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

  • Book
  • © 2001

Overview

Authors:
  1. Jacques Fleuriot

    1. Division of Informatics, University of Edinburgh, Edinburgh, UK

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Part of the book series: Distinguished Dissertations (DISTDISS)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • Jacques Fleuriot
    Pages 1-10

  3. Geometry Theorem Proving

    • Jacques Fleuriot
    Pages 11-30

  4. Constructing the Hyperreals

    • Jacques Fleuriot
    Pages 31-58

  5. Infinitesimal and Analytic Geometry

    • Jacques Fleuriot
    Pages 59-75

  6. Mechanizing Newton’s Principia

    • Jacques Fleuriot
    Pages 77-98

  7. Nonstandard Real Analysis

    • Jacques Fleuriot
    Pages 99-126

  8. Conclusions

    • Jacques Fleuriot
    Pages 127-131

  9. Back Matter

    Pages 133-140
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Keywords

About this book

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.

Authors and Affiliations

  • Division of Informatics, University of Edinburgh, Edinburgh, UK

    Jacques Fleuriot

Bibliographic Information

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

  • Authors: Jacques Fleuriot

  • Series Title: Distinguished Dissertations

  • DOI: https://doi.org/10.1007/978-0-85729-329-9

  • Publisher: Springer London

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag London 2001

  • Hardcover ISBN: 978-1-85233-466-6Published: 08 June 2001

  • Softcover ISBN: 978-1-4471-1041-5Published: 13 September 2012

  • eBook ISBN: 978-0-85729-329-9Published: 30 September 2012

  • Edition Number: 1

  • Number of Pages: XIII, 140

  • Topics: Geometry, Mathematics of Computing

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