  Action at distance in Newtonian physics is replaced by finite propagation
speeds in classical post--Newtonian physics. As a result, the differential
equations of motion in Newtonian physics are replaced by functional
differential equations, where the delay associated with the finite propagation
speed is taken into account. Newtonian equations of motion, with
post--Newtonian corrections, are often used to approximate the functional
differential equations. In ``On the origin of quantum mechanics'', preprint,
physics/0505181, May 2005, a simple atomic model based on a functional
differential equation which reproduces the quantized Bohr atomic model was
presented. The unique assumption was that the electrodynamic interaction has a
finite propagation speed. In ``On the origin of the gravitational quantization:
The Titius--Bode Law'', preprint, physics/0507072, Jul 2005, a simple
gravitational model based on a functional differential equation which gives a
gravitational quantification and an explanation of the modified Titius--Bode
law is described. In ``On the origin of the anomalous precession of Mercury's
perihelion'', preprint, physics/0510086, Oct 2005, an explanation of the
anomalous precession of Mercury's perihelion is given in terms of a simple
retarded potential, which, at first order, coincides with Gerber's potential of
1898, and which agrees with the author's previous works. In this paper, it is
shown how the simple retarded potential presented in physics/0510086 also gives
the correct value of the gravitational deflection of fast particles of General
Relativity.
