Confused about Duality in Projective Geometry

[ZLife]

So I'm studying projective geometry and I'm confused about duality. In particular, I'm confused about drawing dual pictures.

If you look at Menelaus's Theorem and Ceva's Theorem, they are supposedly dual diagrams.
http://en.wikipedia.org/wiki/Menelaus'_theorem
http://en.wikipedia.org/wiki/Ceva's_theorem

In the diagram for Menelaus's theorem, there are 6 points and four lines, so that means that there are 6 lines and four points in Ceva's theorem. However, looking at Ceva's theorem, there are indeed 6 lines but there are more than 4 points, there are 7. So how can they be dual diagrams?

 

[pat_connell]

The duality between Menelaus's theorem and Ceva's theorem is not in the number of points or lines, but in the configuration of the lines and points. In Menelaus's theorem, there are three intersecting lines that form pairs of lines that share a common point, while in Ceva's theorem, the points form three intersecting lines that form pairs of points that share a common line. Thus, even though there are more than 4 points in Ceva's theorem, the diagrams remain dual since the configuration of the points and lines is the same.