A Combination of Geometry Theorem Proving and Nonstandard Analysis With Application to Newton's Principia

by Fleuriot, Jacques

• ISBN13: 9781852334666
• ISBN10: 1852334665
• Format: Hardcover
• Copyright: 2001-06-01
• Publisher: Springer-Verlag New York Inc

Summary

Sir Isaac Newton's philosophi Naturalis Principia Mathematica'(the Principia) contains a prose-style mixture of geometric and limit reasoning that has often been viewed as logically vague. In A Combination of Geometry Theorem Proving and NonstandardAnalysis, Jacques Fleuriot presents a formalization of Lemmas and Propositions from the Principia using a combination of methods from geometry and nonstandard analysis. The mechanization of the procedures, which respects much of Newton's original reasoning, is developed within the theorem prover Isabelle. The application of this framework to the mechanization of elementary real analysis using nonstandard techniques is also discussed.

Table of Contents

List of Figures
Introduction	p. 1
Geometry Theorem Proving	p. 11
Constructing the Hyperreals	p. 31
Infinitesimal and Analytic Geometry	p. 59
Mechanizing Newton's Principia	p. 77
Nonstandard Real Analysis	p. 99
Conclusions	p. 127
Bibliography	p. 133
Index	p. 139
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