## Abstract

Sir Isaac Newton's 'Philosophiæ 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.

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.

Original language | English |
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Publisher | Springer London |

Number of pages | 140 |

ISBN (Electronic) | 978-0-85729-329-9 |

ISBN (Print) | 978-1-4471-1041-5 |

DOIs | |

Publication status | Published - 2001 |

### Publication series

Name | Distinguished Dissertations |
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Publisher | Springer London |