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A mathematical history of division in extreme and mean ratio /
A comprehensive study of the historic development of division in extreme and mean ratio (""the golden number""), this text traces the concept's development from its first appearance in Euclid's Elements through the 18th century. The coherent but rigorous presentation of...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Waterloo, Ont. :
Wilfrid Laurier University Press,
1998
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- TABLE OF CONTENTS
- PREFACE TO THE DOVER EDITION
- FOREWORD
- A GUIDE FOR READERS
- A. Internal Organization
- B. Bibliographical Details
- C. Abbreviations
- D. Symbols
- E. Dates
- F. Quotations from Primary Sources
- INTRODUCTION
- CHAPTER I. THE EUCLIDEAN TEXT
- Section 1. The Text
- Section 2. An Examination of the Euclidean Text
- A. Preliminary Observations
- B.A Proposal Concerning the Origin of DEMR
- C. Theorem XIII,8
- D. Theorems XIII,1-5
- E. Stages in the Development of DEMR in Book XIII
- CHAPTER II. MATHEMATICAL TOPICSSection 3. Complements and the Gnomon
- Section 4. Transformation of Areas
- Section 5. Geometrical Algebra, Application of Areas, and Solutions of Equations
- A. Geometrical Algebra�Level 1
- B. Geometrical Algebra�Level 2
- C. Application of Areas�Level 3
- D. Historical References
- E. Setting Out the Debate
- F. Other Interpretations in Terms of Equations
- G. Problems in Interpretation
- H. Division of Figures
- I. Theorems VI,28,29 vs II,5,6
- J. Euclid's Data
- K. Theorem II,11
- L. II,11�Application of Areas, Various ViewsSection 6. Side and Diagonal Numbers
- Section 7. Incommensurability
- Section 8. The Euclidean Algorithm, Anthyphairesis, and Continued Fractions
- CHAPTER III. EXAMPLES OF THE PENTAGON, PENTAGRAM, AND DODECAHEDRON BEFORE �400
- Section 9. Examples before Pythagoras (before c. �550)
- A. Prehistoric Egypt
- B. Prehistoric Mesopotamia
- C. Sumerian and Akkadian Cuneiform Ideograms
- D. A Babylonian Approximation for the Area of the Pentagon
- E. Palestine
- Section 10. From Pythagoras until �400
- A. Vases from Greece and its Italian Colonies, Etruria (Italy)B. Shield Devices on Vases
- C. Coins
- D. Dodecahedra
- E. Additional Material
- Conclusions
- CHAPTER IV. THE PYTHAGOREANS
- i. Pythagoras
- ii. Hippasus
- iii. Hippocrates of Chios
- iv. Theodorus of Cyrene
- v. Archytas
- Section 11. Ancient References to the Pythagoreans
- A. The Pentagram as a Symbol of the Pythagoreans
- B. The Pythagoreans and the Construction of the Dodecahedron
- C. Other References to the Pythagoreans
- Section 12. Theories Linking DEMR with the Pythagoreansi. The Pentagram
- ii. Scholia Assigning Book IV to the Pythagoreans
- iii. Equations and Application of Areas
- iv. The Dodecahedron
- v. A Marked Straight-Edge Construction of the Pentagon
- vi. A Gnomon Theory
- vii. Allman's Theory: The Discovery of Incommensurability
- viii. Fritz�Junge Theory: The Discovery of Incommensurability
- ix. Heller's Theory: The Discovery of DEMR
- x. Neuenschwander's Analysis
- xi. Stapleton
- CHAPTER V. MISCELLANEOUS THEORIES