Pappus's Theorem	Take any 2 lines and choose 3 points on each. Taking the points four at a time, two from each line, find the point where the diagonals intersect. The three such points are collinear.
Desargues's Theorem	Two triangles have corresponding vertices as projections of each other from one point. Find the 3 points where corresponding sides intersect. The 3 points are collinear.