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-s1777" xml:space="preserve">
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            10. </s>
            <s xml:id="echoid-s1778" xml:space="preserve">& </s>
            <s xml:id="echoid-s1779" xml:space="preserve">ſic in infinitum. </s>
            <s xml:id="echoid-s1780" xml:space="preserve">Ratio eſt, quia ex ſchol.
              <lb/>
            </s>
            <s xml:id="echoid-s1781" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s1782" xml:space="preserve">8. </s>
            <s xml:id="echoid-s1783" xml:space="preserve">eiuſdem libri centrum grauitatis exceſ-
              <lb/>
            ſus parallelogrammi E C, ſupra parabolam ſic ſecat
              <lb/>
            ipſam B D.</s>
            <s xml:id="echoid-s1784" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1785" xml:space="preserve">Sed ſupponentes A B C, eſſe vel ſemicirculum,
              <lb/>
            vel ſemiellipſim, vel circuli, aut ellipſis portionem,
              <lb/>
            vel etiam hyperbolam. </s>
            <s xml:id="echoid-s1786" xml:space="preserve">Habebimus centrum gra-
              <lb/>
            uitatis annulorum talium figurarum, ſed ſuppoſita
              <lb/>
            figurarum quadratura. </s>
            <s xml:id="echoid-s1787" xml:space="preserve">Hæcautem patent vera eſſe
              <lb/>
            partim ex dictis in lib. </s>
            <s xml:id="echoid-s1788" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1789" xml:space="preserve">vbi in propoſit. </s>
            <s xml:id="echoid-s1790" xml:space="preserve">24. </s>
            <s xml:id="echoid-s1791" xml:space="preserve">aſſigna-
              <lb/>
            uimus centrum grauitatis ſemicirculi; </s>
            <s xml:id="echoid-s1792" xml:space="preserve">& </s>
            <s xml:id="echoid-s1793" xml:space="preserve">in ſchol.
              <lb/>
            </s>
            <s xml:id="echoid-s1794" xml:space="preserve">prim. </s>
            <s xml:id="echoid-s1795" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s1796" xml:space="preserve">25. </s>
            <s xml:id="echoid-s1797" xml:space="preserve">omnium ipſius portionum; </s>
            <s xml:id="echoid-s1798" xml:space="preserve">& </s>
            <s xml:id="echoid-s1799" xml:space="preserve">in
              <lb/>
            propoſit. </s>
            <s xml:id="echoid-s1800" xml:space="preserve">vltima lib. </s>
            <s xml:id="echoid-s1801" xml:space="preserve">4. </s>
            <s xml:id="echoid-s1802" xml:space="preserve">in qua aſſignauimus centrum
              <lb/>
            grauitatis omnium partium ellipſis; </s>
            <s xml:id="echoid-s1803" xml:space="preserve">partim ex dictis
              <lb/>
            in propoſit. </s>
            <s xml:id="echoid-s1804" xml:space="preserve">22. </s>
            <s xml:id="echoid-s1805" xml:space="preserve">huius, & </s>
            <s xml:id="echoid-s1806" xml:space="preserve">in ſcholio eiuſdem, vbiaſ-
              <lb/>
            ſignauimus centrum grauitatis hyperbolæ. </s>
            <s xml:id="echoid-s1807" xml:space="preserve">Imo ſi
              <lb/>
            in ſchemate illius propoſitionis, intelligamus exceſ-
              <lb/>
            ſum parallelogrammi G C, ſupra hyperbolam
              <lb/>
            A B C, rotari vel circa H C, vel circa ipſi paralle-
              <lb/>
            lam extra parallelogrammum: </s>
            <s xml:id="echoid-s1808" xml:space="preserve">ex dictis ibidem, agno-
              <lb/>
            ſcetur centrum grauitatis annulorum genitorum.</s>
            <s xml:id="echoid-s1809" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1810" xml:space="preserve">Exiſtimantes autem A B C, eſſe cycloidem pri-
              <lb/>
            mariam; </s>
            <s xml:id="echoid-s1811" xml:space="preserve">placitis Torricellij in lib. </s>
            <s xml:id="echoid-s1812" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1813" xml:space="preserve">de motu grau.
              <lb/>
            </s>
            <s xml:id="echoid-s1814" xml:space="preserve">ſchol. </s>
            <s xml:id="echoid-s1815" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s1816" xml:space="preserve">18. </s>
            <s xml:id="echoid-s1817" xml:space="preserve">annuentes, intelligemus centrum
              <lb/>
            grauitatis annuli ex cycloide ſic ſecare F C, vt pars
              <lb/>
            terminata ad F, ſit ad partem terminatam ad C, vt
              <lb/>
            7. </s>
            <s xml:id="echoid-s1818" xml:space="preserve">ad 5.</s>
            <s xml:id="echoid-s1819" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1820" xml:space="preserve">Sed accipiamus ſchema ſequens, in quo intelli-
              <lb/>
            gamus ſemiparabolam B A D, duplicari ad </s>
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