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Mathematical Treasures - Bettini's Aerarium Philosophiae Mathematicae

Frank J. Swetz and Victor J. Katz


Bettini Title Page

This is the title page of Mario Bettini’s Aerarium Philosophiae Mathematicae [Treasury of Mathematics], published in 1648. Bettini (1582 - 1657) was a Jesuit, a mathematician and a well respected astronomer. This book is an encyclopedic collection of mathematical curiosities.

Bettini frontispiece

The frontispiece of Bettini’s book. The picture is a pun on the title, The Treasury of Mathematics. The picture shows a Prince providing a Jesuit with a chest of money. The Jesuits are thus paid to provide the common people with knowledge of mathematics.

Bettini sun


Pages 48 and 49 of Bettini’s Treasury discuss the generation of a spiral as a path around the surface of a cylinder. The diagram on page 49 shows that if a spiral is unrolled from its cylinder it will revert into the hypotenuse of a right triangle.


Bettini sun

Pages 74 and 75 of Bettini’s book illustrate the erroneous use of simple geometry in determining the diameter of the sun.


Platonic solids

A fold-out plate from Bettini’s book provides views of various solids and nets for the construction of polyhedra.

Index to Mathematical Treasures

Frank J. Swetz and Victor J. Katz, "Mathematical Treasures - Bettini's Aerarium Philosophiae Mathematicae," Convergence (January 2011)

Mathematical Treasures from the Smith and Plimpton Collections at Columbia University