Euclid's Elements and Methodology

Euclid starts from undemonstrated premises. His proofs are not just about a specific triangle, their sides are a three, four and five but about any right angle triangle. The sound in the looks a lot like it in for instance Aristotle's posterior analytics. We find a similar method in Archimedes, we find it in Apollonius to the point where some historians of mathematics identify a whole tradition of mathematics in the line of Euclids.