CAVALIERI, BONAVENTURA Italian mathematician, was born at Milan; his name also occurs in the forms Cavallieri, Cavaglieri, Cavalerius, and de Cavalerris. He became a Jesuit at an early age and later was inspired to study mathematics by reading a copy of Euclid. On the recommenda tion of his Order he was made a professor at Bologna in 1629; the post, which he held until he died, was renewed periodically. In 163 5 Cavalieri wrote Geometria indivisibilium continuorum nova quadam ratione promota, in which he first stated his principle of indivisibles. The form of the principle was unsatisfactory and was attacked by Guldin. In reply to this attack Cavalieri wrote Exercitationes geometricae sex (1647), stating the principle in the more satisfactory form in which it was used by i 7th century mathematicians. This work also contained the first rigid proof of Guldin's theorem relating to the volume of a solid of revolution. The theorem had occurred in the writings of Pappus and had been used in an unsatisfactory fashion by Kepler. Using the prin ciple of indivisibles as a sort of integral calculus, Cavalieri solved a number of problems proposed by Kepler. Other books by Cavalieri are : Lo specchio ustorio ovvero trattato delle settioni coniche (1632), Directorium generale uranometricum, in quo trigonometriae logaritlemicae fundamenta ac regula demonstrantur (163 2) and Trigonometria plana et spliaerica (1643) . Cavalieri died at Bologna on Dec. 3, 1647.
The life of Cavalieri has been written by P. Frisi (Milan, 1776), and by F. Predari (Milan, 1843) .