Angeli, Stefano degli, Miscellaneum hyperbolicum et parabolicum : in quo praecipue agitur de centris grauitatis hyperbolae, partium eiusdem, atque nonnullorum solidorum, de quibus nunquam geometria locuta est, parabola nouiter quadratur dupliciter, ducuntur infinitarum parabolarum tangentes, assignantur maxima inscriptibilia, minimaque circumscriptibilia infinitis parabolis, conoidibus ac semifusis parabolicis aliaque geometrica noua exponuntur scitu digna

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          <p>
            <s xml:id="echoid-s2738" xml:space="preserve">
              <pb o="149" file="0161" n="161"/>
            librij in D C. </s>
            <s xml:id="echoid-s2739" xml:space="preserve">Nam eodem modo patebit, dari ra-
              <lb/>
            tionem ſolidi A B C, ad ſolidum D B C Z H ℟.
              <lb/>
            </s>
            <s xml:id="echoid-s2740" xml:space="preserve">Sed etiam datur ratio ex hypotheſi, D B C Z H ℟,
              <lb/>
            ad annulum ſtrictum ex D B C, circa C F. </s>
            <s xml:id="echoid-s2741" xml:space="preserve">Ergo
              <lb/>
            ex æquali, dabitur ratio A B C, ſolidi ad prædi-
              <lb/>
            ctum annulum ſtrictum. </s>
            <s xml:id="echoid-s2742" xml:space="preserve">Quare ex cit propoſit. </s>
            <s xml:id="echoid-s2743" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2744" xml:space="preserve">
              <lb/>
            dabitur quoque in D C, centrum æquilibrij quæſi-
              <lb/>
            tum. </s>
            <s xml:id="echoid-s2745" xml:space="preserve">Quod &</s>
            <s xml:id="echoid-s2746" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2747" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div131" type="section" level="1" n="84">
          <head xml:id="echoid-head96" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s2748" xml:space="preserve">Ex his tribus propoſitionibus poſſumus necdum
              <lb/>
            ex ſola quadratura in finitarum parabolarum inuenire
              <lb/>
            rationem cylindrorum circumſcripto ũ ad infinitos
              <lb/>
            fuſos parabolicos; </s>
            <s xml:id="echoid-s2749" xml:space="preserve">ſed etiam centrum grauitatis in-
              <lb/>
            finitarum parabolarum. </s>
            <s xml:id="echoid-s2750" xml:space="preserve">Nam cum in propoſit. </s>
            <s xml:id="echoid-s2751" xml:space="preserve">4.
              <lb/>
            </s>
            <s xml:id="echoid-s2752" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2753" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2754" xml:space="preserve">& </s>
            <s xml:id="echoid-s2755" xml:space="preserve">in ſcholijs eiuſdem, oſtenſum ſit in ſchema-
              <lb/>
            te illius propoſit. </s>
            <s xml:id="echoid-s2756" xml:space="preserve">data qualibet ſemiparabola R B E,
              <lb/>
            cuius baſis R E, diameter B E, quæ reuoluatur
              <lb/>
            cum ſibi circumſcripto parallelogrammo R B, cir-
              <lb/>
            ca B S: </s>
            <s xml:id="echoid-s2757" xml:space="preserve">cylindrum R K, eſſe ad ſolidum E R B Z k,
              <lb/>
            vt parallelogrammum R B, ad ſemiparabolam
              <lb/>
            E R B, cuius baſis E R, diameter E B, quæ ſit
              <lb/>
            gradus dupli, gradus ſemiparabolæ reuolutæ circa
              <lb/>
            S B; </s>
            <s xml:id="echoid-s2758" xml:space="preserve">patet ex data quadratura infinitarum parabola-
              <lb/>
            rum, dari rationem cylindri R K, ad annuIum
              <lb/>
            E R B Z k. </s>
            <s xml:id="echoid-s2759" xml:space="preserve">Data hac ratione, dabitur etiam ex pro-
              <lb/>
            poſit. </s>
            <s xml:id="echoid-s2760" xml:space="preserve">anteced. </s>
            <s xml:id="echoid-s2761" xml:space="preserve">ratio cylindri R k, velei æqualis or-
              <lb/>
            ti ex R B, circa R E, ad ſolidum ex E R B, </s>
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