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

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        <div xml:id="echoid-div1103" type="section" level="1" n="661">
          <p style="it">
            <s xml:id="echoid-s12044" xml:space="preserve">
              <pb o="472" file="0490" n="490" rhead="GEOMETRIÆ"/>
            diametro circuli, vel ellipſis, quæ reuoluitur, eſſe æqualem dicto anu-
              <lb/>
              <note position="left" xlink:label="note-0490-01" xlink:href="note-0490-01a" xml:space="preserve">_Coro. 13._
                <lb/>
              _34. l. 3._</note>
            lo ſtricto. </s>
            <s xml:id="echoid-s12045" xml:space="preserve">Conſimiliter autem inueniemus cylindrum æqualem anulo
              <lb/>
            lato circulari, vel elliptico; </s>
            <s xml:id="echoid-s12046" xml:space="preserve">& </s>
            <s xml:id="echoid-s12047" xml:space="preserve">eius portionibus, abſciſſis planis ad
              <lb/>
            axem reuolutionis rectis; </s>
            <s xml:id="echoid-s12048" xml:space="preserve">ſiue cuicunq; </s>
            <s xml:id="echoid-s12049" xml:space="preserve">ex figuris Corollariorum 26.
              <lb/>
            </s>
            <s xml:id="echoid-s12050" xml:space="preserve">27. </s>
            <s xml:id="echoid-s12051" xml:space="preserve">28. </s>
            <s xml:id="echoid-s12052" xml:space="preserve">29. </s>
            <s xml:id="echoid-s12053" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s12054" xml:space="preserve">3. </s>
            <s xml:id="echoid-s12055" xml:space="preserve">Similiter inueniemus cylindrum æqualem Malo
              <lb/>
            Roſeo, vel Cotoneo, vel Citri@, vel Oliuæ; </s>
            <s xml:id="echoid-s12056" xml:space="preserve">Conoidi Parabolico, Vel
              <lb/>
            hyperbolico, eiuſdem fruſto, Apici parabolico, Semianulo ſtricto, vel
              <lb/>
            lato, & </s>
            <s xml:id="echoid-s12057" xml:space="preserve">ſemibaſibus ſtrictis, medijs, vel latis, Aceruis minori, vel
              <lb/>
            maiori parabolicis. </s>
            <s xml:id="echoid-s12058" xml:space="preserve">Tympano hyperbolico, & </s>
            <s xml:id="echoid-s12059" xml:space="preserve">portionibus eorundẽ
              <lb/>
            ſupra conſideratis, & </s>
            <s xml:id="echoid-s12060" xml:space="preserve">cylindricis, vel conicis, qui in baſibus ſpatijs
              <lb/>
            ſub ſpiralibus, & </s>
            <s xml:id="echoid-s12061" xml:space="preserve">volutis conſtituuntur. </s>
            <s xml:id="echoid-s12062" xml:space="preserve">Triplicatis autem altitu-
              <lb/>
            dinibus inuentorum cylindrorum, in quibus, & </s>
            <s xml:id="echoid-s12063" xml:space="preserve">eiſdem baſibus cum
              <lb/>
            cylindris, conſtituantur coni, iſti prædictis ſolidis æquales erunt, & </s>
            <s xml:id="echoid-s12064" xml:space="preserve">
              <lb/>
            iuxta Coroll. </s>
            <s xml:id="echoid-s12065" xml:space="preserve">_1_ antecedentis inueniemus pariter cylindrum, vel co-
              <lb/>
            num, qui ad quoduis ex prædictis ſolidis datam ratione mhabeat.</s>
            <s xml:id="echoid-s12066" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1105" type="section" level="1" n="662">
          <head xml:id="echoid-head692" xml:space="preserve">PROBLEMA III. PROPOS. XXVI.</head>
          <p>
            <s xml:id="echoid-s12067" xml:space="preserve">SPhæram inuenire æqualem dato cylindro. </s>
            <s xml:id="echoid-s12068" xml:space="preserve">Similiter, & </s>
            <s xml:id="echoid-s12069" xml:space="preserve">
              <lb/>
            ſphæroidem circa datum axim æqualem dato cyin-
              <lb/>
            dro -</s>
          </p>
          <p>
            <s xml:id="echoid-s12070" xml:space="preserve">Sit cylindrus datus, A, oportet illi æqualem ſphæram inuenire.
              <lb/>
            </s>
            <s xml:id="echoid-s12071" xml:space="preserve">Fiat cylindrus rectus, CFD, ſexquialter cylindri, A, deinde inter,
              <lb/>
              <note position="left" xlink:label="note-0490-02" xlink:href="note-0490-02a" xml:space="preserve">Vide Da-
                <lb/>
              uidem Ri
                <lb/>
              ualtum in
                <lb/>
              Commé.
                <lb/>
              in Arch.
                <lb/>
              ad prop.
                <lb/>
              1. ſecundi
                <lb/>
              de Sphæ-
                <lb/>
              ra, & Cy-
                <lb/>
              lindro.</note>
              <figure xlink:label="fig-0490-01" xlink:href="fig-0490-01a" number="332">
                <image file="0490-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0490-01"/>
              </figure>
            altitudinem, FE, & </s>
            <s xml:id="echoid-s12072" xml:space="preserve">
              <lb/>
            baſis diametrũ, CD,
              <lb/>
            duæ mediæ continuè
              <lb/>
            proportionales, iuxta
              <lb/>
            methodũ ab alijs tra-
              <lb/>
            ditam, inueniantur,
              <lb/>
            quę ſint, M, GH, de-
              <lb/>
            ſcripto autem circu-
              <lb/>
            lo circa alterà dictarũ
              <lb/>
            mediarum tanquam
              <lb/>
            diametrum, vt circa,
              <lb/>
            GH, fiat is baſis cu-
              <lb/>
            uſdam cylindri altitu-
              <lb/>
            dinis æqualis ipſi, G
              <lb/>
            H, & </s>
            <s xml:id="echoid-s12073" xml:space="preserve">ſit tandem ſphæra, B, circa diametrum æqualem ipſi, GH,
              <lb/>
            conſt tuta. </s>
            <s xml:id="echoid-s12074" xml:space="preserve">Dico ſphæram, B, eſſe æqualem cylindro, A. </s>
            <s xml:id="echoid-s12075" xml:space="preserve">Eſt en@m
              <lb/>
            CD, ad, GH, vt, M, ad, FF, permutando, CD, ad, M, eſt vt, </s>
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