the narrower sense) had to be replaced by a more general theory that contains the former as a limiting case" [9]. But the extended theory of relativity, constructed by Einstein, could not embrace the general case of extended gravity. However, with the geometric power of Absolute Differential Calculus Einstein reached in the equations the general covariance that he presented to the final as the realization of the general principle of relativity supposedly encompassing the general case of extended gravity. Einstein highlights the independence of the guv of the choice of the spacetime coordinates xv although in function of the xv but which are determined by the physical process happenings in all of the rest of the universe according to named principle of Mach (principle of Einstein really becauseEinstein in front of the hard competition, between July and November of 1915, with the best germane mathematician of the epoch David Hilbert; which working similar equations, threatened with overcoming him. On November 18 of 1915, Einstein with the previous collaboration of his friend Besso had coincided, using his new general covariant equations, with the correct calculi of the then anomalous orbit of Mercury. Thus, his limited covariance, imperative for save gravitational field with stress-energy, was abandon although the principal cause was which under it the equations failed in the Newton s limit. Therefore, now his new updated equations were working but the theory no. The competition of Einstein with Hilbert was turned critic; on final they interchanged letters almost daily. In this desperate scenery was adopted definitely