The Zermelo-Fraenkel axioms with the axiom of choice (ZFC) are nowadays by many considered as the foundation for contemporary mathematics, and according to several mathematicians all mathematics is a logical consequence of this type of set theory.
For example, the Peano axioms for the natural numbers can be constructed from Zermelo-Fraenkel set theory and deriving classical subjects in mathematics from Peano's axioms is well-known.
I was wondering whether Euclidean geometry can also be constructed from Zermelo-Fraenkel set theory. To be more precise: can Hilbert's axioms for geometry be derived from Zermelo-Fraenkel set theory in a similar fashion as Peano's axioms? I would think this is possible since Zermelo-Fraenkel set theory is, as already mentioned above, considered as the basis of all extant mathematics, but I never came across such a derivation.
Any comment is appreciated.