A Combination of Geometry Theorem Proving and Nonstandard Analysis with Application to Newton’s Principia

Download or read book A Combination of Geometry Theorem Proving and Nonstandard Analysis with Application to Newton’s Principia written by Jacques Fleuriot and published by Springer Science & Business Media. This book was released on 2012-09-30 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Nonstandard Analysis, 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.