Mathematical Treasures - Cavalieri's Geometry of Indivisibles

Bonaventura Cavalieri (1598–1647) was an Italian Jesuit priest who eventually became Professor of Mathematics at the University of Bologna. In 1653, a printing of his 1635 Geometria indivisibilibus continuorum, in which he extended Archimedes’ method of exhaustion, appeared. Cavalieri stated that any two solids with the same height and equal cross-sectional areas at any point will be equal in volume. This concept became known as “Cavalieri’s Principle”; however, in China it had been realized and used in the 6th century. The title page of Geometria indivisibilibus is shown above.

Pages 86 and 87 state Theorems XLI through XLIII dealing with the volumes of “spheroides” and “conoides”.

These images from its George Arthur Plimpton Collection are presented through the courtesy of the Columbia University Libraries.

Index to Mathematical Treasures