To whom it may concern,
After looking at your website (which I source all the time) I now have cause to email you.
I'm having extreme trouble trying to find out the answers to this question, I wonder if you can help me.
If you could possibly forward me some websites which could give an indicator to these answers, I would be most grateful or if you do have the answer yourself, that would be even better.
First, some general comments about the history of Greek mathematics. Almost the documents have been lost. There are almost no historical FACTS -- all that is "known" comes from conjectures made by clever and wise scholars who have studied these things all their lives. The stories are nice and carefully conceived, but how close they come to the truth is anybody's guess.
In particular, most of the story of Pythagoras (500 BC) and Euclid (300 BC) is based on legend. Pythagoras founded a secret society whose mathematics was just one part of their activity. Although it is possible that Pythagoras was a brilliant mathematician, it is also possible that all the mathematical discoveries were made by his followers and attributed to the leader. It is certain that the theorem and some sort of proof came from the Pythagoreans at the time of Pythagoras. (The theorem itself has been discovered independently both before and after by various other cultures; of course, those cultures had no real notion of a mathematical proof -- the concept of "proof" originated with the Greeks shortly before the time of Pythagoras.)
Euclid is best known for having compiled a geometry text that gathered together all that was known at the time about geometry and proofs. The book was so brilliantly written that it replaced all the mathematics that preceded it, and all the earlier work was subsequently lost. As a consequence, there is no way to be certain about what Euclid himself contributed. The first of the 13 books that make up Euclid's ELEMENTS is devoted to a proof of theorem 47, which is the theorem of Pythagoras. That proof is generally thought to have been devised by Euclid himself for his book. It depends on most of the 46 theorems that precede it. Of course, there are hunreds of different ways to prove the Pythagorean theorem. There is no way of knowing how or if Pythagoras proved it.Chris