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Journal for Geometry and Graphics 23 (2019), No. 2, 167--178
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

We propose a well-justified 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 cross-ratios and homogeneous coordinates of points.

Keywords: Desargues theorem, Gallucci's axiom, Pappus axiom, projective space.

MSC: 51A05; 51A20, 51A30

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