Projective Generalization of Maxwell's Theorem

Michel Cabart has observed that Maxwell's theorem is of projective nature. The projective formulation goes like this:

Assume there are two triangles ABC and MNP and two triples of points on L such that A₀, B₀, C₀ are intersections of L with sides of ΔABC and also with cevians of ΔMNP; A₁, B₁, C₁ are intersections of L with sides of ΔMNP and also with cevians of ΔABC.

Choosing the infinite line as line L gives Maxwell's theorem as a particular case.

The applet below illustrates the projective generalization. You can drag the vertices of the two triangles as well as the triangles themselves, line L and the points on that line. I must admit that the original theorem is by far the easier to illustrate.

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