Quadri-Figures in Cayley-Klein Planes: All Around the Newton Line

Abstract

The Newton line and the associated theorems by Newton and Gauss for tetragons and quadrilaterals are closely linked to some other theorems of Euclidean geometry: a theorem by Bocher on the existence of a nine-point conic of a quadrangle, a theorem by Shatunov and Tokarev, and a theorem by Anne. This paper examines to which extent all these theorems can be transferred to other metric planes, in particular the elliptic and hyperbolic planes.