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Archytas of Tarentum was a central figure in fourth-century Greek life and thought and the last great philosopher in the early Pythagorean tradition. He solved a famous mathematical puzzle, saved Plato from the tyrant of Syracuse, led a powerful Greek city state, and was the subject of three books by Aristotle. This first extensive study of Archytas' work in any language presents a radically new interpretation of his significance for fourth-century Greek thought and his relationship to Plato, as well as a full commentary on all the fragments and testimonia.
- Sales Rank: #3169335 in Books
- Published on: 2010-09-09
- Original language: English
- Number of items: 1
- Dimensions: 9.02" h x 1.50" w x 5.98" l, 2.17 pounds
- Binding: Paperback
- 682 pages
Review
“Huffman gives readers the clearest picture yet of this important thinker about whom Aristotle wrote more books that about anyone else. Highly recommended.”
Choice
"We have here another blockbuster offering from Carl Huffman (hereafter H.), who has already put us in his debt by a definitive (and similarly vast) study of (Philolaus of Croton, Pythagorean and Presocratic, Cambridge, 1993). This work will serve in turn to establish Archytas as a philosopher in his own right, and not simply a footnote to Pythagoras, as has all too often been the case hitherto. Archytas had views on other aspects of philosophy and science as well, such as optics and the theory of motion, as well as some suggestions of a theory of first principles, and all these H. expounds with great fullness. One can only salute his immense industry, while wondering how many punters are actually going to get through the 620 pages of text. Those who do, however, will be rewarded, learning much, not only about Archytas himself, but about many other areas of antiquity as well."
John Dillon, Trinity College, Dublin, Bryn Mawr Classical Reviews
"Archytas of Tarentum is a major achievement. It will stand as the starting point for any serious engagement with the Pythagorean's philosophy, and more generally will enrich the study of ancient music and mathematics, of the Pythagorean movement, of those like Plato who have been presumed to be sympathetic to it, and of those like Aristotle who have been held to react against it." - William Wians, Merrimack College Classical Bulletin
"Aristotle's extant writings mention Archytas only three times, but among his lost writings there were three books about the Archytan philosophy -more than he wrote about any other single figure. Huffman is the first modern scholar to follow Aristotle's lead, devoting an entire work to this philosophy."
Patrick Lee Miller, Journal of the History of Philosophy
About the Author
Carl A. Huffman is Research Professor and Emeritus Professor of Classical Studies at DePauw University. He is author of Archytas of Tarentum: Pythagorean, Philosopher, and Mathematician King (2005) and Philolaus of Croton: Pythagorean and Presocratic (1993).
Most helpful customer reviews
1 of 1 people found the following review helpful.
Everything you want to know about Archytas
By Jordan Bell
Aside from general ideas about change, matter, time, and infinity, the only mathematical material I can find in the fragments and testimonia of the Presocratics are (i) the paradoxes of Zeno (which are not even explicitly mathematical), (ii) Aristotle's attribution of squaring the circle to Antiphon and Bryson, (iii) a paradox of Democritus about cones, and (iv) the construction by Archytas of mean proportionals and his theorem about epimoric ratios. (In fact, Archytas was a contemporary of Plato, but either because he was a Pythagorean or because he was independent of Socrates he is usually counted as Presocratic.)
Huffman has meticulous commentary on the texts, both about their authenticity and their meaning. This book is not meant to be read cover to cover by anyone except a scholar of ancient music, mathematics, or Pythagoreanism, but it will be useful to other scholars as a reliable and thorough presentation of the work of Archytas.
The weightiest discovery of Archytas is the construction of two mean proportionals between given magnitudes, in A14. This amounts to constructing a cube root, which is used to double the cube (A15). Huffman has a large commentary on these testimonia (pages 342-400).
But Archytas's work on proportions probably was more important in ancient Greek mathematics than the particular problem of doubling the cube. In Fragment 2, Archytas defines the arithmetic, geometric, and harmonic means. A19 is the testimonium that states Archytas's proof that an epimoric ratio cannot be divided into equal parts. This amounts to the following: if A,B are positive integers such that B is a proper divisor of A-B, then the square root of A:B is irrational.
Aside from geometry, scholars of acoustics and optics should consult this book. Fragment 1 is about acoustics, and A25 is about vision.
0 of 0 people found the following review helpful.
a great general and philosopher of the 4th century BCE
By Evaggelos Vallianatos
This is first rate collection of original sayings (opinions) about Archytas, a great general and philosopher of the 4th century BCE. The editor, Carl Huffman, is also outstanding in his historical background and translations of the fragments surviving about Archytas. The book is timely, insightful and necessary. I recommend it highly.
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