Projective Geometry

Milivoje Lukić

Abstract

Perspectivity is the projection of objects from a point. A quantity that is preserved by this map, called the cross-ratio, naturally appears in many geometrical configurations. This map and its properties are very useful in a variety of geometry problems. We study the pole of a line, polar of a point, cross ratio, perspectivity, and we prove theorems of Desargue, Pappus, Pascal, Brianchon, and Brokard.

Table of Contents

Cross ratio. Harmonic conjugates. Perspectivity. Projectivity

Dessargue\( \prime \)s theorem

Theorems of Pappus and Pascal

Pole. Polar. Theorems of Brianchon and Brokard

Problems