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.

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet.

What if applet does not run?

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