Geometria euclidiana, postulados e as geometrias não euclidianas

Abstract

This monograph has as its theme Euclidean geometries, a work discussed, but in the historical part of these geometries, using Euclidean geometry and hyperbolic geometries as a foundation, and we will address elliptic and spherical geometry as a single geometry. About Euclid's geometry, we will see historical moments and also its theoretical foundations to develop this famous geometry, we will also see the history of the emergence and what caused the creation of new non-Euclidean geometries or geometries, based on the translation of the book by the author. Euclid by BICUDO (2009), we will study each proposition, postulates and common notions to further study the famous fifth postulate (the parallel postulate) and its consequences during the history and for the lives of many mathematicians. And about non-Euclidean geometries, we will discuss the emergence of each of them, their foundations, consequences and their applications in the field of metaphysics and the theory of relativity, etc. This monograph will work the historical part of these geometries will not have a theoretical deepening about.