Editing Projective geometry (section)

=== Whitehead's axioms ===
These axioms are based on [[Alfred North Whitehead|Whitehead]], "The Axioms of Projective Geometry". There are two types, points and lines, and one "incidence" relation between points and lines. The three axioms are:
* G1: Every line contains at least 3 points
* G2: Every two distinct points, A and B, lie on a unique line, AB.
* G3: If lines AB and CD intersect, then so do lines AC and BD (where it is assumed that A and D are distinct from B and C).

The reason each line is assumed to contain at least 3 points is to eliminate some degenerate cases. The spaces satisfying these
three axioms either have at most one line, or are projective spaces of some dimension over a [[division ring]], or are [[non-Desarguesian plane]]s.