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Because of Geometers scarcity, I was instigated to republish this article and to locate the weakness of proving this Axiom. Weakness created the Non-Euclid geometries which deviated GR in Space-time confinement, so, not conceiving the beyond Plancks existence, not explaining the WHY speed of light is constant, and thus the whole universe. In the manuscript it is proved that parallel postulate is only in Plane (three points only and not a Spherical triangle ) based on the four Postulates for Constructions, and now is proved to be a Theorem, where all properties of Euclidean geometry compactly...

The Special Problems of E-geometry consist the Mould of Quantization, to become Monads of Space Anti-Space as Material Dipole or Conductor in Monad-Structures The One Line-Vector = Conductor AB is of 2 M-Points or 4 Positions, where A Position is Electric motion , and B Position is Magnetic Rest, , motion as Wave or disturbance = vibration that carries Energy = Stress and Travels from A to B. This Motion as Stress Due to Screw Torsion onto Geometry-[MPM]-Mechanism where The 2-Vector, |+|,|-|, of 3-Poles carrie motion through Position Z from A to B, into an Changeable Rotating Squares-System...