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

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    <archimedes>
      <text>
        <body>
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            <p type="main">
              <s id="s.000209">
                <pb pagenum="46" xlink:href="010/01/054.jpg"/>
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              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>
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            <p type="margin">
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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>
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            <p type="main">
              <s id="s.000211">Contra hoc euidentiſſimum ratiocinium afferri
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              ſolet difficultas valdè ſpecioſa, quam examinare, ac
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              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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              ABDC aqua plenum ſit que eius altitudo
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                <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, &
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              HI, erit igitur moles aquea AI duplą
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              aque ę molis HD; igitur pondus aquæ AI
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              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
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              ſtat vis, & energìa grauitatis, vt tendat deorsùm,
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              & ſic è loco infimo corpora minùs grauia expellat) &
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              poſtquàm aqua AI translata eſt ad locum HD, atque
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              aquam ibidem collocatam expulit denuò in ſitu ſu­
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              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
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              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>