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-s206" xml:space="preserve">
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            G N. </s>
            <s xml:id="echoid-s207" xml:space="preserve">Ergo ex æquali, erit A k, ad C L, vt E M, ad
              <lb/>
            G N. </s>
            <s xml:id="echoid-s208" xml:space="preserve">Quod &</s>
            <s xml:id="echoid-s209" xml:space="preserve">c.</s>
            <s xml:id="echoid-s210" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div12" type="section" level="1" n="10">
          <head xml:id="echoid-head20" xml:space="preserve">PROPOSITIO III.</head>
          <p style="it">
            <s xml:id="echoid-s211" xml:space="preserve">Factis ijſdem quæ in prima propoſit. </s>
            <s xml:id="echoid-s212" xml:space="preserve">exceſſus quadratorum
              <lb/>
            ordinatim applicatarum in byperbola ſupra quadrata or-
              <lb/>
            dinatim applicatarum in parab la, erunt ad inuicem, vt
              <lb/>
            quadrata partium diametri interceptarum inter ipſas, & </s>
            <s xml:id="echoid-s213" xml:space="preserve">
              <lb/>
            verticem figurarum.</s>
            <s xml:id="echoid-s214" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s215" xml:space="preserve">IN eodem ſchemate, ſint ordinatim applicatæ ad
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            diametrum A E D C, H K L O. </s>
            <s xml:id="echoid-s216" xml:space="preserve">Dico exceſ-
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            ſum quadrati A D, ſupra quadratum E D, eſſe
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            ad exceſſum quadrati H L, ſupra quadratum k L,
              <lb/>
            vt quadratum D B, ad quadratum B L. </s>
            <s xml:id="echoid-s217" xml:space="preserve">Quo-
              <lb/>
            niam enim quadratum totum A D, eſt ad totum
              <lb/>
            quadratum H L, vt totum rectangulum G D B,
              <lb/>
            ad totum rectangulum G L B: </s>
            <s xml:id="echoid-s218" xml:space="preserve">& </s>
            <s xml:id="echoid-s219" xml:space="preserve">ablatum quadra-
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            tum E D, probatum eſt eſſe ad ablatum quadra-
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            tum K L, vt ablatum rectangulum D B G, ad
              <lb/>
            ablatum rectangulum L B G: </s>
            <s xml:id="echoid-s220" xml:space="preserve">eſtque ablatum qua-
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            dratum D E, ad reliquum rectangulum A E C,
              <lb/>
            vt ablatum quadratum L k, ad ablatum rectangu-
              <lb/>
            lum H k O (quiacum ex hypotheſi, ſit quadratum
              <lb/>
            A D, ad quadratum D E, vt D G, ad G B;
              <lb/>
            </s>
            <s xml:id="echoid-s221" xml:space="preserve">nempe vt rectangulum G D B, ad rectangulum
              <lb/>
            G B D; </s>
            <s xml:id="echoid-s222" xml:space="preserve">erit diuidendo, & </s>
            <s xml:id="echoid-s223" xml:space="preserve">conuertendo, quadra-
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            tum D E, ad rectangulum A E C, vt </s>
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