Waterman Physics

Mathematical logic of the Galilean equation x' = xvt challenged... where x = distance and (x,y,z) = a point  
Given Cartesian coordinate system S(x,y,z), the abscissa x mathematically means the lineal distance along the x axis from S(0,0,0) to S(x,0,0). Given Cartesian coordinate system S'(x',y',z'), the abscissa x' mathematically means the lineal distance along the x' axis from S'(0,0,0) to S'(x',0,0).  
Given that the abscissa x of S equals the abscissa x' of S'; [x' = x] when both systems are coincident, then it is true, that should either system be moved from that coincidence a distance equal to vt, that the abscissa of S = abscissa of S'; [x' = x], therefore [the Galilean transformation equation abscissa of x' = abscissa of x vt is incorrect]. Noting too that S'(x',y',z') = S(xvt,y,z) is true. 
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