<s id="A18-1.33.01">[33 ]Some have thought that inverse proportionality is not present in irregular scales.</s>
<s id="A18-1.33.02">Let us therefore also imagine a differently heavy and dense scale beam of any material that is in balance when it is suspended at point <g>.</s>
<s id="A18-1.33.03">Here, we understand with balance the rest and standstill of the scale beam, even if it is inclined to any side.</s>
<s id="A18-1.33.04">Then we suspend weights at random points, namely <d> and <e>, and we let the beam again be in balance after their suspension.</s>
<s id="A18-1.33.05">Now Archimedes has proven that also in this case weight to weight is inverse to distance to distance.</s>
<s id="A18-1.33.06">As now for the irregular bodies, in which the space is inclined, there we have to imagine the following:</s>
<s id="A18-1.33.07">Let the suspension string situated at point <g> be extended towards <z>.</s>
<s id="A18-1.33.08">Let us now draw a line and imagine it going through point <z> and equal to line <zhq>; let it be "solid", i.e. perpendicular to the string.</s>
<s id="A18-1.33.09">Since now the two strings situated at points <d> and <e>, namely <dh> and <eq>, are like this, then the distance that exists between line <gz> and the weight suspended at point <e> is <zq> and with the scales in rest, just as <zh> is to <zq>, so the load suspended at point <e> is to the one suspended at point <d>, which has been proven in the preceding.</s>
