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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          <head xml:id="echoid-head94" xml:space="preserve">PROPOSITIO XXXIX.</head>
          <p style="it">
            <s xml:id="echoid-s2718" xml:space="preserve">Datis ijſdem, quœ in antecedenti propoſitione in primo
              <lb/>
            ſehemate, datur centrum æquilibrij figuræ in
              <lb/>
            linea, quæ eſt radius rotationis.</s>
            <s xml:id="echoid-s2719" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2720" xml:space="preserve">SEd dentur eadem, quæ ſupra in primo ſchema-
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            te. </s>
            <s xml:id="echoid-s2721" xml:space="preserve">Dico dari in D C, quæ eſt radius rotatio-
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            nis, centrum æquilibrij ſemifiguræ D B C. </s>
            <s xml:id="echoid-s2722" xml:space="preserve">Cum
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            enim exanteced. </s>
            <s xml:id="echoid-s2723" xml:space="preserve">propoſit datis ijs, detur etiam ra-
              <lb/>
            tio cylindri ad alterum ſolidorum. </s>
            <s xml:id="echoid-s2724" xml:space="preserve">Ergo dabitur e-
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            tiam ratio ſolidorum ad inuicem; </s>
            <s xml:id="echoid-s2725" xml:space="preserve">nempe dabitur ra-
              <lb/>
            tio ſolidi A B C, ad ſolidum D B C H V. </s>
            <s xml:id="echoid-s2726" xml:space="preserve">Sed ex
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            propoſit. </s>
            <s xml:id="echoid-s2727" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2728" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2729" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2730" xml:space="preserve">ſolidum ad ſolidum eſt vt pars D C,
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            terminata à D, & </s>
            <s xml:id="echoid-s2731" xml:space="preserve">àcentro æquilibrij figuræ D B C,
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            ad reliquam partem D C. </s>
            <s xml:id="echoid-s2732" xml:space="preserve">Quare patet propo-
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            ſitum.</s>
            <s xml:id="echoid-s2733" xml:space="preserve"/>
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          <head xml:id="echoid-head95" xml:space="preserve">PROPOSITIO XL.</head>
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            <s xml:id="echoid-s2734" xml:space="preserve">Fi ſecundo ſchemate datis ijſdem, & </s>
            <s xml:id="echoid-s2735" xml:space="preserve">dataratione annu-
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            li lati ex ſernifigura ad annulum ſtrictum eiuſdem,
              <lb/>
            dabitur prœdictum centrum.</s>
            <s xml:id="echoid-s2736" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2737" xml:space="preserve">SEd in ſecundo ſchemate, vltra data in ante-
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            cedenti, detur etiam ratio annuli lati
              <lb/>
            D B C Z H ℟, ad annulum ſtrictum exeadem D B C,
              <lb/>
            reuoluta circa F C. </s>
            <s xml:id="echoid-s2738" xml:space="preserve">Dico dari eius centrum </s>
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