Namely rest in {alpha} is represented in {beta} by a velocity along the {alpha}-direction which is equal to the velocity along the {beta}-direction in {alpha} which represents rest in {beta}.
Finally the sixth axiom of congruence is that the relation of congruence is transitive.

So far as this axiom applies to space, it is superfluous.
For the property follows from our previous axioms.

It is however necessary for time as a supplement to the axiom of kinetic symmetry.

The meaning of the axiom is that if the time-unit of system {alpha} is congruent to the time-unit of system {beta}, and the time-unit of system {beta} is congruent to the time-unit of system {gamma}, then the time-units of {alpha} and {gamma} are also congruent.
By means of these axioms formulae for the transformation of measurements made in one time-system to measurements of the same facts of nature made in another time-system can be deduced.

These formulae will be found to involve one arbitrary constant which I will call k.
It is of the dimensions of the square of a velocity.