Coxeter- Theorem 6.22 R on OP

Author:
LexiPasi
Topic:
Geometry
6.22 A homology is determined when its center and axis and one pair of corresponding points (collinear with the center) are given. Let O be the center, o the axis, and P and P’ (collinear with O) the given corresponding points. If R coincides with O or lies on o, it is invariant. If R is on neither o or OP, R’=EP’.OR, where E=o.PR Finally, if R is on OP, we use an auxiliary pair of points Q,Q’ to obtain R’=DQ’.OP, where D=o.QR