 Projective geometry incorporated the other geometries in a variety of ways. Klein indicated that one may seek to add to the list of configurations, in which case the group that keeps them invariant will generally be smaller than the principal group, or one may seek to enlarge the group, in which case the class of invariant configurations will generally shrink. Klein succeeded in showing that non-Euclidean geometry arises as a sub-geometry by confining attention to the interior of a conic in projective space and to the subgroup that maps the interior of that conic to itself (see Klein 1871, 1873).