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Mathematical Treasure: Torricelli’s Geometry

Author(s): 
Frank J. Swetz (The Pennsylvania State University)

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.

Title page from Torricelli's 1644 treatise on geometry.

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?

Page 43 from Torricelli's 1644 treatise on geometry.

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.

Page 95 from Torricelli's 1644 treatise on geometry.

In the Appendix, Torricelli explored properties of the cycloid.

Appendix page 86 from Torricelli's 1644 treatise on geometry.

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

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Torricelli’s Geometry," Convergence (July 2016)

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