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-s1823" xml:space="preserve">
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            pattem terminatam ad N, vt numerus annuli au-
              <lb/>
            ctus ternario ad numerum annuli auctum vnitate.
              <lb/>
            </s>
            <s xml:id="echoid-s1824" xml:space="preserve">Nimirum in primo vt 4. </s>
            <s xml:id="echoid-s1825" xml:space="preserve">ad 2. </s>
            <s xml:id="echoid-s1826" xml:space="preserve">Inſec. </s>
            <s xml:id="echoid-s1827" xml:space="preserve">vt 5. </s>
            <s xml:id="echoid-s1828" xml:space="preserve">ad 3. </s>
            <s xml:id="echoid-s1829" xml:space="preserve">In
              <lb/>
            tertio vt 6. </s>
            <s xml:id="echoid-s1830" xml:space="preserve">ad 4. </s>
            <s xml:id="echoid-s1831" xml:space="preserve">& </s>
            <s xml:id="echoid-s1832" xml:space="preserve">ſic in infinitum. </s>
            <s xml:id="echoid-s1833" xml:space="preserve">Ita enim ex
              <lb/>
            ſchol. </s>
            <s xml:id="echoid-s1834" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1835" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s1836" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1837" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1838" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1839" xml:space="preserve">centrum æquilibrij ſemi-
              <lb/>
            parabolæ A B D, ſeù centrum grauitatis figuræ
              <lb/>
            N A B, diuidit A D.</s>
            <s xml:id="echoid-s1840" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1841" xml:space="preserve">Prædictæ autem figuræ circumſcripto parallelo-
              <lb/>
            grammo E N, & </s>
            <s xml:id="echoid-s1842" xml:space="preserve">figura conſtante ex duobus trili-
              <lb/>
            neis N O A B E, reuoluta prædicto modo: </s>
            <s xml:id="echoid-s1843" xml:space="preserve">centrum
              <lb/>
            grauitatis ſolidi geniti ſic fecabit O N, vt pars ter-
              <lb/>
            minata ad O, ſit ad partem terminatam ad N, vt
              <lb/>
            vnitas ad numerum annuli vnitate auctum. </s>
            <s xml:id="echoid-s1844" xml:space="preserve">Nempe
              <lb/>
            in primo vt 1. </s>
            <s xml:id="echoid-s1845" xml:space="preserve">ad 2. </s>
            <s xml:id="echoid-s1846" xml:space="preserve">In ſec: </s>
            <s xml:id="echoid-s1847" xml:space="preserve">vt 1. </s>
            <s xml:id="echoid-s1848" xml:space="preserve">ad 3. </s>
            <s xml:id="echoid-s1849" xml:space="preserve">In tertio vt 1.
              <lb/>
            </s>
            <s xml:id="echoid-s1850" xml:space="preserve">ad 4. </s>
            <s xml:id="echoid-s1851" xml:space="preserve">Et ſic in infinitum. </s>
            <s xml:id="echoid-s1852" xml:space="preserve">Ratio eſt quia centrum
              <lb/>
            grauitatis talium trilincorum ſimul coniunctorum
              <lb/>
            ſic diuidit A D, vt centrum æquilibrij vnius v. </s>
            <s xml:id="echoid-s1853" xml:space="preserve">g. </s>
            <s xml:id="echoid-s1854" xml:space="preserve">
              <lb/>
            A E B, diuidit E B. </s>
            <s xml:id="echoid-s1855" xml:space="preserve">Atex ſchol. </s>
            <s xml:id="echoid-s1856" xml:space="preserve">prim. </s>
            <s xml:id="echoid-s1857" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s1858" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1859" xml:space="preserve">
              <lb/>
            lib. </s>
            <s xml:id="echoid-s1860" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1861" xml:space="preserve">E B, in prædicta ratione ſecatur à tali centro
              <lb/>
            æquilibrij. </s>
            <s xml:id="echoid-s1862" xml:space="preserve">Quare patet propoſitum.</s>
            <s xml:id="echoid-s1863" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1864" xml:space="preserve">At ſi ſemiparabola quælibet intelligatur duplicari
              <lb/>
            ad partes B F, vt figura conſtans ſit C D B Q P, & </s>
            <s xml:id="echoid-s1865" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s1866" xml:space="preserve">hæc rotetur vel circa D C, vel circa ipſi paralle-
              <lb/>
            lam. </s>
            <s xml:id="echoid-s1867" xml:space="preserve">Centrum grauitatis ſolidi geniti ſecabit pari-
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            ter D C, vt pars terminata ad C, ſit ad partem ter-
              <lb/>
            minatam ad D, vt numerus annuli ternario auctus,
              <lb/>
            ad numerum annuli vnitate auctum. </s>
            <s xml:id="echoid-s1868" xml:space="preserve">Nempe vt 4,
              <lb/>
            ad 2. </s>
            <s xml:id="echoid-s1869" xml:space="preserve">vt 5. </s>
            <s xml:id="echoid-s1870" xml:space="preserve">ad 3. </s>
            <s xml:id="echoid-s1871" xml:space="preserve">&</s>
            <s xml:id="echoid-s1872" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1873" xml:space="preserve">Item ſi trilineum C B Q, ſic ro-
              <lb/>
            tetur; </s>
            <s xml:id="echoid-s1874" xml:space="preserve">D C, ſic ſecabitur vt pars terminata ad </s>
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