Geodesic
The Theorem of Gallucci Revisited
Journal for geometry and graphics, Tome 23 (2019) no. 2, pp. 167-178 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 51A05, 51A20, 51A30
Mots-clés : Desargues theorem, Gallucci's axiom, Pappus axiom, projective space 
@article{JGG_2019_23_2_JGG_2019_23_2_a2,
     author = {A. G. Horv\'ath },
     title = {The {Theorem} of {Gallucci} {Revisited}},
     journal = {Journal for geometry and graphics},
     pages = {167--178},
     year = {2019},
     volume = {23},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2019_23_2_JGG_2019_23_2_a2/}
}
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A. G. Horváth . The Theorem of Gallucci Revisited. Journal for geometry and graphics, Tome 23 (2019) no. 2, pp. 167-178. http://geodesic.mathdoc.fr/item/JGG_2019_23_2_JGG_2019_23_2_a2/