On the proof of the Π-theorem in dimension theory

The 100-year anniversary of the proof of one of the brightest and most universal theorems in mechanics and physics, the Π-theorem in dimension theory is approaching. In connection with this anniversary, it is of interest to trace the main chronological stages in the mid nineteenth and early twentieth centuries concerning the understanding and proof of the Π-theorem treated both as a purely mathematical assertion and from the point of view of physics and the theory of experiment. Below we reproduce and comment out these stages.