Borelli, Giovanni Alfonso, De motionibus naturalibus a gravitate pendentibus, 1670

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.001025">
                <pb pagenum="198" xlink:href="010/01/206.jpg"/>
                <arrow.to.target n="marg262"/>
                <lb/>
              contentum in vaſe FDE tantæ profunditatis, vt cy­
                <lb/>
              lindrus AC vniuersè, & perpendicularitèr ad Hori­
                <lb/>
              zontem mergi poſſit, vt eius baſis non contingat
                <expan abbr="fũ-dum">fun­
                  <lb/>
                dum</expan>
              vaſis FDE, atque ſupremus terminus C fluidi li­
                <lb/>
              bellam contingat. </s>
              <s id="s.001026">Præterea applicari debet pondus
                <lb/>
              P ſupra verticem cylindri CA, itaut pondus P immi­
                <lb/>
              neat ſupra fluidi libellam, neque aliqua eius portio
                <lb/>
                <figure id="id.010.01.206.1.jpg" xlink:href="010/01/206/1.jpg" number="78"/>
                <lb/>
              demergatur. </s>
              <s id="s.001027">His præparatis
                <lb/>
              quia exceſſus
                <expan abbr="põderis">ponderis</expan>
              R ſupra
                <lb/>
              S ad ipſum pondus S maiorem
                <lb/>
                <expan abbr="proportionẽ">proportionem</expan>
              habet quam gra­
                <lb/>
              uitas P ad pondus cylindri
                <lb/>
              ACB, ergò componendo, gra­
                <lb/>
              uitas R ad S
                <expan abbr="maiorẽ">maiorem</expan>
              proportio
                <lb/>
              nem habebit quàm duo
                <expan abbr="põde-ra">ponde­
                  <lb/>
                ra</expan>
              P, & CAB, ſimul ſumpta, ad
                <lb/>
              pondus CAB; verùm grauitas
                <lb/>
              molis fluidi M æqualis ſolido AC ad pondus abſolu­
                <lb/>
              tum eiuſdem ſolidi AC habet eamdem
                <expan abbr="proportionẽ">proportionem</expan>
              ,
                <lb/>
              quam R ad S, ergò moles fluidi M æqualis ſolido AC
                <lb/>
              ad ſolidum idipſum AC, ſeù illius pondus ad graui­
                <lb/>
              tatem huius habebit maiorem proportionem quàm
                <lb/>
              pondera P, & CAB ſimùl ſumpta ad pondus AC, &
                <lb/>
              proindè pondus abſolutum molis fluidi M æqualis
                <lb/>
              AC maius erit grauitate ipſius P vnà cum ponderę
                <lb/>
              cylindri AC. </s>
              <s id="s.001028">Verumtamen Archimedes demonſtra­
                <lb/>
                <arrow.to.target n="marg263"/>
                <lb/>
              uit ſolidum innatans tunc ſolummodò in fluido quie­
                <lb/>
              ſcere quando eius pondus abſolutum æquale fuerit
                <lb/>
              grauitati molis fluidi ambientis, quæ ſit æqualis por-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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