DelMonte, Guidubaldo, In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <pb xlink:href="077/01/107.jpg" pagenum="103"/>
            <p id="N13E04" type="main">
              <s id="N13E06">
                <emph type="italics"/>
              Sit triangulum ABC, &
                <emph.end type="italics"/>
              ab angulo A
                <emph type="italics"/>
              ducatur AD ad dimi­
                <lb/>
              diam BC. BE verò
                <emph.end type="italics"/>
              ab angulo B
                <emph type="italics"/>
              ad dimidiam AC.
                <emph.end type="italics"/>
              quę quidem
                <lb/>
              lineę AD BE ſeinuicem ſecent in
                <expan abbr="pū">pum</expan>
                <lb/>
                <arrow.to.target n="fig47"/>
                <lb/>
              cto H.
                <emph type="italics"/>
              Quoniam igitur centrum grauita­
                <lb/>
              tis trianguli ABC est in vtra〈que〉 linea
                <lb/>
              AD BE; hoc enim demonstratum eſt
                <emph.end type="italics"/>
              in
                <lb/>
              pręcedenti. </s>
              <s id="N13E34">erit vti〈que〉 centrum graui­
                <lb/>
              tatis, vbilineç AD BE ſe
                <expan abbr="inuicẽ">inuicem</expan>
                <expan abbr="ſecãt">ſecant</expan>
              .
                <lb/>
              ſecant verò ſeſe in H.
                <emph type="italics"/>
              ergo punctum
                <lb/>
              H centrum eſt grauitatis
                <emph.end type="italics"/>
              trianguli ABC.
                <lb/>
              quod demonſtrare oportebat. </s>
            </p>
            <figure id="id.077.01.107.1.jpg" xlink:href="077/01/107/1.jpg" number="66"/>
            <p id="N13E50" type="head">
              <s id="N13E52">SCHOLIVM.</s>
            </p>
            <p id="N13E54" type="main">
              <s id="N13E56">Similiter ſi ducta fuerit CH, & producta, bifariam ſecaret
                <lb/>
              AB. In hac enim linea eſſet centrum grauitatis trianguli;
                <expan abbr="cẽ">cem</expan>
                <lb/>
              trum verò eſt in linea ab angulo ad dimidiam baſim ducta:
                <lb/>
              ergo hæc linea ab angulo C ad dimidiam AB ducta eſſet.
                <lb/>
              Præterea ſi linea à puncto C ad dimidiam AB ducta
                <expan abbr="nõ">non</expan>
              tran
                <lb/>
              ſiret per H; eſſet vti〈que〉 in hac linea centrum grauitatis;
                <arrow.to.target n="marg158"/>
                <expan abbr="cẽ-trum">cen­
                  <lb/>
                trum</expan>
              quo〈que〉 grauitatis eſt in linea AD, & in linea BE, ut in
                <lb/>
              H; vnius igitur figurę plura darentur centra grauitatis. </s>
              <s id="N13E76">quod
                <lb/>
              fieri non poteſt. </s>
              <s id="N13E7A">quod quidem, cùm ſit in con ueniens, nos in
                <lb/>
              noſtro Mechanicorum libro dari non poſſe ſuppoſuimus.
                <lb/>
              Quare linea CH indirectum ducta, bifariam ſecaret AB.
                <lb/>
              quod quidem paulò infra aliter quo〈que〉 oſtendemus,
                <expan abbr="nõnul">nonnul</expan>
                <lb/>
              lis prius demonſtratis; quæ Archimedes ob ſe〈que〉ntem
                <expan abbr="demõ-ſtrationem">demon­
                  <lb/>
                ſtrationem</expan>
              , tanquam demonſtrata ſupponit. </s>
              <s id="N13E8E">Vult enim Ar­
                <lb/>
              chimedes, poſtquam inuenit centrum grauitatis cuiuſlibet
                <lb/>
              trianguli, centrum quo〈que〉 grauitatis quærere trapetij duo la­
                <lb/>
              tera ęquidiſtantia habentis. </s>
              <s id="N13E96">quod eſt quidem pars trianguli,
                <lb/>
              & tanquam fruſtum a triangulo abſciſſum. </s>
              <s id="N13E9A">ſupponitquè den
                <lb/>
              trum grauitatis cuiuſlibet trianguli eſſe in recta linea baſi du
                <lb/>
              cta ęquidiſtante, quæ latera ita diuidat, vt partes ad uerticem
                <lb/>
              ſint reliquarum partium duplæ. </s>
              <s id="N13EA2">quod quidem ortum ducit
                <lb/>
              ex cognitione alterius theorematis oſtendentis centrum </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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