...Guthrie

W. K. C. Guthrie, A History of Greek Philosophy, vol. 1 (Cambridge: Cambridge University Press, 1962), p. 70.

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...proofs

Exactly why Thales needed to prove theorems and propostions that the Egyptians and Babylonians accepted without justification is even now a subject of conjecture. Many standard philosophical explanations have been given. A more practical one might be the poor arithmetical algorithms that would make ``proofs" easier to discover that make measurements.

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...diameter.

These propositions, particularly this one comes from Proclus. But we should be careful with what ``proof" means here. Even Euclid states this as a fact.

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