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Hilbert took years to make a rigorous revision and formalization of Euclidean geometry in his Foundations of Geometry. As he intended to organize only the most basic aspects of the theory, he didn't write about things like the Pythagorean Theorem or the sum of the angles of a triangle. He would say "it is easily deduced from the previous theorems." Even though it can be easy I don't seem to find any book where there is the Euclidean geometry presented as in the Euclid's Elements, but using Hilbert's axioms.

What I mean is: Is there an Elements of geometry as Euclid's, but deduced from Hilbert's rigorous axiomatic?

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Try Robin Hartshorne's book http://www.amazon.com/Geometry-Euclid-Beyond-Robin-Hartshorne/dp/0387986502.

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Thank you so much. It helped a lot. –  m.Os Jun 4 '13 at 14:23

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