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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            <s xml:id="echoid-s1584" xml:space="preserve">COnoidibus hyperbolico A B C, & </s>
            <s xml:id="echoid-s1585" xml:space="preserve">parabolico
              <lb/>
            E B F, ſint circumſcripti cylindri Q C, T F.
              <lb/>
            </s>
            <s xml:id="echoid-s1586" xml:space="preserve">Dico tubum cylindricum Q E L C, triplum eſſe ex-
              <lb/>
            ceſſus conoidis A B C, ſupra conoides E B F. </s>
            <s xml:id="echoid-s1587" xml:space="preserve">Quo-
              <lb/>
            niam enim cylindrus Q C, eſt ad cylindrum T F,
              <lb/>
            vt quadratum A D, ad quadratum D E; </s>
            <s xml:id="echoid-s1588" xml:space="preserve">nempe
              <lb/>
            ex hypotheſi, vt D G, ad G B, ergo per conuer-
              <lb/>
            ſionem rationis & </s>
            <s xml:id="echoid-s1589" xml:space="preserve">conuertendo, erit tubus cylin-
              <lb/>
            dricus Q E L C, ad cylindrum Q C, vt B D, ad
              <lb/>
            D G. </s>
            <s xml:id="echoid-s1590" xml:space="preserve">Sed ex propoſit. </s>
            <s xml:id="echoid-s1591" xml:space="preserve">5. </s>
            <s xml:id="echoid-s1592" xml:space="preserve">7. </s>
            <s xml:id="echoid-s1593" xml:space="preserve">& </s>
            <s xml:id="echoid-s1594" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1595" xml:space="preserve">cylindrus Q C,
              <lb/>
            eſt ad conoides A B C, vt D G, ad dimidium B G,
              <lb/>
            cum tertia parte D B: </s>
            <s xml:id="echoid-s1596" xml:space="preserve">ergo ex æquali, erit tubus
              <lb/>
            Q E L C, ad conoides A B C, vt D B, ad dimi-
              <lb/>
            diam G B, cum tertia parte D B. </s>
            <s xml:id="echoid-s1597" xml:space="preserve">Rurſum, quoniam
              <lb/>
            diuidendo, eſt tubus Q E L C, ad cylindrum T F,
              <lb/>
            vt rectangulum A E C, ad quadratum E D, nem-
              <lb/>
            pe ex hypotheſi, vt D B, ad B G, & </s>
            <s xml:id="echoid-s1598" xml:space="preserve">conoides
              <lb/>
            E B F, eſt dimidium cylindri T F, vt oſtendimus
              <lb/>
            præcipuè in lib. </s>
            <s xml:id="echoid-s1599" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1600" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s1601" xml:space="preserve">15. </s>
            <s xml:id="echoid-s1602" xml:space="preserve">Ergo tubus Q E L C,
              <lb/>
            erit ad conoides E B F, vt D B, ad dimidiam G B. </s>
            <s xml:id="echoid-s1603" xml:space="preserve">
              <lb/>
            Sed erat ad totum conoides A B C, vt eadem D B,
              <lb/>
            ad dimidiam G B, cum tertia parte D B. </s>
            <s xml:id="echoid-s1604" xml:space="preserve">Ergo
              <lb/>
            Q E L C, erit ad reliquum, nempe ad differentiam
              <lb/>
            conoideorum, vt D B, ad ſui tertiam partem; </s>
            <s xml:id="echoid-s1605" xml:space="preserve">
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            nempe erit triplus talis exceſſus. </s>
            <s xml:id="echoid-s1606" xml:space="preserve">Quod e@@@ oſten-
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            dendum.</s>
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