Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/238.jpg" pagenum="59"/>
              ad cubum ex ES, triplicata eſt proportio axis, vel la­
                <lb/>
                <gap/>
              eris BE, ad axem, vel latus ES; erit vt cubus ex BE
                <lb/>
              ad cubum ex ES, ita ſolidum GEH ad ſolidum NEO,
                <lb/>
              hoc eſt in eadem proportione, quæ eſt ex contraria parte ip­
                <lb/>
              ſius PR ad RQ. Cum igitur P ſit centrum grauitatis
                <lb/>
              ſolidi NEO, & Q ſolidi GEH; erit compoſiti ex vtro­
                <lb/>
              que centrum grauitatis R. Rurſus, quoniam reliquum ſo­
                <lb/>
              lidi AH dempto hemiſphærio, vel hemiſphæroide ABC,
                <lb/>
              æquale eſt ſolido GEH: & reliquum ſolidi TC dempto
                <lb/>
              ſolido ALMC æquale ſolido NEO; erit vt ſolidum
                <lb/>
              GEH ad ſolidum NEO, ideſt ex contraria parte, vt PR
                <lb/>
              ad RQ, ita reliquum ſolidi AH dempto ABC, ad re­
                <lb/>
              liquum ſolidi TC, dempto ALMC: ſed reliqui ex ſoli­
                <lb/>
              do AH dempto ABC eſt centrum grauitatis Q: & reli­
                <lb/>
              qui ex ſolido TC dempto ALMC, centrum grauitatis
                <lb/>
              P, ex ſuperius demonſtratis; totius igitur reliqui ex cy­
                <lb/>
              lindro, vel portione cylindrica TH dempta ſphæræ, vel
                <lb/>
              ſphæroidis maiori portione LBM centrum grauitatis eſt
                <lb/>
              R. </s>
              <s>Quod demonſtrandum erat. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XXX.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Si ſphæra, vel ſphæroides vnà cum cylindro,
                <lb/>
              vel portione cylindrica ipſi circumſcripta, ſece­
                <lb/>
              tur duobus planis baſi ſolidi circumſcripti pa­
                <lb/>
              rallelis, centrum intercipientibus, & ab eo non
                <lb/>
              æqualiter diſtantibus; reliqui ex cylindro, vel
                <lb/>
              portione cylindrica dictis planis intercepta, dem­
                <lb/>
              pta portione ſphæræ, vel ſphæroidis ipſi reſpon­
                <lb/>
              dente, centrum grauitatis eſt punctum illud, in
                <lb/>
              quo prædicti reliqui ſolidi axis ſegmentum in­</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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