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-s1461" xml:space="preserve">
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            tionaliter analogas tam in magnitudine, quam in
              <lb/>
            grauitate; </s>
            <s xml:id="echoid-s1462" xml:space="preserve">tam ſecundum totum, quam ſecundum
              <lb/>
            partes proportionales. </s>
            <s xml:id="echoid-s1463" xml:space="preserve">Quot ergo nouæ notitiæ de-
              <lb/>
            ducantur ex hac doctrina tam circa magnitudinem,
              <lb/>
            quam circa grauitatem talis annulilati, ex noſtro ope-
              <lb/>
            re cit. </s>
            <s xml:id="echoid-s1464" xml:space="preserve">vniſquiſque poteſt agnoſcere.</s>
            <s xml:id="echoid-s1465" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1466" xml:space="preserve">Ex propoſit. </s>
            <s xml:id="echoid-s1467" xml:space="preserve">enim 9, lib. </s>
            <s xml:id="echoid-s1468" xml:space="preserve">prim. </s>
            <s xml:id="echoid-s1469" xml:space="preserve">agnoſcet quænam
              <lb/>
            ſit ratio, quam habet tubus cylindricus ex G I, ad
              <lb/>
            portionem annuli lati ex portione minori hyperbo-
              <lb/>
            læ A H I; </s>
            <s xml:id="echoid-s1470" xml:space="preserve">nempe eſſe ad ipſum vt tres A N, ad ex-
              <lb/>
            ceſſum ipſarum ſupra A N, N I, & </s>
            <s xml:id="echoid-s1471" xml:space="preserve">harum tertiam
              <lb/>
            minorem proportionalem. </s>
            <s xml:id="echoid-s1472" xml:space="preserve">Vel ſubtriplandotermi-
              <lb/>
            nos, eſſe vt A N, ad ſubſeſquialteram A I, cum
              <lb/>
            tertia parte exceſſus I N, ſupra illam tertiam pro-
              <lb/>
            portionalem.</s>
            <s xml:id="echoid-s1473" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1474" xml:space="preserve">Ex ſchol prim. </s>
            <s xml:id="echoid-s1475" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s1476" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1477" xml:space="preserve">agnoſcet, tubum cy-
              <lb/>
            lindricum ex parallelogrammo S N, eſſe ad portio-
              <lb/>
            nem annuli ex ſegmento hyperbolæ I H B N, vt tri-
              <lb/>
            pla A N, ad duplam A N, vna cum exceſſu ipſius
              <lb/>
            ſupra prædictam tertiam proportionalem. </s>
            <s xml:id="echoid-s1478" xml:space="preserve">Et ſub-
              <lb/>
            triplando terminos, eſſe vt A N, ad A I, cum duo-
              <lb/>
            bus tertijs I N, & </s>
            <s xml:id="echoid-s1479" xml:space="preserve">cum tertia parte exceſſus I N,
              <lb/>
            ſupraillam tertiam proportionalem. </s>
            <s xml:id="echoid-s1480" xml:space="preserve">Imo ex ſchol.
              <lb/>
            </s>
            <s xml:id="echoid-s1481" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1482" xml:space="preserve">cit. </s>
            <s xml:id="echoid-s1483" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s1484" xml:space="preserve">agnoſcet, eſſe eundem tubum cylin-
              <lb/>
            dricum ad eandem portionem annuli, vt triplum
              <lb/>
            recta gulum T S I, ad duplum rectangulum T S I,
              <lb/>
            cum rectangulo T H I. </s>
            <s xml:id="echoid-s1485" xml:space="preserve">Et ſubtriplando terminos,
              <lb/>
            vt rectangulum T S I, ad ſubſeſquialterum ipſius,
              <lb/>
            cum tertia parte rectanguli T H I.</s>
            <s xml:id="echoid-s1486" xml:space="preserve"/>
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