, the possible straight lines are decreased in number. In their aggregate they now constitute a plane, the plane passing through
and perpendicular to
.
Similar reasonings may be applied to any
-dimensional space, whether Euclidean or non-Euclidean. But if the space is non-Euclidean our straight lines, or geodesics, will be curved from the Euclidean standpoint. Hence we see that the geodesics passing through
and perpendicular at