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.
|No.||Title and link|
|1.||Cross ratio. Harmonic conjugates. Perspectivity. Projectivity|
|3.||Theorems of Pappus and Pascal|
|4.||Pole. Polar. Theorems of Brianchon and Brokard|