I was just doing some reading about elliptical geometry and came across a problem. I've read that this type of geometry is pretty much based off the 'rejection' of Euclid's fifth postulate where instead of having one parallel line, you don't have any and this can be pictured by two 'great circles' intersecting on a sphere. My question is why do these two lines have to be 'great circles'. I mean, it's possible for two lines to be drawn on the sphere without touching each other at all - i.e. making it parallel. So, I don't really understand the explanation in which my book / other internet sources are saying ... Thanks in advance.