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

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000209">
                <pb pagenum="46" xlink:href="010/01/054.jpg"/>
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                <lb/>
              dus pilæ AB nil prorsùs imminutum erit, & æquali
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              energia ſuſtineri debet à potentia D, ac ſi eadem pi­
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              la extra aquam in aere libero penderet, ſed hoc eſt
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              falſum, cùm præcisè in ipſa aqua grauitas pilæ æqua­
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              lis ſit differentiæ ponderis eius abſoluti à grauitatę
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              aquæ ſibi æqualis mole, vt ex Archimede deducitur,
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              igitur neceſſariò
                <expan abbr="fatendũ">fatendum</expan>
              eſt aquam in ipſamet aqua
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              collocatam ponderare, & grauitatem exercere. </s>
            </p>
            <p type="margin">
              <s id="s.000210">
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              Cap. 3. flui­
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              dum in ſuo
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              toto quie­
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              ſcens pon­
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              derat.</s>
            </p>
            <p type="main">
              <s id="s.000211">Contra hoc euidentiſſimum ratiocinium afferri
                <lb/>
              ſolet difficultas valdè ſpecioſa, quam examinare, ac
                <lb/>
              diſſoluere erit operæ pretium, vtque ea ritè percipi­
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              atur, conſideretur hæc figura. </s>
              <s id="s.000212">Sit vas cylindricum̨
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                <arrow.to.target n="marg48"/>
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              ABDC aqua plenum ſit que eius altitudo
                <lb/>
                <figure id="id.010.01.054.1.jpg" xlink:href="010/01/054/1.jpg"/>
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              diſſecta in quotcumque partes æquales,
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              ductis nempè planis imaginarijs MO, &
                <lb/>
              HI, erit igitur moles aquea AI duplą
                <lb/>
              aque ę molis HD; igitur pondus aquæ AI
                <lb/>
              duplum eſt ponderis aquæ HD. quia ve­
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              rò corpus grauius minùs graue ſuperare
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              debet, hocque è ſuo loco expellere (cùm in eo conſi­
                <lb/>
              ſtat vis, & energìa grauitatis, vt tendat deorsùm,
                <lb/>
              & ſic è loco infimo corpora minùs grauia expellat) &
                <lb/>
              poſtquàm aqua AI translata eſt ad locum HD, atque
                <lb/>
              aquam ibidem collocatam expulit denuò in ſitu ſu­
                <lb/>
              periori fiſtulæ AI aqua dupli ponderis, & molis ibi­
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              dem reſtituitur quæ pariter ſuperat grauitatem ſub­
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              duplam aquæ, quæ ad occupandum infimum locum
                <lb/>
              HD ſucceſſit, igitur denuò aqua ſuprema vt grauior
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              infimam è ſuo loco extrudere, atque expellere de-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>