Perspective (geometry)

Although stated here for figures in a plane, the concept is easily extended to higher dimensions.

A dual transformation, taking all the lines through a point (a pencil) to another pencil by means of an axis of perspectivity is called an axial perspectivity.

[2] An important special case occurs when the figures are triangles.

[4] Desargues' theorem states that a central couple of triangles is axial.

The converse statement, that an axial couple of triangles is central, is equivalent (either can be used to prove the other).