## The Mathematics of Plato's Academy: A New ReconstructionThis 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. |

### Contents

Anthyphairetic ratio theory | 32 |

The dimension of squares | 67 |

b Historical observations | 100 |

Copyright | |

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### Common terms and phrases

abbreviations AC₁ algorism algorithm alogoi anthyphairetic ratios apotome approximations Archimedes Archytas Aristotle arithmetic arithmētikē arithmetised arithmoi artabas astronomical ratios binomial Book calculation century Chapter column commensurable common fractions construction contains context continued fractions convergents definition described discussion division early Greek mathematics Elements epimoric equal equation Euclid Euclid's Elements Euclidean Euler Eutocius evaluate evidence example expansion exploration expressible lines extreme and mean figure fragment further Gauss generalised geometrical give given gnomon Greek mathematics Heath Heiberg Hence Hippias Minor illustrate incommensurable integer interval kind Knorr less logistikē manipulations manuscripts mathematicians multiplication n₁ n₂ notation numbers Opera papyrus Parmenides Parmenides proposition passage Pell's equation pentagon photograph Plato problem Proclus proof proportion quadratic quadratic surd ratio theory reconstruction rectangle reference result Section side and diagonal SOCRATES square straight line subtraction tables Theaetetus topic translation triangle unit fractions