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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.