Monge's Theorem #6

After reading the article, I am aware of all the ways that Monge's Theorem can be generalized. First, Monge's Theorem is very similar to Desargues' Theorem. Desargues' Theorem applies to two triangles and the intersections of the lines through corresponding sides of the triangles. Since we have discussed Monge's Theorem in relation to dilations, this all seems to fit quite nicely. The other very interesting generalization is of Monge's Theorem to three dimensional objects. In this case, you would consider /the lines of intersection of tangent planes to spheres!! Interesting! They also addresesed the fact that the three circles of Monge's Theorem do not have to be disjoint. The circles are allowed to intersect or lie within one another. This would be an interesting thing to investigate using a Sketchpad sketch. Finally, you can also find a "collinear triple" using one external tangent and two internal ones. These are considered "oriented tangents"