The Third Epoch

1. The beginning of this period is marked by a change in point of view that is rather abrupt by earlier standards. In less than 25 years, starting from the publi cation of Monge’s Géométrie ( 1795) and owing to the work of Monge’s school, especially of Poncelet, a tremendous expansion of all geometric concepts occurs with the systematic introduction of points at infinity and imaginary points. The movement is so successful that, for close to 100 years, “geometry” will mean the geometry of the complex projective plane P₂ (C) or of complex projective three- space P₃ (C).