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© 2001

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

Book

Part of the Distinguished Dissertations book series (DISTDISS)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Jacques Fleuriot
    Pages 1-10
  3. Jacques Fleuriot
    Pages 11-30
  4. Jacques Fleuriot
    Pages 31-58
  5. Jacques Fleuriot
    Pages 59-75
  6. Jacques Fleuriot
    Pages 77-98
  7. Jacques Fleuriot
    Pages 99-126
  8. Jacques Fleuriot
    Pages 127-131
  9. Back Matter
    Pages 133-140

About this book

Introduction

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.

Keywords

Artificial Intelligence Automated Reasoning Geometry Mechanical Theorem Mechanised analysis Newton's principia calculus proving

Authors and affiliations

  1. 1.Division of InformaticsUniversity of EdinburghEdinburghUK

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
  • Copyright Information Springer-Verlag London 2001
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-1-85233-466-6
  • Softcover ISBN 978-1-4471-1041-5
  • eBook ISBN 978-0-85729-329-9
  • Edition Number 1
  • Number of Pages XIII, 140
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Geometry
    Mathematics of Computing
  • Buy this book on publisher's site