  It is traditionally believed that the Lorentz transformations (LT) and
Einstein's theorem of velocity addition (ETVA), underlying special relativity,
cannot be obtained from non-relativistic (classical) mechanics. In the present
paper it is shown, however, that both the LT and the ETVA are derivable within
the framework of classical kinematics if the speeds of material points are
bounded above by a certain universal limit $c_+$ which can coincide with the
speed of light $c$ in a vacuum.
