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

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          <pb o="474" file="0492" n="492" rhead="GEOMETRIÆ"/>
          <p>
            <s xml:id="echoid-s12094" xml:space="preserve">Vtamur antecedentis figura, in qua ſupponamus dato cylin-
              <lb/>
            dro, A, conſticuendum eſſe æqualem apicem ſphæralem, vel ſphę-
              <lb/>
            roidalem, & </s>
            <s xml:id="echoid-s12095" xml:space="preserve">hunc circa datum axem. </s>
            <s xml:id="echoid-s12096" xml:space="preserve">Exponatur autem cylin-
              <lb/>
            drus, FCD, qui ad cylindrum, A, ſit, vt 21. </s>
            <s xml:id="echoid-s12097" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s12098" xml:space="preserve">deinde inter, C
              <lb/>
            D, FE, ſumantur duæ inediæ continuè proportionales, GH, M, & </s>
            <s xml:id="echoid-s12099" xml:space="preserve">
              <lb/>
            fiat cylindrus altitudinis, GH, qui ſit, GLH, ac ſupponatur ipſi,
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            LK, aſſumptam eſſe æqualem ipſam, NO, igitur ductis tangenti-
              <lb/>
            bus circulum circa, NO, in punctis, O, R, N, quæ ſint, OZ, Z℟,
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            ℟N, concurrentibus in Z, ℟, patet, OZ, eſſe æqualem ipſi, GK,
              <lb/>
            &</s>
            <s xml:id="echoid-s12100" xml:space="preserve">, ℟Z, æquatur ipſi, Lk, crgo cylindrus, qui naſceretur ex reuò-
              <lb/>
            lutione parallelogrammi, NZ, circa manentem axem, ℟Z, eſſet
              <lb/>
            æqualis cylindro, GLH, oſtendemus autem, vt in antecedenti cy-
              <lb/>
            lindrum, GLH, eſſe æqualem cylindro, CFD, vnde patebit cylin-
              <lb/>
            drum genitum ex, NZ, ad cylindrum, A, eſſe vt 21. </s>
            <s xml:id="echoid-s12101" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s12102" xml:space="preserve">ſedidem
              <lb/>
            ad apicem, qui naſceretur ex reuolutione trilinei, OZR, circa, RZ,
              <lb/>
              <note position="left" xlink:label="note-0492-01" xlink:href="note-0492-01a" xml:space="preserve">Corol. 11.
                <lb/>
              34. l. 3.</note>
            eſt vt 21. </s>
            <s xml:id="echoid-s12103" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s12104" xml:space="preserve">nam cylindrus ex, NZ, duplus eſt cylindriex, BZ,
              <lb/>
            ergo apex genitus ex trilineo, OZR, æqualis erit cylindro, A.</s>
            <s xml:id="echoid-s12105" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12106" xml:space="preserve">Sit nunc inueniendus apex ſphæroidalis circa datum axem, RZ,
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            vel illi æqualem, qui ſit æqualis cylindro, A, ſi ergo talis eſſet apex
              <lb/>
            ſphæralis, qui fit ex, OZR, non eſſet alius apex ſphæroidalis circa,
              <lb/>
            RZ, vel illi æqualem, qui eſſet æqualis cylindro, A; </s>
            <s xml:id="echoid-s12107" xml:space="preserve">ſi verò non
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            ſit, inueniatur apex ſphæralis, vt, ΤΔ4, æqualis cylindro, A, dein-
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            de vt, RZ, ad huius facti apicis axim, 4Δ, ita fiat dimidij diametri
              <lb/>
            baſis eiuſdem, ideſt, ΤΔ, quadratum ad quadratum, OY, ſiue, BI,
              <lb/>
            & </s>
            <s xml:id="echoid-s12108" xml:space="preserve">per, 1, tranſeat elliplis, NIO, & </s>
            <s xml:id="echoid-s12109" xml:space="preserve">ducatur eandem tangens in, I,
              <lb/>
            quę fit, IY, igitur quia, RZ, ad, 4Δ, axim facti apicis ſphæralis eſt,
              <lb/>
            vt quadratum, ΤΔ, dimidij diametri baſis, ad quadratum, OY,
              <lb/>
            ideſt, vt circulus, qui eſt baſis facti apicis ſphæralis, ΤΔ4, ad cir-
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            culum, qui eſt baſis alterius, ideò iſti apices erunt æquales: </s>
            <s xml:id="echoid-s12110" xml:space="preserve">nam
              <lb/>
            ſe habebunt, vt cylindri in eiſdem cum illis baſibus, & </s>
            <s xml:id="echoid-s12111" xml:space="preserve">circa eoſ-
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            dem axes exiſtentes, qui cylindrici erunt æquales, nam axes baſi-
              <lb/>
            bus reciprocè reſpondet; </s>
            <s xml:id="echoid-s12112" xml:space="preserve">ergo apex ſuphæroidalis, qui fiet ex, O
              <lb/>
            YI, & </s>
            <s xml:id="echoid-s12113" xml:space="preserve">eſt circa axim, IY, æqualem ipſi, RZ, datæ, erit æqualis cy-
              <lb/>
            lindro, A, quæ inuenienda erant.</s>
            <s xml:id="echoid-s12114" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1112" type="section" level="1" n="665">
          <head xml:id="echoid-head695" xml:space="preserve">COR OLL ARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s12115" xml:space="preserve">_P_Atet autem, quod iuxta Corollarium antec@dentis poterimus etiã
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            inuenire apices ſphęrales, vel ſphæroidales circa datum axim, ad
              <lb/>
            datum quodcunq; </s>
            <s xml:id="echoid-s12116" xml:space="preserve">ſolidum ex enumeratis in dicto Corollario datam
              <lb/>
            ratoinem habentes.</s>
            <s xml:id="echoid-s12117" xml:space="preserve"/>
          </p>
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