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.(55) and others in which geometric problems are translated into corresponding algebraic ones that are then solved by ... the two approaches but his work mainly uses the logical reasoner for expressing the geometric problem (through the use anbsp;...

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

Author | : | Jacques Fleuriot |

Publisher | : | Springer Science & Business Media - 2012-09-30 |

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