The spherical geometry thought that in the surface does not have the parallel line, actually this idea is wrong, should say: In the spherical surface does not have the straight line parallel line, but in the spherical surface has the curve parallel line.
Is very actually good about the curve parallel concept understood. If we acknowledge any thing own and oneself always parallel, then we can not but acknowledge that the curve and the curve are also parallel. For instance a straight line, it own and oneself is parallel. Similarly, a circle, it own and oneself is also parallel. Therefore the curve and the curve are may mutually parallel.
In the spherical surface, the latitude parallel is mutually parallel. Therefore may not remove the parallel postulation in the spherical surface.
What is the parallel essence? The parallel essence is the distance maintains invariable. The curve parallel definition is, if two curve's distances maintain invariable, then these two curves are parallel. In curve parallel, does not intersect was not equal to that is parallel. ======= In the analytic geometry, Supposition the straight line L1 equation is y=kx, the straight line L2 equation is y=kx+c,
then L1?L2 is parallel, if reduces c, then still L1?L2. When c=0, L1 and L2 superposition, still L1?L2, if L1 and L2 not parallel, then L1 and L2 will not superpose, will intersect. Therefore the straight line own and oneself is parallel, otherwise the straight line will not be a straight line, will intersect. The curve is also so, the curve is also own and own parallel, therefore the curve is also may mutually parallel.