Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="35" xlink:href="023/01/077.jpg"/>
            <p type="main">
              <s id="s.000721">Sit fruſtum ae a pyramide, quæ triangularem baſim ha­
                <lb/>
              beat abſciſſum: cuius maior baſis triangulum abc, minor
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              def; & axis gh. </s>
              <s id="s.000722">ducto autem plano per axem & per
                <expan abbr="lineã">lineam</expan>
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              da, quod ſectionem faciat dakl quadrilaterum; puncta
                <lb/>
              Kl lineas bc, ef bifariam ſecabunt. </s>
              <s id="s.000723">nam cum gh ſit axis
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              fruſti: erit h centrum grauitatis trianguli abc: & g
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                <figure id="id.023.01.077.1.jpg" xlink:href="023/01/077/1.jpg" number="68"/>
                <lb/>
                <arrow.to.target n="marg87"/>
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              centrum trianguli def: cen­
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              trum uero cuiuslibet triangu
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              li eſt in recta linea, quæ ab an­
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              gulo ipſius ad
                <expan abbr="dimidiã">dimidiam</expan>
              baſim
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              ducitur ex decimatertia primi
                <lb/>
              libri Archimedis de
                <expan abbr="cẽtro">centro</expan>
              gra
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                <arrow.to.target n="marg88"/>
                <lb/>
              uitatis planorum. </s>
              <s id="s.000724">quare
                <expan abbr="cen-trũ">cen­
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                trum</expan>
              grauitatis trapezii bcfe
                <lb/>
              eſt in linea kl, quod ſit m: & à
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              puncto m ad axem ducta mn
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              ipſi ak, uel dl æquidiſtante;
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              erit axis gh diuiſus in portio­
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              nes gn, nh, quas diximus: ean
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              dem enim proportionem ha­
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              bet gn ad nh,
                <expan abbr="quã">quam</expan>
              lm ad mk. </s>
              <lb/>
              <s id="s.000725">At lm ad mK habet eam,
                <expan abbr="quã">quam</expan>
                <lb/>
              duplum lateris maioris baſis
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              bc una cum latere minoris ef
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              ad duplum lateris ef unà cum
                <lb/>
              latere bc, ex ultima eiuſdem
                <lb/>
              libri Archimedis. </s>
              <s id="s.000726">Itaque à li­
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              nea ng abſcindatur, quarta
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              pars, quæ fit np: & ab axe hg abſcindatur itidem
                <lb/>
              quarta pars ho: & quam proportionem habet fruſtum ad
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              pyramidem, cuius maior baſis eſt triangulum abc, & alti­
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              tudo ipſi æqualis; habeat op ad pq.</s>
              <s id="s.000727"> Dico centrum graui­
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              tatis fruſti eſſe in linea po, & in puncto q.</s>
              <s id="s.000728"> namque ipſum
                <lb/>
              eſſe in linea gh manifeſte conſtat. </s>
              <s id="s.000729">protractis enim fruſti pla</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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