Saccheri's Rectilinear Quadrilaterals

2013/08/11 by Prodromos Filippidis, Filippidis, Prodromos
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #History and Overview (math.HO) #Mathematics and Applications #Robotic Mechanisms and Dynamics

paper · pdf · doi:10.48550/arxiv.1308.2419

openalex publication_date 2013/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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