Note 103 — Introductory material

We have good ground for expecting, therefore, that the axioms of projective Geometry will be the simplest and most complete expression of the indispensable requisites of any geometrical reasoning: and this expectation, I hope, will not be disappointed. Projective Geometry, in so far as it deals only with the properties common to all spaces, will be found, if I am not mistaken, to be wholly à priori, to take nothing from experience, and to have, like Arithmetic, a creature of the pure intellect for its object. If this be so, it is that branch of pure mathematics which Grassmann, in his Ausdehnungslehre of 1844, felt to be possible, and endeavoured, in a brilliant failure, to construct without any appeal to the space of intuition.