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

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <pb xlink:href="077/01/117.jpg" pagenum="113"/>
            <p id="N144FF" type="main">
              <s id="N14501">Curautem hoc modo centra grauitatum in præfatis figu­
                <lb/>
              ris poſitione tantùm, & non determinatè ea indeterminata,
                <lb/>
              linea, & in tali ſitu exiſtere inuenerimus, vt in parallelogram
                <lb/>
              mis & in triangulis factum fuitab Archimede; explicabitur in
                <lb/>
              ſecundo libro poſt tertiam proportionem; vbi oſtendemus,
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              in quibus figuris determinatè inueniri poteſt centrum graui­
                <lb/>
              tatis. </s>
            </p>
            <p id="N1450F" type="main">
              <s id="N14511">Antequam autem finem primolibro imponamus,
                <expan abbr="reliquũ">reliquum</expan>
                <lb/>
              eſt; vt ea quæ in præfatione ſuppoſuimus, oſtendamus. </s>
              <s id="N14519">pri­
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              mùm què quando ſecundùm rectam lineam aliqua diuiditur
                <lb/>
              figura per centrum grauitatis, aliquando diuidi in partes ſem
                <lb/>
              per ęquales, & aliquando in partes inæquales. </s>
            </p>
            <p id="N14521" type="head">
              <s id="N14523">PROPOSITIO.</s>
            </p>
            <p id="N14525" type="main">
              <s id="N14527">Figura dari poteſt, quę per centrum grauitatis recta li­
                <lb/>
              nea diuiſa, ſemper in partes diuidatur æquales. </s>
            </p>
            <p id="N1452B" type="main">
              <s id="N1452D">Sit
                <expan abbr="parallelogrammũ">parallelogrammum</expan>
                <lb/>
                <arrow.to.target n="fig57"/>
                <lb/>
              ABCD, cuius
                <expan abbr="centrũ">centrum</expan>
              gra­
                <lb/>
              uitatis E. Ducaturquè per
                <lb/>
              E
                <expan abbr="vtcunq́">vtcun〈que〉</expan>
              ; linea GEF, quę
                <lb/>
              vel diameter eſt, vel min^{9}.
                <lb/>
              ſi eſt diameter, iam
                <expan abbr="cõſtat">conſtat</expan>
                <lb/>
                <expan abbr="parallelogrãmum">parallelogrammum</expan>
              in duo
                <lb/>
              ęqua eſſe diuiſum. </s>
              <s id="N14555">Si verò non eſt diameter,
                <expan abbr="ducãtur">ducantur</expan>
                <arrow.to.target n="marg189"/>
                <lb/>
              AC BD, quæ per E tranſibunt. </s>
              <s id="N14560">Quoniam igitur AF eſt æqui­
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              diftans ipſi CG, eritangulus EAF ipſi ECG, & EFA ipſi
                <arrow.to.target n="marg190"/>
                <lb/>
              æqualis, eſt autem AEF ipſi GEC ad verticem æqualis,
                <expan abbr="latusq́">latus〈que〉</expan>
                <arrow.to.target n="marg191"/>
                <lb/>
              AE ipſi EC æquale; erit triangulum AEF triangulo CEG ęqua
                <lb/>
              le. </s>
              <s id="N14574">eodemquè modo oſtendetur triangulum FEB triangulo
                <lb/>
              EGD. & triangulum AED ipſi BEC æquale. </s>
              <s id="N14578">Ex quibus patet.
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              figuram ex tribus triangulis compoſitam, hoc eſt figuram
                <lb/>
              FGDA ipſi FGCB æqualem eſſe. </s>
              <s id="N1457E">diuiditurergo
                <expan abbr="parallelogrã-mum">parallelogran­
                  <lb/>
                mum</expan>
              à linea per centrum grauitatis ducta in partes ſem perç­
                <lb/>
              quales. </s>
              <s id="N14588">quod demonſtrare oportebat. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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