Definitions

Francesco Bonaventura Cavalieri

[kav-uhl-yair-ee; It. kah-vah-lye-ree]
Cavalieri, Francesco Bonaventura, 1598-1647, Italian mathematician, a Jesuit priest. Professor at Bologna from 1629, he invented the method of indivisibles (1635) that foreshadowed integral calculus.
Bonaventura Francesco Cavalieri (in Latin, Cavalerius) (1598 - November 30, 1647) was an Italian mathematician known for Cavalieri's principle, which states that the volumes of two objects are equal if the areas of their corresponding cross-sections are in all cases equal. Two cross-sections correspond if they are intersections of the body with planes equidistant from a chosen base plane. The principle was originally discussed by the 3rd century Chinese mathematician Liu Hui in his commentary on The Nine Chapters on the Mathematical Art. Cavalieri developed a "method of the indivisibles," which he used to determine areas and volumes. It was a significant step on the way to modern infinitesimal calculus ().

Life

Born in Milan, Cavalieri studied theology in the monastery of San Gerolamo in Milan and geometry at the University of Pisa. He published eleven books, his first being published in 1632. He worked on the problems of optics and motion. His astronomical and astrological work remained marginal to these main interests, though his last book, Trattato della ruota planetaria perpetua (1646), was dedicated to the former. He was introduced to Galileo through academic and ecclesiastical contacts. Cavalieri would write at least 112 letters to Galileo. Galileo said of Cavalieri, "few, if any, since Archimedes, have delved as far and as deep into the science of geometry."

Galileo exerted a strong influence on Cavalieri encouraging him to work on his new method and suggesting fruitful ideas. Building on the classic method of exhaustion, Cavalieri developed a geometrical approach to calculus and published a treatise on the topic, Geometria indivisibilibus continuorum nova quadam ratione promota (Geometry, developed by a new method through the indivisibles of the continua, 1635). In this work, an area is considered as constituted by an indefinite number of parallel segments and a volume as constituted by an indefinite number of parallel planar areas. Such elements are called indivisibles respectively of area and volume and provide the building blocks of Cavalieri's method.

Cavalieri also constructed a hydraulic pump for his monastery and published tables of logarithms, emphasizing their practical use in the fields of astronomy and geography. He died at Bologna.

The lunar crater Cavalerius is named for the Latin name of Bonaventura Cavalieri.