# Projective Geometry

Milivoje Lukiæ

## 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

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