THE ANCIENT-GREEK SPECIAL PROBLEMS, AS THE QUANTIZATION MOULDS OF SPACES.

Abstract

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. [39-41]

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 consistentnon - 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] , Antispace [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 =   m = 0 m , which is nothing  and zero space .[43-46] -The Geometrical solution of  the Special Problems is now presented.