Consequences of a generalized law of the lever

We discuss the controversy about the demonstration of the law of the lever as given by Archimedes. One aspect of the discussion concentrates on the meaning of the postulates which he utilized. We analyze what consequences would arise if nature behaved in such a way that the lever followed a generalized power law. In particular, we consider the cases of a torque independent of the distances of the bodies to the fulcrum, proportional to these distances, and quadratic in the distances.