  It is shown that for a relativistic particle moving in an electromagnetic
field its equations of motion written in a form of the second law of Newton can
be reduced with the help of elementary operations to the Hamilton-Jacobi
equation. The derivation is based on a possibility of transforming the equation
of motion to a completely antisymmetric form. Moreover, by perturbing the
Hamilton-Jacobi equation we obtain the principle of least action.\
  The analogous procedure is easily extended to a general relativistic motion
of a charged relativistic particle in an electromagnetic field. It sis also
shown that the special-relativistic Hamilton-Jacobi equation for a free
particle allows one to easily demonstrate the wave-particle duality inherent to
this equation and, in addition, to obtain the operators of the four-momentum
whose eigenvalues are the classical four-momentum
