It have been shown that the only Space-Energy geometry is the Euclidean, on primary and on any vector unit AB, (AB = The Quantization of points and of Energy) on the contrary to the general relativity of Space-time which is based on the rays of the non-Euclidean geometries and to the limited velocity of light. Projective, Hyperbolic and Elliptic geometry is proved to be an Extrema (deviations) in Euclidean geometry where on them Einstein's theory of general relativity is implicated and calls a segment as line and the disk as plane in physical space. In the manuscript is proved that parallel postulate is only in Plane (three points only) and is based on the four Postulates for Constructions, where all properties of Euclidean geometry compactly exist as Extrema on points, lines, planes, circles and spheres. Because nobody until now succeeded to prove the parallel postulate, many self consistent non-Euclidean geometries have been discovered based on Definitions, Axioms or Postulates, in order that non of them contradicts any of the other postulates of what actually are or mean. Although many of Euclid’s results have been stated by earlier Greek mathematicians, Euclid was the first to show how these propositions could be fit together into a comprehensive deductive and logical system self consistent. Euclid’s elements consist of assuming a small set of intuitively appealing axioms and from them, proving many other propositions (theorems).
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