Mathematical Treasure: Galileo’s Two New Sciences

Galileo’s Discoursi e demnostrezioni matematiche intorno a due nuoue scienze (Discourses and Mathematical Demonstrations Concerning Two New Sciences) of 1638 presented some of his experimental findings in statics and dynamics to a larger audience. The title page for this historic work is shown here.

On this page Galileo discussed the motion of a rotating rigid body. A point near the center of rotation moves more slowly than a point farther away. In the case of the concentric rotating hexagons, a point on the larger perimeter moves in a continuous manner; however, the perimeter of the smaller figure moves in discontinuous “jumps.”

Here, a demonstration is provided showing that a rectangular prism circumscribing a parabolic solid exceeds the contained paraboloid in volume by one-third.

A complete English language translation of the Discourses is available for consultation.

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

Index to Mathematical Treasures