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It is shown that, given choices of units and of synchronization in the moving systems which are independent of the time and space coordinates, the linearity of the transformation equations connecting uniformly moving reference systems is a consequence of the fact that the functions deciding the behaviour of moving bodies and clocks are independent of the time and space coordinates ("homogeneity of time and space").

On the Linearity of Certain Coordinate Transformations Including the Lorentz Transformation