Yeah, there are two equivalent definitions of a straight line, “don’t turn” and “shortest path”, both known to the ancient Greeks, I’m sure, but not formalizable in any easy way until differential calculus was invented, and not well until Riemann. Still, if someone actually asked Euclid “what do you think the closest thing to a straight line might be on a sphere, and which postulates hold there?” he would probably have done the rest.
Yeah, there are two equivalent definitions of a straight line, “don’t turn” and “shortest path”, both known to the ancient Greeks, I’m sure, but not formalizable in any easy way until differential calculus was invented, and not well until Riemann. Still, if someone actually asked Euclid “what do you think the closest thing to a straight line might be on a sphere, and which postulates hold there?” he would probably have done the rest.