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I'm reading a book on an introduction to non-Euclidean geometry, and it starts off with the usual Euclidean geometry. I didn't really need a line to be defined in that case, since it's obvious, but now that the parallel postulate has been replaced and we are working with non-Euclidean geometry, I'm not sure how to connect two points. The author hasn't mentioned a straight line being a geodesic, which is what I assume it would be, he is just proving stuff based on the first four of Euclid's postulates, and the new fifth one. Can you deduce what a line is based on that alone?