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.
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.
The Heirs of Plato is the first book exclusively devoted to an in-depth study of the various directions in philosophy taken by Plato's followers in the first seventy years or so following his death in 347 BC. - the period generally known as 'The Old Academy'. Speusippus, Xenocrates, and Polemon, the three successive heads of the Academy in this period, though personally devoted to the memory of Plato, were independent philosophers in their own right, and felt free to develop his heritage in individual directions. This is also true of other personalities attached to the school, such as Philippus of Opus, Heraclides of Pontus, and Crantor of Soli. After an introductory chapter on the school itself, and a summary of Plato's philosophical heritage, John Dillon devotes a chapter to each of the school heads, and another to the other chief characters, exploring both what holds them together and what sets them apart. There is a final short chapter devoted to the turn away from dogmatism to scepticism under Arcesilaus in the 270s, and some reflections on the intellectual debt of Stoicism to the thought of Polemon, in particular. Dillon's clear and accessible book fills a significant gap in our understanding of Plato's immediate philosophical influence, and will be of great value to scholars and historians of ancient philosophy.
Founded by Cosimo de' Medici in the early 1460s, the Platonic Academy shaped the literary and artistic culture of Florence in the later Renaissance and influenced science, religion, art, and literature throughout Europe in the early modern period. This major study of the Academy's beginnings presents a fresh view of the intellectual and cultural life of Florence from the Peace of Lodi of 1454 to the death of Cosimo a decade later. Challenging commonly held assumptions about the period, Arthur Field insists that the Academy was not a hothouse plant, grown and kept alive by the Medici in the splendid isolation of their villas and courts. Rather, Florentine intellectuals seized on the Platonic truths and propagated them in the heart of Florence, creating for the Medici and other Florentines a new ideology. Based largely on new or neglected manuscript sources, this book includes discussions of the earliest works by the head of the Academy, Marsilio Ficino, and the first public, Platonizing lectures of the humanist and poet Cristoforo Landino. The author also examines the contributions both of religious orders and of the Byzantines to the Neoplatonic revival. Originally published in 1988. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Geometry defines the world around us, helping us make sense of everything from architecture to military science to fashion. And for over two thousand years, geometry has been equated with Euclid's Elements, arguably the most influential book in the history of mathematics In The King of Infinite Space, renowned mathematics writer David Berlinski provides a concise homage to this elusive mathematician and his staggering achievements. Berlinski shows that, for centuries, scientists and thinkers from Copernicus to Newton to Einstein have relied on Euclid's axiomatic system, a method of proof still taught in classrooms around the world. Euclid's use of elemental logic -- and the mathematical statements he and others built from it -- have dramatically expanded the frontiers of human knowledge. The King of Infinite Space presents a rich, accessible treatment of Euclid and his beautifully simple geometric system, which continues to shape the way we see the world.
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.
The definitive sequel to New York Times bestseller How the Scots Invented the Modern World is a magisterial account of how the two greatest thinkers of the ancient world, Plato and Aristotle, laid the foundations of Western culture—and how their rivalry shaped the essential features of our culture down to the present day. Plato came from a wealthy, connected Athenian family and lived a comfortable upper-class lifestyle until he met an odd little man named Socrates, who showed him a new world of ideas and ideals. Socrates taught Plato that a man must use reason to attain wisdom, and that the life of a lover of wisdom, a philosopher, was the pinnacle of achievement. Plato dedicated himself to living that ideal and went on to create a school, his famed Academy, to teach others the path to enlightenment through contemplation. However, the same Academy that spread Plato’s teachings also fostered his greatest rival. Born to a family of Greek physicians, Aristotle had learned early on the value of observation and hands-on experience. Rather than rely on pure contemplation, he insisted that the truest path to knowledge is through empirical discovery and exploration of the world around us. Aristotle, Plato’s most brilliant pupil, thus settled on a philosophy very different from his instructor’s and launched a rivalry with profound effects on Western culture. The two men disagreed on the fundamental purpose of the philosophy. For Plato, the image of the cave summed up man’s destined path, emerging from the darkness of material existence to the light of a higher and more spiritual truth. Aristotle thought otherwise. Instead of rising above mundane reality, he insisted, the philosopher’s job is to explain how the real world works, and how we can find our place in it. Aristotle set up a school in Athens to rival Plato’s Academy: the Lyceum. The competition that ensued between the two schools, and between Plato and Aristotle, set the world on an intellectual adventure that lasted through the Middle Ages and Renaissance and that still continues today. From Martin Luther (who named Aristotle the third great enemy of true religion, after the devil and the Pope) to Karl Marx (whose utopian views rival Plato’s), heroes and villains of history have been inspired and incensed by these two master philosophers—but never outside their influence. Accessible, riveting, and eloquently written, The Cave and the Light provides a stunning new perspective on the Western world, certain to open eyes and stir debate. Praise for The Cave and the Light “A sweeping intellectual history viewed through two ancient Greek lenses . . . breezy and enthusiastic but resting on a sturdy rock of research.”—Kirkus Reviews “Examining mathematics, politics, theology, and architecture, the book demonstrates the continuing relevance of the ancient world.”—Publishers Weekly “A fabulous way to understand over two millennia of history, all in one book.”—Library Journal “Entertaining and often illuminating.”—The Wall Street Journal
