Desargues' theorem with LiveGraphics3D

Two triangles are perspective from a line if the extensions of their three pairs of corresponding sides meet in collinear
points. The line joining these points is called the perspective axis.
Two triangles are perspective from a point if their three pairs of corresponding vertices are joined by lines which meet in a point of concurrence. This point is called the perspective centre.
Desargues' theorem guarantees that if two triangles are perspective from a point, they are perspective from a line (and if they are perspective from a line, they are perspective from a point).

If we consider the Desargues' configuration as a 3D image, the proof of the theorem becomes obvious.


Desargues' theorem is a projective theorem : it remains true when the configuration is viewed in perspective : by moving the perspective centre, a point or the perspective line may be "send to the infinity" (we then get special cases with parallel lines... whose intersection point is on "the line at infinity").