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Mathematical Treasure: Galileo’s Two New Sciences

Frank J. Swetz (The Pennsylvania State University)

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.

Title page of Galileo's 1638 Two New Sciences.

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.”

Page 22 of Galileo's 1638 Two New Sciences.

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

Page 142 of Galileo's 1638 Two New Sciences.

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

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Galileo’s Two New Sciences," Convergence (July 2016)