The Mathematics of Plato's Academy

Divided into three parts, this presents new interpretations of the ideas of ratio in early Greek mathematics. It also discusses what we know of Plato's academy and early Greek numerical practice and gives an historical account of the theory of continued fractions.

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Ancient sources tell us of Plato's zeal for mathematics, but the problem of interpreting many of the mathematical references in his Dialogues has perplexed later commentators. Part One of this book presents several new interpretations of the ideas of ratio in early Greek mathematics, and illustrates them in detailed discussions of several texts. Principally, it looks at the advanced mathematics curriculum described by Plato in Republic VII as part of the training of future guardians of the state, at early Greek and Egyptian calendars, at Euclid's Elements, and at the Sectio Canonis . Part Two discusses three questions: Just what do we know of Plato's Academy during his lifetime? From where do we get our text of Euclid's Elements ? What do we know of early Greek numerical practice? Part Three contrasts some of the evidence from early and late antiquity and then gives a historical account, starting in the seventeenth century, of the theory of continued fractions - today's version of the mathematics underlying the reconstruction. Full indexes and bibliography complete the book. This is a bok for mathematicians; historians of mathematics; classicists; and papyrologists.