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-head18" xml:space="preserve">PROPOSITIO PRIMA.</head>
          <p style="it">
            <s xml:id="echoid-s151" xml:space="preserve">Si circa diametrum hyperbolæ ſit etiam parabola ita diui-
              <lb/>
            dens baſim byperbolæ, vt quadratum ſemibaſis, ſit ad
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            quadratum ſemibaſis parabolæ, vt compoſita ex latere
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            tranſuerſo hyperbolæ, & </s>
            <s xml:id="echoid-s152" xml:space="preserve">ex diametro, ad tranſuerſam
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            latus. </s>
            <s xml:id="echoid-s153" xml:space="preserve">Tota parabola cadet intra hyperbolam.</s>
            <s xml:id="echoid-s154" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s155" xml:space="preserve">TRes ſequentes propoſit. </s>
            <s xml:id="echoid-s156" xml:space="preserve">probantur ferè ijſdem
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            terminis à Luca Valerio in append. </s>
            <s xml:id="echoid-s157" xml:space="preserve">ad lib. </s>
            <s xml:id="echoid-s158" xml:space="preserve">3.
              <lb/>
            </s>
            <s xml:id="echoid-s159" xml:space="preserve">de cent grauit. </s>
            <s xml:id="echoid-s160" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s161" xml:space="preserve">pri & </s>
            <s xml:id="echoid-s162" xml:space="preserve">2. </s>
            <s xml:id="echoid-s163" xml:space="preserve">Efto ergo hyper-
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            bola A B C, cuius latus tranſuerſum G B, diame-
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            ter B D, circa quam ſit etiam parabola E B F, ſic
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            fecans A C, vt quadratum A D, ſit ad quadra-
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            tum D E, vt D G, ad G B. </s>
            <s xml:id="echoid-s164" xml:space="preserve">Dico totam para-
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            bolam E B F, cadereintra hyperbolam. </s>
            <s xml:id="echoid-s165" xml:space="preserve">Accipia-
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            tur arbitrariè punctum L, per quod ducatur ordi-
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            natim applicata H K L. </s>
            <s xml:id="echoid-s166" xml:space="preserve">Quoniam ex propoſit. </s>
            <s xml:id="echoid-s167" xml:space="preserve">21. </s>
            <s xml:id="echoid-s168" xml:space="preserve">
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            prim. </s>
            <s xml:id="echoid-s169" xml:space="preserve">conic. </s>
            <s xml:id="echoid-s170" xml:space="preserve">quadratum H L, eſt ad quadratum
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            A D, vt rectangulum G L B, ad rectangulum
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            G D B; </s>
            <s xml:id="echoid-s171" xml:space="preserve">& </s>
            <s xml:id="echoid-s172" xml:space="preserve">ex hypotheſi, eſt quadratum A D, ad
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            quadratum D E, vt D G, ad G B; </s>
            <s xml:id="echoid-s173" xml:space="preserve">nempeſum-
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            pta communi altitudine D B, vt rectangulum
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            G D B, ad rectangulum G B D. </s>
            <s xml:id="echoid-s174" xml:space="preserve">Ergo ex æquali,
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            erit quadratum H L, ad quadratum E D, vt re-
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            ctangulum G L B, ad rectangulum G B D. </s>
            <s xml:id="echoid-s175" xml:space="preserve">Rur-
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            ſum; </s>
            <s xml:id="echoid-s176" xml:space="preserve">quoniam in parabola eſt ex propoſit. </s>
            <s xml:id="echoid-s177" xml:space="preserve">20. </s>
            <s xml:id="echoid-s178" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s179" xml:space="preserve">
              <lb/>
            eit. </s>
            <s xml:id="echoid-s180" xml:space="preserve">quadratum E D, ad quadratum K L, vt D </s>
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