Table of contents for Euclid and his twentieth century rivals : diagrams in the logic of Euclidean geometry / by Nathaniel Miller.

Bibliographic record and links to related information available from the Library of Congress catalog.

Note: Contents data are machine generated based on pre-publication provided by the publisher. Contents may have variations from the printed book or be incomplete or contain other coding.


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CONTENTS
1 Background 1
 1.1 A Short History of Diagrams, Logic, and Geometry 4
 1.2 The Philosophy Behind this Work 12
 1.3 Euclid's Elements 14
2 Syntax and Semantics of Diagrams 23
 2.1 Basic Syntax of Euclidean Diagrams 23
 2.2 Advanced Syntax of Diagrams: Corresponding
 Graph Structures and Diagram Equivalence Classes 29
 2.3 Diagram Semantics 33
3 Diagrammatic Proofs 37
 3.1 Construction Rules 37
 3.2 Inference Rules 42
 3.3 Transformation Rules 45
 3.4 Dealing with Areas and Lengths of Circular Arcs 47
 3.5 CDEG 55
4 Meta-mathematical Results 67
 4.1 Lemma Incorporation 67
 4.2 Satisfiable and Unsatisfiable Diagrams 74
 4.3 Transformations and Weaker Systems 78
5 Conclusions 85
Appendix A: Euclid's Postulates 91
Appendix B: Hilbert's Axioms 93
Appendix C: Isabel Luengo's DS1 97
Appendix D: A CDEG transcript 105
References 117
Index 119

Library of Congress Subject Headings for this publication:

Euclid.
Geometry -- Miscellanea.