Note 106 — Introductory material

The distinction between various points, then, is not a result, but a condition, of the projective coordinate system. The coordinate system is a wholly extraneous, and merely convenient, set of marks, which in no way touches the essence of projective Geometry. What we must begin with, in this domain, is the possibility of distinguishing various points from one another. This may be designated, with Veronese, as the first axiom of Geometry[119]. How we are to define a point, and how we distinguish it from other points, is for the moment irrelevant; for here we only wish to discover the nature of projective Geometry, and the kind of properties which it uses and demonstrates. How, and with what justification, it uses and demonstrates them, we will discuss later.