Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="043/01/050.jpg" pagenum="42"/>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XX.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Omnis trapezij habentis duo latera parallela
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              centrum grauitatis eſt in illa recta, quæ prædi­
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              ctorum bipartitorum laterum ſectiones iungit.
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              </s>
              <s>atque in eo puncto, in quo tertia pars eius media
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              ſic diuiditur, vt ſegmentum propinquius mino­
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              ri parallelarum ad reliquum eam proportionem
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              habeat, quam maior parallelarum ad minorem.
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              </s>
              <s>Talis autem rectæ lineæ ſic diuiſæ, ſegmentum
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              minorem parallelarum attingens eſt ad reliquum,
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              vt dupla maioris parallelarum vna cum minori,
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              ad duplam minoris vna cum maiori. </s>
            </p>
            <p type="main">
              <s>Sit trapezium ABCD, cuius duæ AD, BC, ſint pa­
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              rallelæ: ſitque AD, maior. </s>
              <s>Sectiſque AD, BC, bifa­
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              riam in punctis F, E,
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              iunctaque EF, & ſe­
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              cta in tres partes æ­
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              quales in punctis K,
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              H, fiat vt AD, ad
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              BC, ita HG, ad GK.
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              </s>
              <s>Dico G, eſse centrum
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              grauitatis trapezij A
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              BCD: & vt eſt du­
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              pla ipſius AD, vna
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              cum BC, ad duplam
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              ipſius BC, vna cum
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              AD, ita eſse EG, ad
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                <figure id="id.043.01.050.1.jpg" xlink:href="043/01/050/1.jpg" number="29"/>
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              GF. </s>
              <s>Ducta enim per punctum H, ipſis AD, BC, pa-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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