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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          <p style="it">
            <s xml:id="echoid-s991" xml:space="preserve">
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            intercepta inter ſecundam diametrum, & </s>
            <s xml:id="echoid-s992" xml:space="preserve">aſymptotum,
              <lb/>
            reuoluto cicca ſecundam diametrum; </s>
            <s xml:id="echoid-s993" xml:space="preserve">& </s>
            <s xml:id="echoid-s994" xml:space="preserve">hoc tam ſecun-
              <lb/>
            dum totum, quam ſecundum partes proportionales.</s>
            <s xml:id="echoid-s995" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s996" xml:space="preserve">ESto ſemihyperbola A B C, cuius diameter A B;
              <lb/>
            </s>
            <s xml:id="echoid-s997" xml:space="preserve">E B dimidium lateris tranſuerſi; </s>
            <s xml:id="echoid-s998" xml:space="preserve">centrum E; </s>
            <s xml:id="echoid-s999" xml:space="preserve">
              <lb/>
            aſymptotus E G; </s>
            <s xml:id="echoid-s1000" xml:space="preserve">ſecunda diameter E F; </s>
            <s xml:id="echoid-s1001" xml:space="preserve">& </s>
            <s xml:id="echoid-s1002" xml:space="preserve">pa-
              <lb/>
            rallelogrammum A D, ſemihy perbolæ circumſcri-
              <lb/>
            ptum cum triangulo E F G, rotentur circa E F. </s>
            <s xml:id="echoid-s1003" xml:space="preserve">Di-
              <lb/>
            co annulum latum ortum ex rotatione trilinei mixti
              <lb/>
            C B D, circa E F, æqualem eſſe cono G E M, & </s>
            <s xml:id="echoid-s1004" xml:space="preserve">
              <lb/>
            hoc tam ſecundum totum, quam ſecundum partes
              <lb/>
            proportionales. </s>
            <s xml:id="echoid-s1005" xml:space="preserve">Intelligantul oppoſitæ ſectiones vt
              <lb/>
            in ſchemate, & </s>
            <s xml:id="echoid-s1006" xml:space="preserve">ſumatur a bitrariè in E F, quodli-
              <lb/>
            bet punctum I, per quod ducatur O I N, paralle-
              <lb/>
            la L C, ſecans aſymptotum E G, in P. </s>
            <s xml:id="echoid-s1007" xml:space="preserve">Quadra-
              <lb/>
            tum I O, eſt æquale tam rectangulo O P N, cum
              <lb/>
            quadrato P I, quam rectangulo O Q N, cum. </s>
            <s xml:id="echoid-s1008" xml:space="preserve">
              <lb/>
            quadrato Q I. </s>
            <s xml:id="echoid-s1009" xml:space="preserve">Ergo rectangulum O P N, cum
              <lb/>
            quadrato P I, erit æquale rectangulo O Q N, cum
              <lb/>
            quadrato Q I. </s>
            <s xml:id="echoid-s1010" xml:space="preserve">Sed ex propoſit. </s>
            <s xml:id="echoid-s1011" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1012" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s1013" xml:space="preserve">conic. </s>
            <s xml:id="echoid-s1014" xml:space="preserve">re-
              <lb/>
            ctangulum O P N, eſt aquale quadrato B E, ſeù
              <lb/>
            quadrato Q I. </s>
            <s xml:id="echoid-s1015" xml:space="preserve">Ergo reliquum rectangulum O Q N,
              <lb/>
            erit æquale reliquo quadrato P I. </s>
            <s xml:id="echoid-s1016" xml:space="preserve">Quare & </s>
            <s xml:id="echoid-s1017" xml:space="preserve">armil-
              <lb/>
            la circularis O Q N, erit æqualis circulo P R. </s>
            <s xml:id="echoid-s1018" xml:space="preserve">Cum
              <lb/>
            vero punctum I, ſumptum ſit arbitrariè ergo om-
              <lb/>
            nes armillæ circulares parallelæ armillæ C D L, or-
              <lb/>
            tæ ex rotatione trilinei C B D, circa E F, erunt
              <lb/>
            æquales omnibus circulis coni G E M. </s>
            <s xml:id="echoid-s1019" xml:space="preserve">Et </s>
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