologna, 3 December, 1647. At the age of fifteen he entered the Congregation of Hieronymites, or Jesuates. He taught theology for a time, but, as he showed a decided preference and talent for mathematics, his superiors sent him to the university at Pisa. Here lie studied under Castelli, and became one of the most illustrious of the disciples of Galileo. In 1629 he became professor of mathematics at Bologna, where he continued to teach until his death. He suffered many years from gout, and, like Pascal, sought relief from pain in mathe- matical researches. Cavalieri was one of the leading mathematicians of his time, and is celebrated for his "Method of Indivisibles", to which he was led by his investigations on the determination of areas and volumes. The principle was known to Kepler. Cavalieri published an account of his method in 1635 in his "Geometria indivisibilibus continuorum nova quadam ratione promota". It is an improve- ment over the method of exhaustions employed by the Greek mathematicians and was a forerunner of the integral calculus, which has since superseded it. In his "Geometria" he assumes that lines are made up of an infinite number of points, surfaces of an infinite number of lines, and solids of an infinite number of surfaces. This statement was attacked, especially by Guldinus, as being unscientific, and in 1647 in lus " Exercitationes Geometrical sex", Cavalieri endeavours to put it into better form, and answer the objections of his critics. In this work he also gives the first rigid demonstration of the theorem of Pappus, which Guldinus had redis- covered, though he was unable to give a statisfactory proof of it. A later edition of the "Geometria" appeared in 1653. Cavalieri did much to render common the use of logarithms in Italy. Besides the works already mentioned, he was the author of "Lo Specchio ustorio, ovvero trattato delle settioni coniche", 1632; "Directorium generale urano- metricum in quo trigonometriae logarithmicae funda- menta ac reguke demonstrantur", 1632; "'Rota planetaria", 1640; "Trigonometria plana et sphaerica linearis et logarithmica", 1635.

Ball, Hist, of Math. (London, 1S93); Cajori, Hist, of Math. (New York. 1894); Bwg. Univ.. VII; Frisi, Elogio di B. Cavalieri (Milan, 1829), I.

H. M. Brock.

Cavanagh, James, soldier, b. in County Tipperary, Ireland, 1831; d. in New York, 7 January, 1901. He emigrated to New York when he was sixteen years old and went to work as a carpenter. In 1852 he enlisted as a private in the Sixty-Ninth Regiment of the Militia, and was captain of Company C of the same command when it went to take part in the Civil War, 23 April, 1861. When the regiment returned after the battle of Bull Run and was reorganized as the Sixty-Ninth New York Volunteers of the Irish Brigade, he again went to the front as its major. In this rank he served during the campaigns of the Army of the Potomac, until the battle of Fredericks- burg, 13 December, 1862, when he was shot in the hip while leading the regiment in one of the charges up Marye's Heights. He was then discharged from the army because of the disabilities from his wound. When the State Militia was reorganized as the Na- tional Guard, In- rejoined the regiment and was made its lieutenant-colonel. In 1867 he was elected colonel, which command he held for more than twenty years. He received the brevet of brigadier- general, 10 January, 1893, the first time that rank was conferred on an officer of the New York State Militia, and in 1894 he retired, after a service of

forty-two years. For a number of years before his death he was attached to the New York Custom House as a special customs inspector.

Conyngham, The Irish Brigade and its Campaigns (Boston, 1869); The Irish American (New York), files; Michael Cavanagh, Memoirs of Gen. Thomas Francis Meagher (Wor- cester, 1892).

Thomas F. Meehan.

Cavazzi, Giovanni Antonio, of Montecucolo, a Capuchin friar of the province of Bologna, date of birth uncertain; d. at Genoa, 1692. In 1654 a band of friars was sent to the Congo to supply the place of those who had died or were incapacitated by sick- ness, and amongst the new-comers was Cavazzi. He suffered much on the long sea- voyage, yet his zeal was unabated when he landed in the Congo, where he laboured for many years with much spiritual fruit. Being invalided. home, he was summoned by the Propa- ganda to give an account of the mission, and from this he got the idea of setting down in writing his observations and experiences. He produced a volu- minous work, but had hardly finished it when he was again sent on the mission. The manuscript was entrusted by the superiors of the order to Fortu- nato da Bologna, who rewrote the book in more elegant style, and published it at Bologna in 1687 under the title "Istorica Descrizione de' Tre Regni Congo, Matamba et Angola". The work is profusely illustrated. In the "BibliothecaScriptorumOrdinis" Fortunato da Bologna is stated to have rewritten an already published work of Cavazzi, but the "Biblio- theca " seems in error on this point, as may be gathered from Fortunato's prefatory remarks.

Father Cuthbert.

Cavedoni, Celestino, an Italian ecclesiastic, archaeologist, and numismatist; b. 18 May, 1795, at Levizzano-Rangone, near Modena; d. 26 November, 1865, at Modena. He pursued his theological studies in the diocesan seminary, and from 1816 to 1821 distinguished himself in the study of archaeology and the Greek and Hebrew languages at the Univer- sity of Bologna. He was then appointed custodian of the Numismatical Museum of Modena, and received a position in the City Library, of which he became librarian in 1847. From 1830 to 1863 he held the chair of hermeneutics at the University of Modena. Cavedoni was, moreover, a corresponding member of the commission created by Napoleon III to edit the works of Count Bartolommeo Borghesi, to which collection he contributed numerous scientific notes. Among his numismatic works may be mentioned: " Saggio di osservazioni sulle medaglie di famiglie romane" (1829); "Carellii nummorum Italian Veteris tabulae" (Leipzig, 1850); " Numisniatica Biblica" (Modena, 1850; German tr. by Werlhof, Hanover, 1855-56). Cavedoni contributed numerous his- torical and archaeological papers to the "Annali" and the "Bullettino" of the Archaeological Institute of Rome and to other Italian publications. In re- ligious polemics he wrote a refutation of Renan's " Life of Jesus", which passed through four editions in several months: " Confutazione dei principali errori di Ernesto Renan nella sua Vie de Jesus" (Modena, 1863).

Bertadx, in La Grande Enciiclojn'dic. IX, 967; Horter, Nomenclator (Innsbruck 1S95), III, 1024-25.

N. A. Weber.

Cavellus, Hugo. See MacCaghwill, Hugo.

Cavo, Andres, a writer frequently quoted on Spanish-Mexican history; b. at Guadalajara in Mexico, 21 January, 1729. He entered the Society of Jesus, 14 January, 175S, and went to Italy with the other members of the order after their expulsion from Mexico in 1767. An important chronicle of events from the date of the conquest of Mexico (1521) to the year 1767, which Cavo wrote for the