Geometria et Geometriae. E mathematica ad philosopiam

Abstract

This article was written to demonstrate the meaning of Euclidean and non-Euclidean geometries as well as their ap-plications and their philosophical foundations. Nevertheless, not only do I refer to the mathematical conditions according to new geometries, but also to the philosophical aims. There are many different positions on the philosophical foundations of the different metrics. There are also very important formulations, from gnoseology to ontology, on the extensions of the higher geometry.