Der Satz von v. Staudt-Schleiermacher in Minkowski-Ebenen

Abstract

Let\(M\) be a Minkowski-(incidence-)plane and let\(\Pi _f M\) be the group of “free” projectivities of\(M\), i. e. the subgroup generated by pairs of proper perspectivities with identical centers. Our theorem then asserts that\(M\) is miquelian if\(\Pi _f M\) satisfies condition (P5), i. e. every free projectivity with 5 fixed points is the identity. But first a lemma is shown, which holds in Mobius- and Laguerre-(incidence-)planes too: if\(\Pi _f M\) fulfills (P5), then every affine derivation of\(M\) is pappian.