The Ancient-Greek Special Problems, as the Quantization Moulds of Spaces

The Special Problems of E-geometry consist the , Mould Quantization , of Euclidean Geometry in it , to become → Monad , through mould of Space –Anti-space in itself , which is the material dipole in inner monad Structure as the Electromagnetic cycloidal field → Linearly , through mould of Parallel Theorem [44-45], which are the equal distances between points of parallel and line → In Plane , through mould of Squaring the circle [46] , where the two equal and perpendicular monads consist a Plane acquiring the common Plane-meter → and in Space (volume) , through mould of the Duplication of the Cube [46] , where any two Unequal perpendicular monads acquire the common Space-meter to be twice each other , as analytically all methods are proved and explained . [39-41]. The Unification of Space and Energy becomes through [STPL] Geometrical Mould Mechanism of Elements , the minimum Energy-Quanta , In monads → Particles , Anti-particles , Bosons , Gravity –Force , Gravity -Field , Photons , Dark Matter , and Dark-Energy ,consisting Material Dipoles in inner monad Structures i.e. the Electromagnetic Cycloidal Field of monads. Euclid's elements consist of assuming a small set of intuitively appealing axioms , proving many other propositions . Because nobody until [9] succeeded to prove the parallel postulate by means of pure geometric logic , many self-consistent non - Euclidean geometries have been discovered , based on Definitions , Axioms or Postulates , in order that none of them contradicts any of the other postulates . In [39] the only Space-Energy geometry is Euclidean , agreeing with the Physical reality , on unit AB = Segment which is The Electromagnetic field of the Quantized on AB Energy Space Vector , on the contrary to the General relativity of Space-time which is based on the rays of the non-Euclidean geometries to the limited velocity of light and Planck`s cavity . Euclidean geometry elucidated the definitions of geometry-content ,{ for Point , Segment , Straight Line , Plane , Volume, Space [S] , Anti-space [AS] , Sub-space [SS] , Cave, Space-Anti-Space Mechanism of the Six-Triple-Points-Line , that produces and transfers Points of Spaces , Anti-Spaces and Sub-Spaces in a Common Inertial Sub-Space and a cylinder ,Gravity field [MFMF] , Particles } and describes the Space-Energy beyond Plank´s length level [ Gravity Length 3,969.10 ̄ 62 m ] , reaching the Point = L_( v) = e^(i.(Nπ/2)b=10 ͞ N= - ∞) m = 0 m , which is nothing and zero space .[43-46] -The Geometrical solution of the Special Problems is now presented .