# Coxeter- Figure 2.5A - Theorem 2.51

- Author:
- Pinyi Yao

- Topic:
- Geometry

A harmonic set of four collinear points may be defined to be the special case of a quadrangular set when the line g joins two diagonal points (being point A and point B in the figure) of the quadrangle. Because of the importance of this special case, we write the relation (AA)(BB)(CF) in the abbreviated form H(AB,CF), which evidently has the same meaning as H(BA,CF) or H(AB,FC) or H(BA,FC). We call F the harmonic conjugate of C with respect to A and B. Theorem 2.51: If A,B,C are all distinct, the relation H(AB,CF) implies that F is distinct from C.