Here all demonstration is lacking in the form of any coherent theory.

According to the theory of these lectures the axes to which motion is to be referred are axes at rest in the space of some time-system.

For example, consider the space of a time-system {alpha}.
There are sets of axes at rest in the space of {alpha}.

These are suitable dynamical axes.

Also a set of axes in this space which is moving with uniform velocity without rotation is another suitable set.
All the moving points fixed in these moving axes are really tracing out parallel lines with one uniform velocity.