A theorem on harmonic homologies

A collineation is a one-one mapping of a projective plane onto itself, taking points into points, lines into lines and preserving incidence. ([1], p.247). A perspective collineation (sometimes called a central collineation) is a collineation which leaves invariant all points on a line h called the axis, and all lines through a point H called the centre. The perspective collineation is an elation if H is incident with h; otherwise it is a homology.