Postulates that Euclid neglected to mention?

[LeonhardEuler]

Out of curiosity, I was recently reading through Euclid's Elements online (http://aleph0.clarku.edu/~djoyce/java/elements/elements.html" )

My question is, is this the general opinion of all mathematicians? Also, has anyone tried to fix this problem, and how many more postulates would they need? I'm really surprised because I thought for a long time that only those 5 postulates were needed to axiomize Euclidean geometry.

 

[Martin Rattigan]

It's generally accepted. Hilbert pretty much fixed it. See Foundations of Geometry, D. Hilbert (trans. L. Unger), Open Court Publ.

 

[LeonhardEuler]

Thanks a lot, I'll do that!