Mathematical Treasure: Torricelli’s Geometry

Evangelista Torricelli (1608-1647) was an Italian mathematician and physicist and a strong supporter of Galileo’s theories. His Opera geometrica Evangelistae Torricelli: De solidis sphaeralibus. De motu. De dimensione paraboae. De solido hyperbolico. Cum appendicibus de cycloid & cochlea (1644) demonstrated the prevailing spirit of exploring applications of geometry. In this work Torricelli examined the dynamic properties of the sphere, paraboloid, hyperboloid, and cycloid.

On page 43, Torricelli compared the volume of a paraboloid with that of its circumscribed right cylinder and that of a cone of the same height. How are the volumes related?

On page 95, Torricelli determined that, given a circle, if a right triangle is formed with the circle’s radius as height and the circumference as base, then the area of this triangle will equal the area of the given circle.

In the Appendix, Torricelli explored properties of the cycloid.

The images above are presented courtesy of the University of Pennsylvania Libraries.

Index to Mathematical Treasures