Chapter III - Projective Geometry

Abstract

This chapter describes the different aspects of projective geometry. The extended plane consists of the ordinary points, the ordinary lines, the ideal points, and the ideal line. Two nonparallel ordinary lines intersect as usual in the Euclidean plane, and one do not want them to intersect again at an ideal point, and that's why one add a different ideal point to each family of parallel lines. In the Euclidean plane, any two lines intersect at a unique point, except when the lines are parallel. Parallel lines create exceptions that must be considered in Euclidean geometry. Adding ideal points to the Euclidean plane eliminates these exceptions. Any two lines in the extended plane intersect at a unique point, and two parallel ordinary lines intersect at an ideal point.