The analytic approach relies on a powerful new model of our geometry of points and lines. It is known as RP², the real projective plane.
We need a convenient notation for referring to the points of RP² -- in other words, a way to refer to lines through the origin in R³.
Let's apply homogeneous coordinates to give a simple proof of the Vanishing Point Theorem from Chapter One.
Homogeneous coordinates also give a neat way to compute the projective line determined by two projective points. And also the projective point determined by two projective lines.