The Mathematics Of Plato S Academy

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.

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.

A comprehensive, interdisciplinary history of Plato's Academy, the most prominent philosophical school in antiquity, which lasted for about 300 years. Also includes the first complete annotated translation in English of Philodemus' History of the Academy, preserved on a papyrus from Herculaneum.

First Published in 2001. Routledge is an imprint of Taylor & Francis, an informa company.

The first of two volumes collecting the published work of one of the greatest living ancient philosophers, M.F. Burnyeat.

This book examines Aristotle's critical reaction to the mathematical cosmology of Plato's Academy, and traces the aporetic method by which he developed his own cosmological and metaphysical views, which underpin his philosophy of mathematics.

This lively and accessible introduction to Plato focuses on the philosophy and argument of his writings, drawing the reader into Plato's way of doing philosophy, and the general themes of his thinking. This is not a book to leave the reader standing in the outer court of introduction and background information, but leads directly into Plato's argument. It looks at Plato as a thinker grappling with philosophical problems in a variety of ways, rather than a philosopher with a fully worked-out system. It includes a brief account of Plato's life and the various interpretations that have been drawn from the sparse remains of information. It stresses the importance of the founding of the Academy and the conception of philosophy as a subject. Julia Annas discusses Plato's style of writing: his use of the dialogue form, his use of what we today call fiction, and his philosophical transformation of myths. She also looks at his discussions of love and philosophy, his attitude to women, and to homosexual love, explores Plato's claim that virtue is sufficient for happiness, and touches on his arguments for the immortality of the soul and his ideas about the nature of the universe. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

This anthology, the largest collection of Pythagorean writings ever to appear in English, contains the four ancient biographies of Pythagoras and over 25 Pythagorean and Neopythagorean writings from the Classical and Hellenistic periods. The material of this book is indispensable for anyone who wishes to understand the real spiritual roots of Western civilization.