Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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        <div xml:id="echoid-div1116" type="section" level="1" n="668">
          <pb o="475" file="0495" n="495" rhead="LIBER VI."/>
          <p>
            <s xml:id="echoid-s12173" xml:space="preserve">Sit datus cylindrus, A, oportet illi anulum ſtrictum circularem
              <lb/>
            æqualem inuenire. </s>
            <s xml:id="echoid-s12174" xml:space="preserve">Reperiamus ergo cilindrum, quiad cylindrũ
              <lb/>
            A, ſit, vt duplum cuiuiſuis quadrati ad circulum dicto quadrato
              <lb/>
              <note position="right" xlink:label="note-0495-01" xlink:href="note-0495-01a" xml:space="preserve">Vtin pro.
                <lb/>
              pol. 26,
                <lb/>
              huius.</note>
            inſcriptum, & </s>
            <s xml:id="echoid-s12175" xml:space="preserve">dein de huic inuento cylindro alius inueniatur ęqua-
              <lb/>
              <figure xlink:label="fig-0495-01" xlink:href="fig-0495-01a" number="334">
                <image file="0495-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0495-01"/>
              </figure>
            lis, BC, cuius axis ſit
              <lb/>
            ęqualis diametro ba.
              <lb/>
            </s>
            <s xml:id="echoid-s12176" xml:space="preserve">ſis .</s>
            <s xml:id="echoid-s12177" xml:space="preserve">@. </s>
            <s xml:id="echoid-s12178" xml:space="preserve">MN, ipſi, OC,
              <lb/>
            qui diuidatur bifariã
              <lb/>
            in, R, & </s>
            <s xml:id="echoid-s12179" xml:space="preserve">per, R, du-
              <lb/>
            cto plano oppoſitis
              <lb/>
            baſibus æquidiſtan-
              <lb/>
            te, ſit conſtitutus cy
              <lb/>
            lindrus, DC, in quo
              <lb/>
            planum per axem
              <lb/>
            ductum produxerit
              <lb/>
            parallelogrammum,
              <lb/>
            DC, quod in duo ſe. </s>
            <s xml:id="echoid-s12180" xml:space="preserve">
              <lb/>
            parab tur quadrata per ipſam, RN, ſint illis inſcripti æquales cir-
              <lb/>
            culi, E, F, ex quorum reuolutione circa, RN, intelligatur effectus
              <lb/>
            anulus ſtrictus circularis, EF. </s>
            <s xml:id="echoid-s12181" xml:space="preserve">Dico hunc eſſe æqualem cylindro,
              <lb/>
            A. </s>
            <s xml:id="echoid-s12182" xml:space="preserve">Nam, BC, ad, A, eſt vt parallelogrammum, BN, .</s>
            <s xml:id="echoid-s12183" xml:space="preserve">i. </s>
            <s xml:id="echoid-s12184" xml:space="preserve">vt duplũ
              <lb/>
              <note position="right" xlink:label="note-0495-02" xlink:href="note-0495-02a" xml:space="preserve">Elicitu@
                <lb/>
              ex Corol.
                <lb/>
              13. 34. l. 3.</note>
            quadrati, DN, ad circulum, E, ſic autem eſt, BC, ad anulum ſtri-
              <lb/>
            ctum genitum ex, E, igitur hic anulus cylindro, A, æqualis erit,
              <lb/>
            quod inuenire opus erat.</s>
            <s xml:id="echoid-s12185" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1118" type="section" level="1" n="669">
          <head xml:id="echoid-head699" xml:space="preserve">PROBLEMA VII- PROPOS. XXX.</head>
          <p>
            <s xml:id="echoid-s12186" xml:space="preserve">DAto cylindro anulo latum circularem ęqualem inue-
              <lb/>
            nire, dato circulo, qui per reuolutionem ipſum ge-
              <lb/>
            nerat; </s>
            <s xml:id="echoid-s12187" xml:space="preserve">oportet autem datum cylin drum maiorem eſſe anu-
              <lb/>
            lo ſtricto ab eodem circulo per reuolutionem genito.</s>
            <s xml:id="echoid-s12188" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12189" xml:space="preserve">Sit datus cylindrus, E, datus circulus, CD, ſit autem datus cy-
              <lb/>
            lindrus, E, maior anulo ſtricto per reuolutionem dati circuli circa
              <lb/>
            ipſum rectam tangentem genito. </s>
            <s xml:id="echoid-s12190" xml:space="preserve">Oportet anulum latum circula-
              <lb/>
            rem inuenire ab eodem circulo per reuolutionem genitum, æqua-
              <lb/>
            lem dato cylindro, E. </s>
            <s xml:id="echoid-s12191" xml:space="preserve">Sit tangens circulum, CD, in puncto, D,
              <lb/>
            ipſa, MN, circa quam fieri intelligatur reuolutio, vt deſcribatur
              <lb/>
            anulus ſtrictus circularis ex, CD, fiat deinde, vt anulus ſtrictus ab
              <lb/>
            eo genitus ad cylindrum, E, ita, DC, diameter eiuldem ad aliam,
              <lb/>
            FH, (quæ erit eadem maior, quia etiam c@lindrus, E, eſt </s>
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