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-s233" xml:space="preserve">
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            partes proportionales, erit æqualis differentiæ cono-
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            rum.</s>
            <s xml:id="echoid-s234" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s235" xml:space="preserve">SEd ex hyperbola A B C, & </s>
            <s xml:id="echoid-s236" xml:space="preserve">parabola E B F,
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            intelligantur genita conoidea, in quibus ſint
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            inſcripti pariter coni A B C, E B F. </s>
            <s xml:id="echoid-s237" xml:space="preserve">Dico diffe-
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            rentiam conoideorum, nempe exceſſum conoidis
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            hyperbolici ſupra conoides parabolicum, æqualem
              <lb/>
            fore differentiæ conorum. </s>
            <s xml:id="echoid-s238" xml:space="preserve">Sumatur in diametro
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            B D, arbitrariè punctum L, per quod agatur pla-
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            num H O, plano A C, parallelum, ſecans om-
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            nia dicta ſolida, vt in ſchemate. </s>
            <s xml:id="echoid-s239" xml:space="preserve">Quoniam enim vt
              <lb/>
            quadratum D B, ad quadratum B L, ſic eſt tam
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            quadratum totius A D, ad quadratum totius P L,
              <lb/>
            quam ablatum quadratum E D, ad ablatum qua-
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            dratum M L: </s>
            <s xml:id="echoid-s240" xml:space="preserve">& </s>
            <s xml:id="echoid-s241" xml:space="preserve">quadratum D E, eſt ad rectan-
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            gulum A E C, vt quadratum L M, ad rectangu-
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            lum P M R (quia proportiones horum quadra-
              <lb/>
            torum ad hæc rectangula componuntur ex ijſdem
              <lb/>
            proportionibus, vt facile quilibet modicè in geo-
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            metria expertus poteſt agnoſcere). </s>
            <s xml:id="echoid-s242" xml:space="preserve">Ergo ex propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s243" xml:space="preserve">2. </s>
            <s xml:id="echoid-s244" xml:space="preserve">erit vt quadratum D B, ad quadratum B L, ſic
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            rectangulum A E C, ad rectangulum P M R. </s>
            <s xml:id="echoid-s245" xml:space="preserve">Sed
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            etiam ex propoſit. </s>
            <s xml:id="echoid-s246" xml:space="preserve">antec. </s>
            <s xml:id="echoid-s247" xml:space="preserve">eſt vt quadratum D B, ad
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            quadratum B L, ſic rectangulum A E C, ad rectan-
              <lb/>
            gulum H k O. </s>
            <s xml:id="echoid-s248" xml:space="preserve">Ergo vt rectangulum A E C, ad re-
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            ctangulum P M R, ſic idem rectangulum A E C, ad
              <lb/>
            rectangulum H k O. </s>
            <s xml:id="echoid-s249" xml:space="preserve">Ergo rectangulum P M R,
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            erit æquale rectangulo H k O. </s>
            <s xml:id="echoid-s250" xml:space="preserve">Quare etiam </s>
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