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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            circa D B, ſiue circa F C. </s>
            <s xml:id="echoid-s2693" xml:space="preserve">Ergo quacunque data,
              <lb/>
            dabitur etiam altera; </s>
            <s xml:id="echoid-s2694" xml:space="preserve">nempe data ratione cylindri
              <lb/>
            E C, ad ſolidum A B C, dabitur quoque ratio cy-
              <lb/>
            lindri D H, ad ſolidum ex D B C, circa F C, & </s>
            <s xml:id="echoid-s2695" xml:space="preserve">
              <lb/>
            è contra.</s>
            <s xml:id="echoid-s2696" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2697" xml:space="preserve">Pariter in ſecunda figura. </s>
            <s xml:id="echoid-s2698" xml:space="preserve">Quoniam datur ratio
              <lb/>
            parallelogrammi D F, ad ſemifiguram D B C, ſi-
              <lb/>
            ue parallelogrammi E C, ad integram figuram
              <lb/>
            A B C, dabitur ex propoſit. </s>
            <s xml:id="echoid-s2699" xml:space="preserve">29. </s>
            <s xml:id="echoid-s2700" xml:space="preserve">ratio tubi cylindri-
              <lb/>
            ci E C Y, ad annulum latum A B C Z H G. </s>
            <s xml:id="echoid-s2701" xml:space="preserve">Ergo
              <lb/>
            ex propoſit. </s>
            <s xml:id="echoid-s2702" xml:space="preserve">30. </s>
            <s xml:id="echoid-s2703" xml:space="preserve">dabitur quoque ratio prædicti tubi
              <lb/>
            ad quatuor ſolida ex D B C, duabus vicibus reuo-
              <lb/>
            luta circa B D, & </s>
            <s xml:id="echoid-s2704" xml:space="preserve">duabus circa T S. </s>
            <s xml:id="echoid-s2705" xml:space="preserve">Ergo dabi-
              <lb/>
            tur quoque ratio talis tubiad vnum ſolidum A B C,
              <lb/>
            & </s>
            <s xml:id="echoid-s2706" xml:space="preserve">ad vnum D B C Z H ℟. </s>
            <s xml:id="echoid-s2707" xml:space="preserve">Cum autem detur ratio
              <lb/>
            D S, tam ad A C, quam ad C G (hoc enim eſt
              <lb/>
            ſupponendum, quia danda eſt C S, qua data dantur
              <lb/>
            prædicta) dabitur etiam ratio quadrati D S, ad re-
              <lb/>
            ctangulum A C G; </s>
            <s xml:id="echoid-s2708" xml:space="preserve">nempe dabitur ratio cylindri
              <lb/>
            D H, ad tubum cylindricum E C Y. </s>
            <s xml:id="echoid-s2709" xml:space="preserve">Ergo ex æqua-
              <lb/>
            li, dabitur quoque ratio cylindri B ℟, ad ſolidum
              <lb/>
            A B C, ſimul cum ſolido D B C Z H ℟. </s>
            <s xml:id="echoid-s2710" xml:space="preserve">Siergo de-
              <lb/>
            tur etiam ex hypotheſi, ratio cylindri E C, ad ſoli-
              <lb/>
            dum A B C, quiacum detur ratio cylindri D H, ad
              <lb/>
            cylindrum E C, datur etiam ratio cylindri D H,
              <lb/>
            ad ſolidum A B C. </s>
            <s xml:id="echoid-s2711" xml:space="preserve">Ergo dabitur quoque ratio eiuſ-
              <lb/>
            dem cylindri D H, ad ſolidum D B C Z H ℟. </s>
            <s xml:id="echoid-s2712" xml:space="preserve">Si
              <lb/>
            vero detur ratio ex hypotheſi, cylindri D H, ad ſo-
              <lb/>
            lidum D B C Z H ℟; </s>
            <s xml:id="echoid-s2713" xml:space="preserve">ergo dabitur quoque ratio </s>
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