This is a question on teaching.

I am teaching at this moment a course in algebraic geometry for master students on a very basic level. Today (this was the fourth lecture) I discovered that only four out of 20 students have ever seen the definition of projective space.

I would like to ask you if you know some **nice, short notes** that explain what the projective spaces are and that give some simple but still not tautological statements about them. A nice example that comes to my mind is Desargue's theorem, but I would like to have more of such statements. Maybe there are some theorems from classical plane geometry that can be proven using projective geometry? Even though I know what is projective space for almost 20 years I find a bit hard to find a good way to introduce and motivate it...