 The fundamental geometry was real projective geometry, say in two dimensions. In this geometry the space is real projective space, and the group is the group of all projective transformations. Such a transformation maps points to points, lines to lines, curves of degree \(n\) to curves of degree \(n\), and, importantly, the cross-ratio of four collinear points is left unaltered by any projective transformation. In the Kleinian viewpoint, this establishes that points, lines, curves of degree \(n\), and the cross-ratio of four collinear points are properties of the geometry.