Generally Pappus theorem implies Desargues'. The theory is far from being complete not in logical but in philosophical and even aesthetics meaning. Why this incidence identities looks so beautiful? :) Also what about combinatorics of say free or ... projective or ... submodules of free module over the ring? noncommutative? (there was some old activity on this subject) What about combinatorics of geodesic surfaces in nice Rimanien manifold etc etc...

Pappus theorem implies Desargues'. The theory is far from being complete, not in the logical but in the philosophical and even aesthetic sense. Why do these incidence identities look so beautiful? :) Also what about combinatorics of, say, free or projective or some other submodules of the free module over the ring? noncommutative? (There was some old activity on this subject.) What about combinatorics of geodesic surfaces in nice Riemannian manifolds, and so on?