A Combination of Geometry Theorem Proving and Nonstandard Analysis with Application to Newton's Principia / Edition 1

Hardcover (Print)
Buy New
Buy New from BN.com
$144.20
Used and New from Other Sellers
Used and New from Other Sellers
from $175.79
Usually ships in 1-2 business days
(Save 6%)
Other sellers (Hardcover)
  • All (3) from $175.79   
  • New (1) from $175.79   
  • Used (2) from $201.75   

Overview

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.

Read More Show Less

Product Details

  • ISBN-13: 9781852334666
  • Publisher: Springer London
  • Publication date: 10/25/2007
  • Series: Distinguished Dissertations Series
  • Edition description: 2001
  • Edition number: 1
  • Pages: 140
  • Product dimensions: 0.44 (w) x 9.21 (h) x 6.14 (d)

Table of Contents

Introduction.- A Brief History of the Infinitesimal.- The Principia and its Methods.- On Nonstandard Analysis.- Objectives.- Achieving our Goals.- Organisation of this book.- Geometry Theorem Proving.- Historical Background.- Algebraic Techniques.- Coordinate-Free Techniques.- Formalizing Geometry in Isabelle.- Concluding remarks.- Constructing the Hy perreals.- Isabelle/HOL.- Properties of an Infinitesimal Calculus.- Internal Set Theory.- Constructions Leading to the Reals.- Filters and Ultrafilters.- Ultrapower Construction of the Hyperreals.- Structure of the Hyperreal Number Line.- The Hypernatural Numbers.- An Alternative Construction for the Reals.- Related Work.- Concluding Remarks.- Infinitesimal and Analytic Geometry.- Non-Archimedean Geometry.- New Definitions and Relations.- Infinitesimal Geometry Proofs.- Verifying the Axioms of Geometry.- Concluding Remarks.- Mechanising Newton's Principia.- Formalizing Newton's Properties.- Mechanized Propositions and Lemmas.- Ratios of Infinitesimals.- Case Study: Propositio Kepleriana.- Expanding Newton's Proof.- Conclusions.- Nonstandard Real Analysis.- Extending a Relation to the Hyperreals.- Towards an Intuitive Calculus.- Real Sequences and Series.- Some Elementary Topology of the Reals.- Limits and Continuity.- Differentiation.- On the Transfer Principle.- Related Work and Conclusions.- Conclusions.- Geometry, Newton and the Principia.- Hyperreal Analysis.- Further Work.- Concluding Remarks.-

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)