Projective geometry (Table of contents)

Desargue's Theorem

The triangles \(A_1B_1C_1\) and \(A_2B_2C_2\) are perspective with respect to a center if the lines \(A_1A_2\), \(B_1B_2\), and \(C_1C_2\) are concurrent. They are perspective with respect to an axis if the points \(K=B_1C_1\cap B_2C_2\), \(L=A_1C_1\cap A_2C_2\), \(M=A_1B_1\cap A_2B_2\) are colinear.

Theorem 3 (Desargue's theorem) Two triangles are perspective with respect to a center if and only if they are perspective with respect to a point.