*Cavalieri*, BONAVENTURA, Italian mathematician, b. at Milan in 1598; d. at Bologna, December 3, 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 he 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 mathematical 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 ration promota”. It is an improvement 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of exhaustions employed by the Greek mathematicians and was a forerunner of the integral calculus, which has since superseded it.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 his “Exercitationes Geometricae sex”, Cavalieri endeavors 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 rediscovered, 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 uranometricum in quo trigonometriae logarithmicae fundaments ac regulae demonstrantur”, 1632; “Rota planetaria”, 1640; “Trigonometria plane et spin:erica linearis et logarithmica”, 1635.

H. M. BROCK