In this paper we discuss, from a historical and philosophical point of view,
a variation of the meaning of the five postulates in Euclidean Geometry and we
make a short reference to D. Hilberts formalism. We examine, throughout the
ages, the question what is Geometry by studying the segmentation and the
unification of various geometries, been introduced by F. Kleins Erlangen
Program. We concisely present three out of nine Cayley-Klein geometries and
then we conclude with some didactic perspectives.Comment: 20 pages, in Greek languag