Re: Stupid question: what space was Euclid working in?

Vaughan Pratt writes:

I've seen only two essentially different approaches so far, bottom-up (adding structure) and top-down (forgetting structure).

Where does Euclid's approach fit in this scheme? Starting from say Hilbert's formulation of Euclidean geometry it is certainly possible to get to an inner product space and all the rest, but it's certainly not direct and not easy. -- Bob -- Robert L. Knighten RLK@knighten.org