Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Are there books or article that develop (or sketch the main points) of Euclidean geometry without fudging the hard parts such as angle measure, but might at times use coordinates, calculus or other means so as to maintain rigor or avoid the detail involved in Hilbert-type axiomatizations?

I am aware of Hilbert's foundations and the book by Moise. I was wondering if there is anything more modern that tries to stay (mostly) in the tradition of synthetic geometry.

share|cite|improve this question

3 Answers 3

up vote 3 down vote accepted

You might look at Hartshorne's Geometry: Euclid and Beyond.

share|cite|improve this answer

There are some axioms systems such as Birkoff axioms which assume the existence of a field from the beginning.

For the synthetic approach the main axiom systems are those of Hilbert and Tarski.

You can also use Tarski's axiom as described in W. Schwabhäuser, W Szmielew, A. Tarski, Metamathematische Methoden in der Geometrie.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.