Hilbert's Forgotten Equation of Velocity Dependent Acceleration in a Gravitational Field

The principle of equivalence is used to argue that the known law of decreasing acceleration for high speed motion, in a low acceleration regime, produces the same result as found for a weak gravitational field, with subsequent implications for stronger fields. This result coincides with Hilbert's little explored equation of 1917, regarding the velocity dependence of acceleration under gravity. We derive this result, from first principles exploiting the principle of equivalence, without need for the full general theory of relativity.