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

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000752">
                <pb pagenum="149" xlink:href="010/01/157.jpg"/>
                <arrow.to.target n="marg188"/>
                <lb/>
              AGC eiuſdem olei aſcendentis neceſſariò explana­
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              tam, imò excauatam fore; quia ex hypotheſi pondus
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              ſpecificum aquæ ambientis ſuperat ſpecificam gra­
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              uitatem olei ABC; iam ſi eſt moles aquæ collateralis
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              FQPC æqualis medietati olei BGC, proculdubio
                <lb/>
              aqua FQPC grauior erit oleo BGC, vel ſi moles inę­
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              quales ſunt, aquæ momentum ſuperat olei
                <expan abbr="momentũ">momentum</expan>
              ,
                <lb/>
              hiſce verò inæqualibus ponderibus ineumbunt, &
                <lb/>
              ſubijciuntur moles aquæ æque ponderantes, vel æ­
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              qualium momentorum, ergo in ſiphone compoſito
                <lb/>
              ex cylindri portione aquea VXKL, & ex cylindri
                <lb/>
              portione EIKL compoſita ex aqua, & oleo inæqua­
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              liter premuntur partes aquæ ſubiectæ GPXI. quæ li­
                <lb/>
              bram conſtituunt, nempè aqua CPXK maiori niſu
                <lb/>
              comprimitur ab aqua FQPC, quam aqua GCKI pre­
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              matur ab oleo BGC minus graui, & ideò ex coroll pr.
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              10. oleum BGC ſursùm impelletur ab aqua ſubiecta
                <lb/>
              GIKC, & talis expreſſio fiet (ex prop. 51.) tanta vi,
                <lb/>
              quanta eſt grauitas exceſſus ponderis aquæ FQPC
                <lb/>
              ſupra grauitatem olei BGC. </s>
              <s id="s.000753">præterea quia aqua in­
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              ter EB, & LC dum fertur deorſum ad occupandum̨
                <lb/>
              ſpatium ab aſcendente oleo derelictum, neceſſariò
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              comprimit contunditque ſuperficiem collateralem̨
                <lb/>
              olei BC non duri, ſed cedentis, eſtque motus obli­
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              quus per ſuperficiem decliuem BC, ergo ſpatium̨,
                <lb/>
              ſeù alueus, per quod incumbens aqua pertranſirę
                <lb/>
              debet comprehenſum à ſuperficie aquæ FCK dire­
                <lb/>
              cto, & non impedito motu fluentis, & inclinatam de­
                <lb/>
              cliuemque olei BC ſuperficiem, continentèr magis </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>