The fourth dimension: from its spatial nature in Euclidean geometry to a time-like component of non-Euclidean manifolds

A quarta dimensão: da sua natureza espacial na geometria euclidiana à componente tipo tempo de variedades não euclidianas

In this article, the evolution of the ideas about the fourth spatial dimension is presented, starting from those which come out within classical Euclidean geometry and going through those arose in the framework of non-Euclidean geometries, like those of Riemann and Minkowski. Particular attention is given to the moment when real time is effectively considered as a fourth dimension, as introduced by Einstein.

Keywords
Fourth Dimension; Space; non-Euclidian Geometry; History of Geometry; History of Physics