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