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That's a good point about Hippocrates, I'd forgotten about him. Do you have a source handy on Thales and Pythagoras? I don't doubt it, it's just a gap I should fill. So far as I remember, a proof that the square root of two is irrational came out of the Pythagorean school, but that's all I can think of. I hadn't heard anything like that about Thales.
I linked to the relevant Wikipedia articles in my comment.
Ah, but note the 'history' section of the Thales article. It rather supports my picture, if it supports anything at all.
Why? If you mean that Thales learned the result from the Babylonians, the point is that he appears to have been the first to bother proving it.