WildTrig33: Projective geometry and homogeneous coordinates

I've read about the homogeneous coordinates in three different books. But in this video, in 8 minutes, I've understood much moore. Thank you very much!

I'm new to projective geometry. In fact, I have no geometry knowledge whatsoever. Could you suggest a text book that I could buy that would explain projective geometry from an elementary level? I'm also interested in videos and I'm greatly appreciative of the ones you've posted thus far on projective geometry.

... the "jump" to argumentation that horizontal lines are points of infinity confused me. I assume, but am not sure, this is because x/0 and y/0 is indeterminate/infinity?.

More confusing is that there is a horizontal line for every family of parallel lines in a Cartesion plane.Your discussion explained points in the cartesian plane therefore I do not understand where the idea of family of parallel in cartesion plane. Are these simply the same parallel lines from your 2D introduction?

Yes, that is it exactly! As with most really important mathematical ideas, it is surprisingly simple once you get it.

OK, I get it. The projective plane was viewed as R2 + the points at infinity. With this new construction every point of the PP is represented by a line. Horizontal lines represent points at infinity and the others represent the ordinary point that are situated where they meet the plane
z=1