>>12514824The interesting thing about the parallel postulate is not whether it applies to spheres or whatever, but whether it can be proven to follow necessarily from prior concepts (like the concepts of point, line, plane, angularity, etc.). Of course, (the hints in the name) Euclid thought that it was something the geometrician had to take up axiomatically. That did not stop many in the history of maths to try to prove it.
You are probably thinking too physically about it... Mathematics is interested in formal proofs starting from mathematical principles. So we can't just "look at a sphere" and move on.
>>12515024Euclid was very likely aware that it "didn't apply" to the surfaces of spheres etc., just as much the rest of classic Euclidean geometry does not apply to spheres, etc.
