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

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. 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. Front Matter....Pages i-xiii Introduction....Pages 1-10 Geometry Theorem Proving....Pages 11-30 Constructing the Hyperreals....Pages 31-58 Infinitesimal and Analytic Geometry....Pages 59-75 Mechanizing Newton’s Principia ....Pages 77-98 Nonstandard Real Analysis....Pages 99-126 Conclusions....Pages 127-131 Back Matter....Pages 133-140