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

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          <p>
            <s xml:id="echoid-s6708" xml:space="preserve">
              <pb o="271" file="0291" n="291" rhead="LIBER III."/>
            genitum ex figura, NMBEF, habens omnes ſuas figuras ſimiles,
              <lb/>
            quæ ſint circuli, ſiue quod fiet per reuolutionem dictæ figuræ, NM
              <lb/>
            BEF, vocetur, inquam. </s>
            <s xml:id="echoid-s6709" xml:space="preserve">Baſis columnaris ſtricta, & </s>
            <s xml:id="echoid-s6710" xml:space="preserve">circularis, ſi,
              <lb/>
            MBEG, ſit circulus, elliptica autem, ſi is fit ellipſis.</s>
            <s xml:id="echoid-s6711" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div651" type="section" level="1" n="380">
          <head xml:id="echoid-head397" xml:space="preserve">SECTIO II.</head>
          <p>
            <s xml:id="echoid-s6712" xml:space="preserve">IN Coroll. </s>
            <s xml:id="echoid-s6713" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6714" xml:space="preserve">colligitur ſolidum ſimilare genitum ex, HF, ad ſo-
              <lb/>
            lidum ſimilare genitum ex figura, NMBEF, dempto ſolido ſi-
              <lb/>
            milari genito ex, MF, eſſe proximè, vt 84. </s>
            <s xml:id="echoid-s6715" xml:space="preserve">ad 47. </s>
            <s xml:id="echoid-s6716" xml:space="preserve">ideſt in noſtro
              <lb/>
            exemplo cylindrum, H ℟, ad baſem columnarem ſtrictam genitam
              <lb/>
            ex figura, NMBEF, dempto cylindro, MX, eſſe proximè, vt 84.
              <lb/>
            </s>
            <s xml:id="echoid-s6717" xml:space="preserve">ad 47.</s>
            <s xml:id="echoid-s6718" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div652" type="section" level="1" n="381">
          <head xml:id="echoid-head398" xml:space="preserve">SECTIO III.</head>
          <p>
            <s xml:id="echoid-s6719" xml:space="preserve">IN Coroll. </s>
            <s xml:id="echoid-s6720" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6721" xml:space="preserve">habetur ſolidum ſimilare genitum ex, MF, demptis
              <lb/>
            ſolidis ſimilaribus genitis ex trilineis, MNG, GFE, ad ſolidum
              <lb/>
            ſibi ſimilare genitum ex figura, NMBEF, dempto ſolido ſimilari
              <lb/>
            genito ex, MF, eſſe proximè, vt 19. </s>
            <s xml:id="echoid-s6722" xml:space="preserve">ad 47. </s>
            <s xml:id="echoid-s6723" xml:space="preserve">In exemplo autem no-
              <lb/>
            ſtro, dum reuoluitur, HF, apprehende ſuperficiem cylindricam de-
              <lb/>
            ſcriptam linea, ME, quę in duas partes diſſeparat anulum ſtrictum,
              <lb/>
            AI, ſcilicet in vnam, quam poſſumus vocare interiorem, & </s>
            <s xml:id="echoid-s6724" xml:space="preserve">in aliam
              <lb/>
            exteriorem; </s>
            <s xml:id="echoid-s6725" xml:space="preserve">interior eſt, quę gigniture ex reuolutione ſemicirculi, vel
              <lb/>
            ſemiellipſis, MGE; </s>
            <s xml:id="echoid-s6726" xml:space="preserve">exterior autem, quæ generatur ex ſemicirculo,
              <lb/>
            vel ſemiellipſi, MBE, eſtigitur hæc pars interior anuli ſtrictiad par-
              <lb/>
            tem exteriorem proximè, vt 19. </s>
            <s xml:id="echoid-s6727" xml:space="preserve">ad 47. </s>
            <s xml:id="echoid-s6728" xml:space="preserve">vtin cæteris ſolidis ſimilari-
              <lb/>
            bus ſupradictis contingere diximus.</s>
            <s xml:id="echoid-s6729" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div653" type="section" level="1" n="382">
          <head xml:id="echoid-head399" xml:space="preserve">COROLL. XVI. SECTIO PRIOR.</head>
          <p>
            <s xml:id="echoid-s6730" xml:space="preserve">IN Propoſ. </s>
            <s xml:id="echoid-s6731" xml:space="preserve">18. </s>
            <s xml:id="echoid-s6732" xml:space="preserve">habemus ſolidum ſimilare genitum ex, HO, ad
              <lb/>
            ſolidum ſimilare genitum ex figura, CMBEO, eſſe vt quadra-
              <lb/>
            tum, DO, ad rectangulum ſub, DO, OE, vna cum rectangulo
              <lb/>
            ſub, OE, & </s>
            <s xml:id="echoid-s6733" xml:space="preserve">ſub exceſiu, quo dupla, EI, ſuperat, EF, &</s>
            <s xml:id="echoid-s6734" xml:space="preserve">, {2/3}, qua-
              <lb/>
            drati, DE. </s>
            <s xml:id="echoid-s6735" xml:space="preserve">Exemplum conſpici poteſt in figura Coroll. </s>
            <s xml:id="echoid-s6736" xml:space="preserve">14. </s>
            <s xml:id="echoid-s6737" xml:space="preserve">huius,
              <lb/>
            in qua ſolidum ſimilare genitum ex, HO, eſt cylindrus, H ℟, ſoli-
              <lb/>
            dum verò ſimilare genitum ex figura, CMBEO, eſt, quod naſcitur
              <lb/>
            ex reuolutione eiuſdem figurę circa, CO, quod ſolidum vocabimus.
              <lb/>
            </s>
            <s xml:id="echoid-s6738" xml:space="preserve">Baſem columnarem latam, circularem, ſi, MBEG, ſit circulus, el-
              <lb/>
            lipticam verò, ſi ſit ellipſis.</s>
            <s xml:id="echoid-s6739" xml:space="preserve"/>
          </p>
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