A New Construction of Holditch Theorem for Homothetic Motions in

Table 1

Nine Cayley-Klein geometries in the plane.

		Measure of length
		Elliptic	Parabolic	Hyperbolic
Measure of angles	Elliptic	Elliptic geometry	Euclidean geometry	Hyperbolic geometry
	Parabolic (Euclidean)	Co-Euclidean geometry	Galilean geometry	Co-Minkowskian geometry
	Hyperbolic	Cohyperbolic geometry	Minkowskian geometry	Doubly hyperbolic geometry