Synopses & Reviews
This is an updated edition of a groundbreaking examination of early Greek mathematics. The author has revised parts of the text, updated the bibliography, and added a new Appendix where he takes a strong position in the continuing debate about the nature and range of classical mathematics. The first part presents several new interpretations of the idea of ratio in early Greek mathematics and illustrates these in detailed discussions of several texts. Part Two then focuses on the sources themselves and provides a critical look at our knowledge of Plato's Academy during his lifetime, at the source of our text of Euclid's Elements, and at our understanding of early Greek mathematics. The final part contrasts some of the evidence from early and late antiquity and then gives a historical account, beginning in the seventeenth century, of the modern theory of continued fractions, which underlies our reconstruction of early Greek mathematics.
Review
From reviews of the first edition: "...a real treat." --Greece and Rome
"...cites an impressive array of evidence...The result should be widely read by classicists and mathematicians as well as historians of mathematics." --ISIS
"...this fascinating book...will arouse the interest and command the admiration of any historically minded lover of mathematics with a taste for the unorthodox." --Institute of Mathematics and its Applications
Table of Contents
List of plates Notes on the transcriptions of papyri
Part One: Interpretations
1. The Proposal
2. Anthyphairetic Ratio Theory
3. Elements II: The Dimension of Squares
4. Plato's Mathematics Curriculum in Republic VII
5. Elements IV, X, and XIII: The Circumdiameter and Side
Part Two: Evidence
6. The Nature of Our Evidence
7. Numbers and Fractions
Part Three: Later Developments
8. Later Interpretations
9. Continued Fractions
10. Appendix: New Material Added to the Second Edition
11. Epilogue: a Brief Intellectual Autobiography
Bibliography
Index of Cited Passages
Index of Names
General Index