I was reading "Relativity" by Albert Einstein. In chapter 5 page 14, it is written that
If K is a Galilean co-ordinate system, then every other co-ordinate system K' is a Galileian one, when, in relation to K, it is in a condition of uniform motion of translation. Relative to K' the mechanical laws of Galilei-Newton hold good exactly as they do with respect to K.
We advance one step farther in our generation when we express the tenet thus: if, relative to K, K' is a uniformly moving co-ordinate system devoid of rotation, then natural phenomenon run there course with respect to K' according to exactly the same general laws as with respect to K. This Statement is called principle of relativity (in restricted sense).
This generalization is not obvious, well... At least for me. Are there some underlying principles which are used to derive or deduce this principle? moreover how such a generalization can be made(it is not that simple ... Is, it?) ?