Abstract

3.1

A divisible semiplane (or elliptic semiplane) S is a set of points P , a set of lines L , and an incidence relation beteween P and L such that:

Every line is incident with k points, and dually, every point is incident with k lines.

Any two distinct points are incident with at most one line, and dually, any two distinct lines have at most one point in common.

If a point p and a line L are not incident, then there exists at most one line incident with p and parallel to L, and dually, there exists at most one point incident with L and noncollinear with p.