The Mathematics of Plato's Academy: A New Reconstruction

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Clarendon Press, 1987 - History - 401 pages
This book presents a reinterpretation of early Greek mathematics, one of the most tantalizing intellectual subjects of the last 2,000 years. The first part offers several new interpretations of the idea of ratio in early Greek mathematics and illustrates them in detailed discussion of several texts. Part Two discusses the historical context of the subject--what we know of Plato's academy during his lifetime, the origin of our text of Euclid's Elements, and what we know of early Greek numerical practice. The book finishes with an account of the theory of continued fractions and its history since the 17th century.

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Anthyphairetic ratio theory
The dimension of squares
Platos mathematics curriculum in Republic VII

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