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

by Robert Hahn

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Explores Thales's speculative philosophy through a study of geometrical diagrams.

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In the elaborate Introduction (1-43), Hahn continues his theme of linking practical and metaphysical endeavors and, by adding Pythagoras of Samos, he proposes an Ionian comity of knowledge (from the late seventh into the early fifth centuries BCE) rather than a succession of intellectual discoveries. In addition, he posits that the philosophers shared an intention to “resolve a metaphysical problem” (5, 11-2, the author's emphasis) based in part on much earlier Mesopotamian and Egyptian methods of geometric mensuration. These methods had been illustrated with diagrams and figures, as evidenced by cuneiform tablets and mathematical papyri, but as such they were mainly used to train surveyors and storage officials in determining the areas of oddly configured land, the capacity of granaries, and other spatial and practical problems (7-25). There is also some evidence that Egyptian painters used reductions arrived at geometrically to define humans of lesser status in relation to those of higher rank (14-17)—using geometry to denote social significance. A tile incised with a geometrical sketch from the Ephesian Artemision (mid-seventh century BCE) was used to instruct painters on how to locate the centers and cast concentric circles of decorations on roofing-tiles (32-5)—using geometry to generate a small-scale template for monumental repetition.
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