  A curve is geodesic if and only if its tangent direction \(R\) experiences infinitesimal autoparallelism when moved  along all the points of the curve. This characterization of a  geodesic curve constitutes an abstraction from affine geometry.  Through this abstraction, a geodesic curve is definable exclusively  in terms of autoparallelism of tangent directions, and not  tangent vectors. Roughly speaking, an affine geometry is  essentially a projective geometry with the notion of distance defined along the curves. By eliminating all possible notions of distance  along curves, or equivalently, all the parameter descriptions of the  curves, one abstracts the projective geometry form affine geometry. 