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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            Qualium ergo ℟ 2, eſt 5, talium V X, eſt 75,
              <lb/>
            V ℟, 45, & </s>
            <s xml:id="echoid-s2366" xml:space="preserve">V 2, 50. </s>
            <s xml:id="echoid-s2367" xml:space="preserve">Cum ergo qualium ℟ 2, eſt
              <lb/>
            5, talium ℟ +, ſit 3. </s>
            <s xml:id="echoid-s2368" xml:space="preserve">Ergo qualium V X, eſt 75,
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            talium V +, erit 42. </s>
            <s xml:id="echoid-s2369" xml:space="preserve">V X, ergo centrum grauita-
              <lb/>
            tis duorum annulorum ſecabitur in +, & </s>
            <s xml:id="echoid-s2370" xml:space="preserve">conſe-
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            quenter F C, ſic ſecabitur à centro grauitatis præ-
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            dicti annuli quadratici v. </s>
            <s xml:id="echoid-s2371" xml:space="preserve">g. </s>
            <s xml:id="echoid-s2372" xml:space="preserve">in N, vt F N, ſit ad
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            N C, vt 42, ad 33; </s>
            <s xml:id="echoid-s2373" xml:space="preserve">nempe ſubtriplando termi-
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            nos, vt 14, ad 11.</s>
            <s xml:id="echoid-s2374" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2375" xml:space="preserve">Habito autem centro grauitatis talis annuli, non
              <lb/>
            ignorabitur centrum grauitatis conici B C H, orti
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            ex rotatione trilinei B F C, circa baſim F C. </s>
            <s xml:id="echoid-s2376" xml:space="preserve">Quod
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            licet poſſit haberi independenter ab inuento centro
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            grauitatis annuli, vt patet ex ſuperioribus, conſide-
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            rando perſe, ſolidum ortum ex reuolutione exceſſus
              <lb/>
            parallelogrammi E C, ſupra parabolam A B C,
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            circa F C, faciendo diſpoſtionem vt ſupra; </s>
            <s xml:id="echoid-s2377" xml:space="preserve">faci-
              <lb/>
            lius tamen inuenietur ex centro annuli ex ſemipara-
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            bola prius inuento. </s>
            <s xml:id="echoid-s2378" xml:space="preserve">Nam habetur etiam centrum
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            grauitatis totius cylindri D H; </s>
            <s xml:id="echoid-s2379" xml:space="preserve">& </s>
            <s xml:id="echoid-s2380" xml:space="preserve">ex propoſit. </s>
            <s xml:id="echoid-s2381" xml:space="preserve">15.
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            </s>
            <s xml:id="echoid-s2382" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2383" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2384" xml:space="preserve">habetur ratio prædicti annuli ad conicum. </s>
            <s xml:id="echoid-s2385" xml:space="preserve">
              <lb/>
            B C H. </s>
            <s xml:id="echoid-s2386" xml:space="preserve">Hoc autem ſic in numeris inuenietur in co-
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            nico quadratico: </s>
            <s xml:id="echoid-s2387" xml:space="preserve">ſupponamus in ſecunda figura (in
              <lb/>
            qua faciemus operationem in V X, & </s>
            <s xml:id="echoid-s2388" xml:space="preserve">quam in ip-
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            ſa faciemus intelligemus factam in F C) V X, eſſe
              <lb/>
            ſectam bifariam in ℟, & </s>
            <s xml:id="echoid-s2389" xml:space="preserve">in 2, vt V 2, ſit ad 2 X,
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            vt 14, ad 11. </s>
            <s xml:id="echoid-s2390" xml:space="preserve">Ergo ℟, erit centrum grauitatis to-
              <lb/>
            tius cylindri annulo circumſcripti, & </s>
            <s xml:id="echoid-s2391" xml:space="preserve">2, erit ex di-
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            ctis, centrum grauitatis annuli. </s>
            <s xml:id="echoid-s2392" xml:space="preserve">Ergo qualium </s>
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