
Journal for Geometry and Graphics 23 (2019), No. 2, 167178 Copyright Heldermann Verlag 2019 The Theorem of Gallucci Revisited Akos G. Horváth Dept. of Geometry, University of Technology and Economics, Egry Jozsef u. 1, 1111 Budapest, Hungary ghorvath@math.bme.hu We propose a welljustified synthetic approach to the projective space. We define the concepts of plane and space of incidence and also the statement of Gallucci as an axiom of our classical projective space. For this purpose, we deduce from our axioms the theorems of Desargues, Pappus, and the fundamental theorem of projectivities. Our approach does not use any information about analytical projective geometry like the concept of crossratios and homogeneous coordinates of points. Keywords: Desargues theorem, Gallucci's axiom, Pappus axiom, projective space. MSC: 51A05; 51A20, 51A30 [ Fulltextpdf (183 KB)] 