### Abstract

We formalize the basics of projective geometry. In particular, we give
a proof of the so-called Hessenberg's theorem in projective plane
geometry. We also provide a proof of the so-called Desargues's
theorem based on an axiomatization of (higher) projective space
geometry using the notion of rank of a matroid. This last approach
allows to handle incidence relations in an homogeneous way dealing
only with points and without the need of talking explicitly about
lines, planes or any higher entity.

BSD License