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Contents 8 Preface 10 A 10 B 13 C 13 Acknowledgments 16 Introduction Metaphysics, Geometry, and the Problems with Diagrams 18 A. The Missed Connection between the Origins of Philosophy-Science and Geometry: Metaphysics and Geometrical Diagrams 18 B. The Problems Concerning Geometrical Diagrams 21 C. Diagrams and Geometric Algebra: Babylonian Mathematics 24 D. Diagrams and Ancient Egyptian Mathematics: What Geometrical Knowledge Could Thales have Learned in Egypt? 29 E. Thales’s Advance in Diagrams Beyond Egyptian Geometry 42 F. The Earliest Geometrical Diagrams Were Practical: The Archaic Evidence for Greek Geometrical Diagrams and Lettered Diagrams 49 G. Summary 58 Chapter 1 The Pythagorean Theorem: Euclid I.47 and VI.31 62 A. Euclid: The Pythagorean Theorem I.47 63 (i) The Pythagorean theorem of Euclid I.47 (following Heath): 63 (ii) Reflections on the strategies of Euclid I.47: 65 (iii) The geometrical intuitions: the sequence of ideas that are connected in the proof: 71 B. The “Enlargement” of the Pythagorean Theorem: Euclid VI.31 83 (i) The Pythagorean theorem of Euclid VI.31 (following Heath): 83 (ii) Reflections on the strategies of Euclid VI.31: 86 (iii) The geom

Author

Robert Hahn;

Language

EN