Cavalleri, Bonaventura

, an eminent Italian mathematician, was born at Milan in 1593, and entered at an early age into the order of Jesuates or Hieronymites. In the course of his studies he manifested such talents, that his superiors, after he had taken orders, thought proper to send him to the university of Pisa, a circumstance to which, though at first against his will, he owed the celebrity which he afterwards acquired. Here, with the advice of Benedict Castelli, the disciple and friend of Galileo, he applied to the study of geometry, in order to relieve the pains of the gout to which he was subject; and in this science he made such progress, and acquired such an accurate acquaintance with the ancient geometers, that Castelli and Galileo concurred in predicting the eminence at which he afterwards arrived. Soon after this period he invented his method of indivisibles. In 1629 he communicated to some ingenious persons and to the magistrates of Bologna, his treatise of indivisibles, and another on the conic sections; and obtained the honour of succeeding Maginus as professor in the university, in 1629. His celebrated work on indivisibles, entitled, “Geometria Indivisibilibus continuorum nova quadam ratione prornota,” and published at Bologna in 1635, 4to? and again in 1653, is a curious original work, in which the author conceives the geometrical figures as resolved into their very small elements, or as made up of an infinite number of infinitely small parts, and on account of which he passes in Italy for the inventor of the infinitesimal calculus. He also published a treatise of conic sections, under the title of “La Spechio Ustorio overo Trattato delle Settioni Coniche,” or “De Speculo Ustorio, &c.” Bologn. 1632, 4to; a system of trigonometry under the title of “Directorium generale Uranometricum,” 1632, 4to, including an account of logarithms, together with tables of the logarithms of common numbers and trigonometrical tables of natural sines, and logarithmic sines, tangents, fluents, and versed sines; of which a new and enlarged edition was published at Bologna in 1643, 4to, entitled “Trigonometria Plana. ac Sphaerica, Linearis ac Logarithmica, &c.” a “Compendium Regularum de Triangulis; and a” Centuria Problematum Astronomicorum.“He was also the author of a treatise of astrology, entitled” Rota Planetaria,“and published under the appellation of Sylvius Philomantius; and this publication was the more surprising, as he was an enemy of judicial astrology. The last of his works was | entitled” Fxercitationes Geometricae sex," Bonon. 1647, 4to, and contains exercises on the method of indivisibles; answers to the objections ofGuldinus; the use of indivisibles in cossic powers, or algebra, and in considerations about gravity: with a miscellaneous collection of problems. Towards the close of this year, 1647, he died a martyr to the gout, which had deprived him of the use of his fingers. ¹