  In the new setting, the projective properties of figures can be defined unexceptionably. a one-one mapping f of projective space onto itself is a collineation if it sends any three collinear points A, B, and C, to three points (A), (B), and (C), which are collinear too. Projective properties (and relations) are those which are preserved by collineations. Here are a few examples of projective properties. Of three or more points: to lie on the same straight line; to lie on the same plane. Of three or more straight lines: to meet at the same point; to lie on the same plane. Of three or more planes: to intersect along the same straight line; to share the same point. Of curves: to be a conic. Of surfaces: to be a quadric.