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

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              <pb o="471" file="0489" n="489" rhead="LIBER VI."/>
              <figure xlink:label="fig-0489-01" xlink:href="fig-0489-01a" number="331">
                <image file="0489-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0489-01"/>
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            ſic cylindrus, BF, ad ſolidum, DAF,
              <lb/>
            vnde cylindrus, GF, erit æqualis ſo-
              <lb/>
            lido, DAF. </s>
            <s xml:id="echoid-s12026" xml:space="preserve">Rurſus triplicetur alti-
              <lb/>
            tudo, EI, & </s>
            <s xml:id="echoid-s12027" xml:space="preserve">fiat conus eiuſdem al-
              <lb/>
            titudinis in baſi, DF, hic igitur co-
              <lb/>
            nus erit æqualis cylindro, GF, & </s>
            <s xml:id="echoid-s12028" xml:space="preserve">
              <lb/>
            ſubinde ſolido, DAF, quod inueni-
              <lb/>
            re opus erat.</s>
            <s xml:id="echoid-s12029" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1098" type="section" level="1" n="658">
          <head xml:id="echoid-head688" xml:space="preserve">COROLLARIVM I.</head>
          <p style="it">
            <s xml:id="echoid-s12030" xml:space="preserve">_H_Inc patet nos etiam poſſe inuenire cylindrum, & </s>
            <s xml:id="echoid-s12031" xml:space="preserve">conum, nedũ
              <lb/>
            æqualem dicto ſolido, ſed qui ad ipſum babeat datam rationem,
              <lb/>
            ſi enim altitudo inuenti cylindri, vel coni æqualis dicto ſolido, fiat
              <lb/>
            id ali am altitudinem in data ratione, tamen conuerſa, & </s>
            <s xml:id="echoid-s12032" xml:space="preserve">harum al-
              <lb/>
            tatudinum vltimò inuentarum in eiſdem baſibus cum prædictis fiant
              <lb/>
            cylindrus, & </s>
            <s xml:id="echoid-s12033" xml:space="preserve">conus, habebunt iſti ad dictum ſolidum datam ratio-
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            nem, vt facilè apparet.</s>
            <s xml:id="echoid-s12034" xml:space="preserve"/>
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        <div xml:id="echoid-div1099" type="section" level="1" n="659">
          <head xml:id="echoid-head689" xml:space="preserve">COROLL. II. SECTIO I.</head>
          <note position="right" xml:space="preserve">A</note>
          <p style="it">
            <s xml:id="echoid-s12035" xml:space="preserve">_H_Inc etiam patet cylindrum in baſi apicis ſphæralis, vel ſphæ-
              <lb/>
              <note position="right" xlink:label="note-0489-02" xlink:href="note-0489-02a" xml:space="preserve">_Coro. 21._
                <lb/>
              _34. l. 3._</note>
            roidalis, conſtitutum cuius altitudo ad altitudinem eiuſdem
              <lb/>
            apicis ſit, vt, _2._ </s>
            <s xml:id="echoid-s12036" xml:space="preserve">ad _21._ </s>
            <s xml:id="echoid-s12037" xml:space="preserve">eſſe æqualem eidem apici.</s>
            <s xml:id="echoid-s12038" xml:space="preserve"/>
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        <div xml:id="echoid-div1101" type="section" level="1" n="660">
          <head xml:id="echoid-head690" xml:space="preserve">SECTIO II.</head>
          <note position="right" xml:space="preserve">B</note>
          <p style="it">
            <s xml:id="echoid-s12039" xml:space="preserve">_V_Lterius habetur quoq; </s>
            <s xml:id="echoid-s12040" xml:space="preserve">cylindrum, ad cuius altitudinem altitu-
              <lb/>
            do tympani ſphæralis, vel ſphæroidalis ſit, vt ſemidiameter
              <lb/>
            baſis tympani ad reliquum, dempta ab eadem recta linea, ad quam di-
              <lb/>
            midia ſecundæ diametri circuli, vel ellipſis ſit, vt circulus ad qua-
              <lb/>
            dratum, cui circumſcribitur ſimul cum exceſſu, quo dicta linea exce-
              <lb/>
            dit _{2/3}_. </s>
            <s xml:id="echoid-s12041" xml:space="preserve">tertiæ proportionalis ſemidiametri baſis tympani, & </s>
            <s xml:id="echoid-s12042" xml:space="preserve">dimidiæ
              <lb/>
            ſecundæ diametri dicti circuli, vel ellipſis, eſſe æqualem dato tym-
              <lb/>
              <note position="right" xlink:label="note-0489-04" xlink:href="note-0489-04a" xml:space="preserve">Corò. 12
                <lb/>
              34. l. 3.</note>
            pano ſphærali, vel ſphæroidali, ſi ſit in baſi eiuſdcm tympani.</s>
            <s xml:id="echoid-s12043" xml:space="preserve"/>
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        <div xml:id="echoid-div1103" type="section" level="1" n="661">
          <head xml:id="echoid-head691" xml:space="preserve">SECTIO III.</head>
          <note position="right" xml:space="preserve">C</note>
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            <s xml:id="echoid-s12044" xml:space="preserve">_E_T cylindrum, ad cuius altitudinem, altitudo anuli ſtricti circu-
              <lb/>
            laris, vel elliptici, ſit vt quadratum ad circulum, cui circum-
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            ſcribitur, in baſi exiſtentem circulo, cuius radius ſit æqualis </s>
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