Lagrange equation of motion for a single point ( Primary Point A is the only Space ) , states that this point must move from the Initial Position A to another position say B . This Equilibrium for points A and B , presupposes in Mechanics the Principle of Virtual Displacements and the work done is W = ∫ P.ds = 0 , or when ds = distance AB then → [ ds .( PA + P B ) = 0 ] ...(1).. From Equation (1) are self created all the Spaces [S] the equilibrium Anti-Spaces [AS] and the Sub-Spaces [SS] with infinite points in them and with a finite work on it . Monad dš (dipole AB) is a complex number of type [ dš = z = x+i.y ] ..(1a) representing the real part (x) , the distance AB , and imaginary parts (i.y) which is the work of …(1) . Complex number , z , the first dimentional unit AB , is such that either repeated by itself as monad ( z• = z.z.z.z. w-times ) or repeated times itself in monad ( ⁿ√z = z /ⁿ = z• , z/ⁿ.z/ⁿ.z/ⁿ….w = 1/n-times , or the nth roots of z equal to w = 1/n ) remains unaltered forming Spaces ( z•) , Anti-spaces( - z•) and the inversing Sub-spaces (ⁿ•z) , meaning that , unit circle is mapped on itself simultaneously on the two bases , 1 and n=1/w , where w.n = 1. This duality of coexistance on AB [ the w.th power and the n.th root of z where w.n =1 ] presupposes a common base ,m, which creates this unit polynomial exponentiation . Analysing this exponentiation according to one of the four basic properties of logs then becomes → log.w(1= w.n) = log.w(w)+log.w(n=1/w) = 1+1/w = 1+ n and it is the base of natural logarithms e and since 1= w.n then → ( 1+ n )• = (1+1/w)• = constant = m = e ← ....(2) Since the first dimentional unit AB is a complex number with many imaginary parts (and this because of the infinite variables) then this unit has the general type of quaternion .i.e. m^±(ª+₫.i) = q• = (Tq)•.[cos.wφ + ε.sin.wφ] ……where m = lim(1+1/w)• for w = 1→ ∞ , q = z = ± ( x+y.i ) sinφ = y/•x²+y² , cosφ = x/•x²+y² , |z| = •x²+y², Tq = • x²+y1²+y2²+ ….yn² , Ty = • y1²+y2²+ ….yn² ε = (y.i/Ty)=[y.i ] / [Ty]=(y1.a1+y2.a2+.)/(• y1²+y2²+yn²) [PNS] ↔ quaternion ↔ [ dŝ = x+i.y ] is a Vector with two components , the one x is the only Space with Scalar Potential field Φo , which is only half lengths of Space , Anti-Space , ( the longitudinal position ) , (x) → (-x) straight line connecting Space [S] , Anti-Space [AS] in [PNS] and in it exist , the initial Work , or Impulse , bounded on points which cannot be created or destroyed which is analogous to the (x) magnitude , and the other one y is the infinite local curl fields So , due to the Spin which is the intrinsic rotation of the Space and Anti-Space . Because in [S] and [AS] forces PA - PB are acting in the same straight line so moment lever is zero ( 0 ) , therefore Primary [S] and [AS] are ir-rotational and so it is possible to express this Primary field as a scalar function (Φo). This shows that [PNS] is a Space Work or Space- Spin or < Space Energy Existence > , where Time is not existing , because Φo and So are not time-varying . The same is holding also for the infinite dipole AiBi which are also complex numbers with all their properties , that of quaternions . Because quaternion properties are wrapped in lower and higher dimensions only by rotation , this is the property of spaces , so all dipole AnBn may have commons , which may bleed off in any Space , a very useful device for Quantum-mechanics . Geometrically states that , this property of commons allows to the dipole AnBn or to Spaces ↔ [ dŝ = xn+i.yn ] , to be also a Space -Time existence wrapped in the , Space-Energy Existence because of , Operation ↔ Quaternion → Notation m^±(ª+₫.i) = q• → = (Tq)•. [cos.wφ + ε.sin.wφ] Scatters , Part or all Content of the quaternion q , in all Spaces and Sub-Spaces as q• [ i.e. The duality of coexistence ↔ of the content of dŝ , from w.th power to the n.th root of q , where w.n =1 , is the measuring of , drag areas and other trapped accumulator , and by rotation to convert them in Spaces ]. An extend analysis of this unification follows in [23]