The Metaphysics of the Pythagorean Theorem: Thales, Pythagoras, Engineering, Diagrams, and the Construction of the Cosmos out of Right Triangles

SUNY Press
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 Explores Thales’s speculative philosophy through a study of geometrical diagrams.
Bringing together geometry and philosophy, this book undertakes a strikingly original study of the origins and significance of the Pythagorean theorem. Thales, whom Aristotle called the first philosopher and who was an older contemporary of Pythagoras, posited the principle of a unity from which all things come, and back into which they return upon dissolution. He held that all appearances are only alterations of this basic unity and there can be no change in the cosmos. Such an account requires some fundamental geometric figure out of which appearances are structured. Robert Hahn argues that Thales came to the conclusion that it was the right triangle: by recombination and repackaging, all alterations can be explained from that figure. This idea is central to what the discovery of the Pythagorean theorem could have meant to Thales and Pythagoras in the sixth century BCE. With more than two hundred illustrations and figures, Hahn provides a series of geometric proofs for this lost narrative, tracing it from Thales to Pythagoras and the Pythagoreans who followed, and then finally to Plato’s Timaeus. Uncovering the philosophical motivation behind the discovery of the theorem, Hahn’s book will enrich the study of ancient philosophy and mathematics alike.
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About the author

 At Southern Illinois University Carbondale, Robert Hahn is Professor of Philosophy and Director of the Ancient Legacies Program, through which he leads traveling seminars to Greece, Turkey, and Egypt. He is the author of Archaeology and the Origins of Philosophy; Anaximander in Context: New Studies in the Origins of Greek Philosophy (with Dirk L. Couprie and Gerard Naddaf); and Anaximander and the Architects: The Contributions of Egyptian and Greek Architectural Technologies to the Origins of Greek Philosophy,all published by SUNY Press.

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Additional Information

Publisher
SUNY Press
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Published on
May 1, 2017
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Pages
300
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ISBN
9781438464916
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Language
English
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Genres
Mathematics / Geometry / General
Philosophy / General
Philosophy / History & Surveys / Ancient & Classical
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Content Protection
This content is DRM protected.
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Eligible for Family Library

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Demetrius of Phalerum (c. 355-280BCE) of Phalerum was a philosopher-statesman. He studied in the Peripatos under Theophrastus and subsequently used his political influence to help his teacher acquire property for the Peripatetic school. As overseer of Athens, his governance was characterized by a decade of domestic peace. Exiled to Alexandria in Egypt, he became the adviser of Ptolemy. He is said to have been in charge of legislation, and it is likely that he influenced the founding of the Museum and the Library.

This edition of the fragments of Demetrius of Phalerum reflects the growing interest in the Hellenistic period and the philosophical schools of that age. As a philosopher-statesman, Demetrius appears to have combined theory and practice. For example, in the work On Behalf of the Politeia, he almost certainly explained his own legislation and governance by appealing to the Aristotelian notion of politeia, that is, a constitution in which democratic and oligarchic elements are combined. In On Peace, he may have defended his subservience to Macedon by appealing to Aristotle, who repeatedly recognized the importance of peace over war; and in On Fortune, he will have followed Theophrastus, emphasizing the way fortune can determine the success or failure of sound policy. Whatever the case concerning any one title, we can well understand why Cicero regarded Demetrius as a unique individual: the educated statesman who was able to bring learning out of the shadows of erudition into the light of political conflict, and that despite an oratorical style more suited to the shadows of the Peripatos then to political combat.

The new edition of secondary reports by Stork, van Ophuijsen, and Dorandi brings together the evidence for these and other judgments. The facing translation which accompanies the Greek and Latin texts opens up the material to readers who lack the ancient languages, and the accompanying essays introduce us to important issues. The volume will be of interest to those interested in Greek literature, Hellenistic philosophy, Hellenistic history, and generally to persons captivated by the notion of philosopher-statesman.

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