  The formulas for the 3-dimensional distance and the velocity modulus in the
4-dimensional linear space with the Berwald-Moor metrics are obtained. The used
algorithm is applicable both for the Minkowski space and for the arbitrary
poly-linear Finsler space in which the time-like component could be chosen. The
constructed here modulus of the 3-dimensional velocity in the space with the
Berwald-Moor metrics coincides with the corresponding expression in the
Galilean space at small (non-relativistic) velocities, while at maximal
velocities, i.e. for the world lines lying on the surface of the cone of
future, this modulus is equal to unity. To construct the 3-dimensional
distance, the notion of the surface of the relative simultaneity is used which
is analogous to the corresponding speculations in special relativity. The
formulas for the velocity transformation when one pass from one inertial frame
to another are obtained. In case when both velocities are directed along one of
the three selected straight lines, the obtained relations coincide with the
analogous relations of special relativity, but they differ in other cases.
Besides, the expressions for the transformations that play the same role as
Lorentz transformations in the Minkowski space are obtained. It was found that
if the three space coordinate axis are straight lines along which the
velocities are added as in special relativity, then taking the velocity of the
new inertial frame collinear to the one of these coordinate axis, one can see
that the transformation of this coordinate and time coordinate coincide with
Lorentz transformations, while the transformations of the two transversal
coordinates differ from the corresponding Lorentz transformations.
