This is a new edition of an original and controversial book. As well as revising parts of the text and substantially updating the bibliography, the author takes a more polemical stance and enters into a discussion of the nature and range of different interpretations.
The book is divided into three parts: Interpretation, Evidence and Later Developments. The first part presents several new interpretations of the idea of ratio in early Greek mathematics and illustrates them in detailed discussions of several texts. Part Two focuses on the sources themselves, and questions the depth of modern knowledge of Plato's Academy during his lifetime, the source of our text of Euclid's Elements, and modern understanding of early Greek mathematics. The final part contrasts some of the evidence from early and late antiquity and then gives a historical account, since the seventeenth century, of the theory of continued fractions, our version today of the mathematics underlying the reconstruction.
From reviews of the first edition:
"...a real treat." Greece and Rome
"...he enters into classical scholarship here with a really "new reconstruction" of early Greek mathematics." Nature.
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