<s id="A18-1.32.01">[32] Some people believe that, when in scales the weights are in balance with the weights, the weights are in the inverse proportional ratio to the distances.</s>
<s id="A18-1.32.02">This must, however, not be said so in general, but one has to introduce a better distinction.</s>
<s id="A18-1.32.03">Let us now assume an evenly thick and heavy scale beam, namely <ab>, whose point of suspension, namely point <g>, lies in its center.</s>
<s id="A18-1.32.04">Let now be suspended at random points, for instance points <de>, ropes, namely the two ropes <dz> and <eh>, to which are fastened two weights and let scales after the suspension of the weights be in balance.</s>
<s id="A18-1.32.05">If we imagine the two ropes going through points <q> and <k>, then in the equilibrium of the scales the distance <qg> will relate to the distance <gk> like weight <h> to weight <z>.</s>
<s id="A18-1.32.06">Archimedes has proven this in his works with the title: Writings on Levers.</s>
<s id="A18-1.32.07">If we now cut off the scale beam the parts on each side, namely <qa> and <kb>, then the scales will no longer be in balance.</s>
