Saccheri's Rectilinear Quadrilaterals
History and Overview
2016-08-03 v3
Abstract
We study Saccheri`s three hypotheses on a two right-angled isosceles quadrilateral, with a rectilinear summit side. We claim that in the Hilbert`s foundation of geometry the euclidean parallelism is a theorem, and in the h-plane the hyperbolic parallelism under a hyperbolic transformation has image the euclidean parallelism. We prove that Saccheri`s rectilinear quadrilaterals can be only rectangle. Finally we believe that the independence of the euclidean parallel postulate is just a matter of philosophy of logic.
Keywords
Cite
@article{arxiv.1308.2419,
title = {Saccheri's Rectilinear Quadrilaterals},
author = {Prodromos Filippidis},
journal= {arXiv preprint arXiv:1308.2419},
year = {2016}
}