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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        <div xml:id="echoid-div151" type="section" level="1" n="97">
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            poſitio vniuerſalis in qualibet portione parabolæ
              <lb/>
            quadraticæ.</s>
            <s xml:id="echoid-s3089" xml:space="preserve"/>
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        <div xml:id="echoid-div152" type="section" level="1" n="98">
          <head xml:id="echoid-head110" xml:space="preserve">PROPOSITIO XLVIII.</head>
          <p style="it">
            <s xml:id="echoid-s3090" xml:space="preserve">Si in quacunque portione parabolœ quadraticœ reſectœ linea
              <lb/>
            diametro parallela inſcribatur triangulum, & </s>
            <s xml:id="echoid-s3091" xml:space="preserve">baſis por-
              <lb/>
            tionts parabolœ ſecetur bifariam, & </s>
            <s xml:id="echoid-s3092" xml:space="preserve">per punctum biſſe-
              <lb/>
            ctionis ducatur parallela diametro. </s>
            <s xml:id="echoid-s3093" xml:space="preserve">Centrum œquilibrij
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            ſecundum baſim prœdictœ portionis ſic ſecabit baſim,
              <lb/>
            vt pars ad curuam terminata ſit ad reliquam, vt pa-
              <lb/>
            rallela diametro ducta à puncto biſſectionis, vna cum tn-
              <lb/>
            tercepta inter punctum bißectionis, & </s>
            <s xml:id="echoid-s3094" xml:space="preserve">latus trianguli,
              <lb/>
            ad prœdictam parallelam diametro.</s>
            <s xml:id="echoid-s3095" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3096" xml:space="preserve">ESto parabola A B C, quadratica, cuius baſis
              <lb/>
            A C, diameter B D, & </s>
            <s xml:id="echoid-s3097" xml:space="preserve">ſit quælibet eius por-
              <lb/>
            tio E F B C, reſecta F E, diametro B D, paralle-
              <lb/>
            la, & </s>
            <s xml:id="echoid-s3098" xml:space="preserve">in portione ſit in ſciiptum triangulum CFE; </s>
            <s xml:id="echoid-s3099" xml:space="preserve">ſit-
              <lb/>
            que C E, ſecta bifariam in G, & </s>
            <s xml:id="echoid-s3100" xml:space="preserve">per G, ducatur
              <lb/>
            GIH, parallela diametro, ſitque K, centrum æ-
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            quilibrij in baſi portionis E F B C. </s>
            <s xml:id="echoid-s3101" xml:space="preserve">Dico C k, eſſe
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            ad k E, vt H G, cum G I, ad H I. </s>
            <s xml:id="echoid-s3102" xml:space="preserve">In tertia figura
              <lb/>
            ſchematis anteced. </s>
            <s xml:id="echoid-s3103" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s3104" xml:space="preserve">intelligatur portio ſphæ-
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            ræ, vel ſphæroidis B A C, proportionalis E F B C,
              <lb/>
            portioni parabolæ, & </s>
            <s xml:id="echoid-s3105" xml:space="preserve">intelligantur in ea omnia,
              <lb/>
            quæ ſupra, Ergo C K, erit ad k E, in portione pa-
              <lb/>
            rabolæ, vt A O, ad O D, in portione ſphæræ; </s>
            <s xml:id="echoid-s3106" xml:space="preserve">nem-
              <lb/>
            pe ex propoſit. </s>
            <s xml:id="echoid-s3107" xml:space="preserve">anteced. </s>
            <s xml:id="echoid-s3108" xml:space="preserve">vt duplum quadratum G </s>
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