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-div93" type="section" level="1" n="63">
          <pb o="108" file="0120" n="120"/>
          <p>
            <s xml:id="echoid-s1934" xml:space="preserve">Supponamus autem A B D, eſſe portionem mi-
              <lb/>
            norem parabolæ cuiuſcunque reſectæ linea B D,
              <lb/>
            diametro parallela, adeovt A D, ſit baſis talis por-
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            tionis; </s>
            <s xml:id="echoid-s1935" xml:space="preserve">& </s>
            <s xml:id="echoid-s1936" xml:space="preserve">intelligamus portionem A B D, duplicari
              <lb/>
            ad partes B D, adeo vt B D, diametro parallela
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            euadat axis figuræ A B C; </s>
            <s xml:id="echoid-s1937" xml:space="preserve">& </s>
            <s xml:id="echoid-s1938" xml:space="preserve">intelligamus con-
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            ſueto modo figuram A B C, rotari circa F C, &</s>
            <s xml:id="echoid-s1939" xml:space="preserve">c.
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            </s>
            <s xml:id="echoid-s1940" xml:space="preserve">Ex propoſit. </s>
            <s xml:id="echoid-s1941" xml:space="preserve">15. </s>
            <s xml:id="echoid-s1942" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1943" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1944" xml:space="preserve">in qua aſſignatur centrum æ-
              <lb/>
            quilibrij portionis A B D, in B D, diametro pa-
              <lb/>
            rallela, & </s>
            <s xml:id="echoid-s1945" xml:space="preserve">conſequenter centrum grauitatis figuræ
              <lb/>
            A B C, habebimus centrum grauitatis talis ſolidi. </s>
            <s xml:id="echoid-s1946" xml:space="preserve">
              <lb/>
            Si vero intelligamus figuræ A B C, circumſcriptum
              <lb/>
            parallelogrammum E C; </s>
            <s xml:id="echoid-s1947" xml:space="preserve">cum exceſſus ipſius habea-
              <lb/>
            mus centrum grauitatis, quia habemus centrum gra-
              <lb/>
            uitatis & </s>
            <s xml:id="echoid-s1948" xml:space="preserve">parallelogrammi, & </s>
            <s xml:id="echoid-s1949" xml:space="preserve">portionis, & </s>
            <s xml:id="echoid-s1950" xml:space="preserve">ex pro-
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            poſit. </s>
            <s xml:id="echoid-s1951" xml:space="preserve">15. </s>
            <s xml:id="echoid-s1952" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1953" xml:space="preserve">pri. </s>
            <s xml:id="echoid-s1954" xml:space="preserve">habemus rationem parallelogram-
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            mi ad ſiguram, & </s>
            <s xml:id="echoid-s1955" xml:space="preserve">conſequenter illius exceſſus ad fi-
              <lb/>
            guram; </s>
            <s xml:id="echoid-s1956" xml:space="preserve">habebimus etiam centrum grauitatis ſolidi
              <lb/>
            ex illo exceſſu circa F C, vel illis parallelam. </s>
            <s xml:id="echoid-s1957" xml:space="preserve">Quod
              <lb/>
            vero dictum eſt de figura A B C, patet ex ſupradi-
              <lb/>
            ctis intelligendum etiam fore de figura B D C R G. </s>
            <s xml:id="echoid-s1958" xml:space="preserve">
              <lb/>
            Sed ſi talis figura intelligeretur duplicata ad partes
              <lb/>
            A D, adeovt baſis D A, euadat axis figuræ N A B. </s>
            <s xml:id="echoid-s1959" xml:space="preserve">
              <lb/>
            Ex propoſit. </s>
            <s xml:id="echoid-s1960" xml:space="preserve">14. </s>
            <s xml:id="echoid-s1961" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1962" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1963" xml:space="preserve">habebimus centrum grauita-
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            tis annulorum ex N A B, circa O N, vel illi pa-
              <lb/>
            rallelam. </s>
            <s xml:id="echoid-s1964" xml:space="preserve">Idemque intelligendum eſt ſi figura intel-
              <lb/>
            ligeretur duplicata vt C D B Q P.</s>
            <s xml:id="echoid-s1965" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1966" xml:space="preserve">Si vero in ſequenti figura, portio maior A I B D,
              <lb/>
            parabolæ cuiuſcunque, cuius baſis A D, </s>
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