The Metaphysics of the Pythagorean Theorem
Thales, Pythagoras, Engineering, Diagrams, and the Construction of the Cosmos out of Right Triangles
1st Edition
Published on 1. May 2017
300 pages
978-1-4384-6491-6 (ISBN)
Description
Explores Thales's speculative philosophy through a study of geometrical diagrams.
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Series
Language
English
Place of publication
Basel/Berlin/Boston
United States
Target group
Professional and scholarly
Edition type
Digital original
Product notice
Reflowable
Illustrations
Total Illustrations: 251
Total Illustrations: 251
ISBN-13
978-1-4384-6491-6 (9781438464916)
Schweitzer Classification
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Additional editions
Robert Hahn
The Metaphysics of the Pythagorean Theorem
Thales, Pythagoras, Engineering, Diagrams, and the Construction of the Cosmos out of Right Triangles
Book
01/2018
State University of New York Press
€59.30
Shipment within 10-20 days
Robert Hahn
The Metaphysics of the Pythagorean Theorem
Thales, Pythagoras, Engineering, Diagrams, and the Construction of the Cosmos out of Right Triangles
Book
06/2017
State University of New York Press
€95.50
Shipment within 10-20 days
Person
At Southern Illinois University Carbondale, Robert Hahn is Professor of Philosophy and Director of the Ancient Legacies Program, through which he leads traveling seminars to Greece, Turkey, and Egypt. He is the author of Archaeology and the Origins of Philosophy; Anaximander in Context: New Studies in the Origins of Greek Philosophy (with Dirk L. Couprie and Gerard Naddaf); and Anaximander and the Architects: The Contributions of Egyptian and Greek Architectural Technologies to the Origins of Greek Philosophy, all published by SUNY Press.
Content
- Intro
- Contents
- Preface
- A
- B
- C
- Acknowledgments
- Introduction Metaphysics, Geometry, and the Problems with Diagrams
- A. The Missed Connection between the Origins of Philosophy-Science and Geometry: Metaphysics and Geometrical Diagrams
- B. The Problems Concerning Geometrical Diagrams
- C. Diagrams and Geometric Algebra: Babylonian Mathematics
- D. Diagrams and Ancient Egyptian Mathematics: What Geometrical Knowledge Could Thales have Learned in Egypt?
- E. Thales's Advance in Diagrams Beyond Egyptian Geometry
- F. The Earliest Geometrical Diagrams Were Practical: The Archaic Evidence for Greek Geometrical Diagrams and Lettered Diagrams
- G. Summary
- Chapter 1 The Pythagorean Theorem: Euclid I.47 and VI.31
- A. Euclid: The Pythagorean Theorem I.47
- (i) The Pythagorean theorem of Euclid I.47 (following Heath):
- (ii) Reflections on the strategies of Euclid I.47:
- (iii) The geometrical intuitions: the sequence of ideas that are connected in the proof:
- B. The "Enlargement" of the Pythagorean Theorem: Euclid VI.31
- (i) The Pythagorean theorem of Euclid VI.31 (following Heath):
- (ii) Reflections on the strategies of Euclid VI.31:
- (iii) The geometrical Intuitions-the sequence of ideas that are connected in the proof:
- C. Ratio, Proportion, and the Mean Proportional (µ?s? ????????)
- D. Arithmetic and Geometric Means
- E. Overview and Summary: The Metaphysics of the Pythagorean Theorem
- Chapter 2 Thales and Geometry: Egypt, Miletus, and Beyond
- A. Thales: Geometry in the Big Picture
- B. What Geometry Could Thales Have Learned in Egypt?
- B.1 Thales's Measurement of the Height of a Pyramid
- Technique 1: When the Shadow Length Was Equal to Its Height
- B.2 Thales's Measurement of the Height of a Pyramid
- Technique 2: When the Shadow Length Was NOT Equal to Its Height
- C. Thales' Lines of Thought to the Hypotenuse Theorem
- Chapter 3 Pythagoras and the Famous Theorems
- A. The Problems of Connecting Pythagoras with the Famous Theorem
- B. Hippocrates and the Squaring of the Lunes
- C. Hippasus and the Proof of Incommensurability
- D. Lines, Shapes, and Numbers: Figurate Numbers
- E. Line Lengths, Numbers, Musical Intervals, Microcosmic-Macrocosmic Arguments, and the Harmony of the Circles
- F. Pythagoras and the Theorem: Geometry and the Tunnel of Eupalinos on Samos
- G. Pythagoras, the Hypotenuse Theorem, and the µ?s? ???????? (Mean Proportional)
- H. The "Other" Proof of the Mean Proportional: The Pythagoreans and Euclid Book II
- I. Pythagoras's Other Theorem: The Application of Areas
- I.1 The Application of Areas Theorems at Euclid I.42, 44, and 45
- I.2 The Application of Areas Theorems in Euclid VI.25, 28, 29 by Ratios and Proportions
- J. Pythagoras's Other Theorem in the Bigger Metaphysical Picture: Plato's Timaeus 53Cff
- K. Pythagoras and the Regular Solids: Building the Elements and the Cosmos Out of Right Triangles
- K.1 The Role of the Cosmic Figures in the Big Picture: Proclus's Insight into the Metaphysical Purpose of Euclid
- K.2 Did Pythagoras Discover the Cosmic Figures?
- Proposition 21
- Remark
- K.3 Pythagoras's Regular Solids and Plato's Timaeous: The Reduction of the Elements to Right Triangles, the Construction of the Cosmos out of Right Triangles
- Chapter 4 Epilogue: From the Pythagorean Theorem to the Construction of the Cosmos Out of Right Triangles
- Notes
- Bibliography
- Image Credits
- Index
- Greek Terms
