Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000337">
                <pb xlink:href="023/01/036.jpg"/>
              habeat circulus, uel ellipſis gh ad aliud ſpacium, in quo u:
                <lb/>
              & in cit culo, uel ellipſi plane deſcribatur rectilinea figura,
                <lb/>
              ita ut
                <expan abbr="tãdem">tandem</expan>
                <expan abbr="relinquãtur">relinquantur</expan>
              portiones minores ſpacio u, quæ
                <lb/>
              ſit opgqrsht:
                <expan abbr="deſcriptaq;">deſcriptaque</expan>
              ſimili figura in oppoſitis pla­
                <lb/>
              nis cd, fe, per lineas ſibi ipſis reſpondentes plana
                <expan abbr="ducãtur">ducantur</expan>
              . </s>
              <lb/>
              <s id="s.000338">Itaque cylindrus, uel cylindri portio diuiditur in priſma,
                <lb/>
              cuius quidem baſis eſt figura rectilinea iam dicta, centrum
                <lb/>
              que grauitatis punctum K: & in multa ſolida, quæ pro baſi
                <lb/>
              bus habent relictas portiones, quas nos ſolidas portiones
                <lb/>
              appellabimus. </s>
              <s id="s.000339">cum igitur portiones ſint minores ſpacio
                <lb/>
              u, circulus, uel ellipſis gh ad portiones maiorem propor­
                <lb/>
              tionem habebit, quàm linea mk ad Kl. </s>
              <s id="s.000340">fiat nk ad Kl, ut
                <lb/>
              circulus uel ellipſis gh ad ipſas portiones. </s>
              <s id="s.000341">Sed ut circulus
                <lb/>
              uel ellipſis gh ad figuram rectilineam in ipſa deſcri­
                <lb/>
              ptam, ita eſt cylindrus uel cylindri portio ce ad priſma,
                <lb/>
              quod rectilineam figuram pro baſi habet, & altitudinem
                <lb/>
              æqualem; id, quod infra demonſtrabitur. </s>
              <s id="s.000342">crgo per conuer
                <lb/>
              ſionem rationis, ut circulus, uel ellipſis gh ad portiones re
                <lb/>
              lictas, ita cylindrus, uel cylindri portio ce ad ſolidas por­
                <lb/>
              tiones, quate cylindrus uel cylindri portio ad ſolidas por­
                <lb/>
              tiones eandem proportionem habet, quam linea nk ad k
                <lb/>
              & diuidendo priſma, cuius baſis eſt rectilinea figura ad ſo­
                <lb/>
              lidas portiones eandem proportionem habet, quam nl ad
                <lb/>
              lk & quoniam a cylindro uel cylindri portione, cuius gra­
                <lb/>
              uitatis centrum eſt l, aufertur priſma baſim habens rectili­
                <lb/>
              neam
                <expan abbr="figurã">figuram</expan>
              , cuius
                <expan abbr="centrũ">centrum</expan>
              grauitatis eſt K: reſiduæ magnitu
                <lb/>
              dinis ex ſolidis portionibus
                <expan abbr="cõpoſitæ">compoſitæ</expan>
              grauitatis
                <expan abbr="cẽtrũ">centrum</expan>
              erit
                <lb/>
              in linea kl protracta, & in puncto n; quod eſt
                <expan abbr="abſurdũ">abſurdum</expan>
              . </s>
              <s id="s.000343">relin
                <lb/>
              quitur ergo, ut
                <expan abbr="cẽtrum">centrum</expan>
              grauitatis cylindri; uel cylindri por
                <lb/>
              tionis ſit
                <expan abbr="punctũ">punctum</expan>
              k. </s>
              <s id="s.000344">quæ omnia
                <expan abbr="demonſtrãda">demonſtranda</expan>
              propoſuimus.</s>
            </p>
            <p type="margin">
              <s id="s.000345">
                <margin.target id="marg45"/>
              4. huius</s>
            </p>
            <p type="main">
              <s id="s.000346">At uero cylindrum, uel cylindri
                <expan abbr="portionẽ">portionem</expan>
              ce
                <lb/>
              ad priſma, cuius baſis eſt rectilinea figura in ſpa­
                <lb/>
              cio gh deſcripta, & altitudo æqualis; eandem </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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