Abstract From [40]–The Special Problems of Euclidean Geometry [47] consist the, Moulds of Quantization, of E-Geometry in it, to become → Monad, through mould of Space – Anti-space in itself , which is the material dipole in inner monad Structure and which is identical with the Electromagnetic cycloidal field → Linearly through the mould of the 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 monad-Vectors consist a Plane acquiring the common Plane-meter, π, → and in Space (volume) through mould of the Duplication of the Cube [46] , where any two Unequal Perpendicular monads acquire the common Space-meter ³√2 , to be twice each other , as analytically all methods are Proved and explained . [44-47] 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 the Material Dipoles in inner monad Structures i.e. , the innate 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 no one 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 Postulates , in order that none of them contradicts any of the other Postulates . It was Proved [39] , that the only Space - Energy Geometry is Euclidean , agreeing with the Physical reality , on unit AB ≡ Segment ≡ Vector which is The Electromagnetic field of the Quantized on AB Energy Space Vector of Angular Momentum = Spin , 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 in Planck’s cavity .Euclidean Geometry elucidated the definitions of its geometry-content , i.e. { [ Point , Segment , Straight Line , Plane , Volume , Space [S] , Anti-space [AS] , Sub-space [SS] , Cave , The 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 , in Gravity field [MFMF] Particles } and describes the Space-Energy vacuum by Planck’s length level [ Gravity’s Length 3,969·10⁻⁶² m ] , reaching the absolute Point = Lᵥ = ε (iNτh)ᵝ = 10⁻ᴺ = ∞ m , which is nothing , and the Absolute Primary Neutral Space [PNS] = cave [ r = 10⁻³⁵ ~ 10⁻⁶² m [43-46] . In Mechanics , The Gravity-cave Energy Volume quantity | c̅ | = [wr] is doubled , and is Quantized in Planck’s cave Space quantity (h/2π) = The Spin = 2.[wr]³ → i.e. Energy Space quantity [wr] is Quantized , doubled , and becomes the Space quantity h/π following Euclidean Space-mould of Duplication of the cube , in Sphere volume V = (4π/3).[wr]³ and follows the Squaring of the circle π , and in Sub-Space-Sphere volume ³√2 , as Trisection . In article [123] , are given on the 2-Vectors , 3-Poles Rotating Squares Mechanism , such the Geometrical as the Mechanical Proof , by using the Conjugate circles of Polhode and Herpolhode which consist the Spin of Photons and which is their motion . The frequency needed for the velocity vector c̅ to rotate , is used the Kepler’s Unit of Time k = f²e a³ , where a = λ / 2 , and which is the clock measuring the changes of motions.