Heron Alexandrinus, Mechanica, 1999

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    <archimedes>
      <text>
        <body>
          <chap n="1">
            <pb n="27">
              <s id="A18-1.27.01">[27] If that is so, then we assume the supports <ab> and <gd> in equal positions; </s>
              <s id="A18-1.27.02">let an evenly thick and heavy body rest on them, namely <ag>.</s>
              <s id="A18-1.27.03">We just said that half the weight of <ag> falls to each of the two supports <ab> and <gd>.</s>
              <s id="A18-1.27.04">If we now move support <gd> and bring it closer to <ab>, namely to position <ez>, then we want to know which of the weight falls to <ab> and <ez>.</s>
              <s id="A18-1.27.05">Now we say that distance <ae> is either equal to distance <eg> or smaller or greater than it.</s>
              <s id="A18-1.27.06">Let it first be equal to it, then we see that the weight of <ae> keeps the balance of the weight of <eg>.</s>
              <s id="A18-1.27.07">Thus if we remove the support <ab>, the weight <ab> remains steadily in its position and we see that none of the weight fell to support <ab>, but the weight <ag> was only on <ez>.</s>
              <s id="A18-1.27.08">If now distance <ge> is greater than distance <ea>, then the load inclines towards <g>.</s>
              <s id="A18-1.27.09">Let now the space <ge> be smaller than space <ea> and let <ge> equal <eh>, then <gh> remains balanced on <ez> alone.</s>
              <s id="A18-1.27.10">If we now put in a pillar at <h>, then, if we imagine the entire load cut at point <h>, <hg> rests on <ez> alone and half of <ah> rests on each of the two supports <ag> and <hq>.</s>
              <s id="A18-1.27.11">If we now remove support <hq>, point <h> obtains its force, if the body is joined, and to <ab> falls half the weight of <ha>, to <ez> the rest, namely <gh> and half of <ah>; if we imagine <ag> bisected at point <k>, then <ke> is half of <ah>.</s>
              <s id="A18-1.27.12">If now the support that was first at <e> moves under point <k>, then it is affected by the entire weight of <ag>.</s>
              <s id="A18-1.27.13">And the further the support moves away from the point of intersection which divides the load in half, the more of the load goes to <ab>, while the rest of it rests on the other support.</s>
            </pb>
          </chap>
        </body>
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    </archimedes>