The evolution of the euclidean elements

Title page
I/ INTRODUCTION
I. The Pre-Euclidean Theory of Incommensurable Magnitudes
II. General Methodological Observations
III. Indispensable Definitions
II/ THE SIDE AND THE DIAMETER OF THE SQUARE
I. The Received Proof of the Incommensurability of the Side and Diameter of the Square
II. Anthyphairesis and the Side and Diameter
III. Impact of the Discovery of Incommensurability
IV. Summary of the Early Studies
III/ PLATO'S ACCOUNT OP THE WORK OF THEODORUS
I. Formulation of the Problem: etc
II. The Role of Diagrams: etc
III. The Ideal of Demonstration: etc
IV. Why Separate Cases?
V. Why Stop at Seventeen?
VI. The Theorems of Theaetetus
VII. Theodorus' Style of Geometry
VIII. Summary of Interpretive Criteria
IV/ A CRITICAL REVIEW OF RECONSTRUCTIONS OF THEODORUS' PROOFS
I. Reconstruction via Approximation Techniques
II. Algebraic Reconstruction
III. Anthyphairetic Reconstruction
V/ THE PYTHAGOREAN ARITHMETIC Of THE FIFTH CENTURY
I. Pythagorean Studies of the Odd and the Even
II. The Pebble-Representation of Numbers
III. The Pebble-Methods Applied to the Study of the Odd and the Even
IV. The Theory of Figured Numbers
V. Properties of Pythagorean Number Triples
VI/ THE EARLY STUDY OP INCOMMENSURABLE MAGNITUDES: THEODORUS
I. Numbers Represented as Magnitudes
II. Right Triangles and the Discovery of Incommensurability
III. The Lesson of Theodorus
IV. Theodorus and Elements II
VII/ THE ARITHMETIC Of INCOMMENSURABILITY: THEAETETUS AND ARCHYTAS
I. The Theorem of Archytas on Epimoric Ratios
II. The Theorems of Theaetetus
III. The Arithmetic Proofs of the Theorems of Theaetetus
IV. The Arithmetic Basis of Theaetetus' Theory
V. Observations on Pre-Euclidean Arithmetic
VIII/ THE GEOMETRY Of INCOMMENSURABILITY: THEAETETUS AND EUDOXUS
I. The Theorems of Theaetetus: Proofs of the Geometric Part
II. Anthyphairesis and the Theory of Proportions
III. The Theory of Proportions in Elements X
IV. Theaetetus and Eudoxus
V. Summary of the Development of the Theory of Irrationals
IX/ CONCLUSIONS AND SYNTHESES
I. The Pre-Euclidean Theory of Incommensurable Magnitudes
II. The Editing of the Elements
III. The Pre-Euclidean Foundations-Crises
APPENDICES
A. On the Extension of Theodorus' Method
B. On the Anthyphairetic Proportion Theory
A LIST Of THE THEOREMS IN CHAPTERS V-VIII AND THB APPENDICES
REFERENCING CONVENTIONS AND BIBLIOGRAPHY
I. Referencing Conventions
II. Abbreviations used in the Notes and the Bibliography
III. Bibliography of Works Consulted: Ancient Authors
IV. Modem Works: Books
V. Modem Works: Articles
INDEX Of NAMES
INDEX OF PASSAGES CITED FROM ANCIENT WORKS