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>
            <s xml:id="echoid-s1908" xml:space="preserve">
              <pb o="106" file="0118" n="118"/>
            cycloidem primariam A B C, reuoluto vel cir-
              <lb/>
            ca F C, vel circa dictam parallelam: </s>
            <s xml:id="echoid-s1909" xml:space="preserve">Item in
              <lb/>
            quo puncto ipſius R G, vel ipſi parallelæ ſit cen-
              <lb/>
            trum grauitatis duplicatæ ſemicycloidis B D C R G,
              <lb/>
            ad partes F C: </s>
            <s xml:id="echoid-s1910" xml:space="preserve">ſed admonebimus, centrum graui-
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            tatis ſolidi orti ex reuolutione figuræ B D C R G, ſic
              <lb/>
            ſecare dictam R G, vt pars terminata ad R, ſit ad
              <lb/>
            partem terminatam ad G, vt 7. </s>
            <s xml:id="echoid-s1911" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s1912" xml:space="preserve">Ratio eſt,
              <lb/>
            quia ita diuidit B D, centrum grauitatis cycloidis
              <lb/>
            A B C, ſicuti diuidit FC, centrum figuræ B D C R G.
              <lb/>
            </s>
            <s xml:id="echoid-s1913" xml:space="preserve">Item admonebimus, centrum grauitatis ſolidi orti
              <lb/>
            ex gyratione figuræ A E B F C, circa F C, ſic ſeca-
              <lb/>
            re F C, vt pars terminata ad F, ſit ad partem ter-
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            minatam ad C, vt 1. </s>
            <s xml:id="echoid-s1914" xml:space="preserve">ad 3. </s>
            <s xml:id="echoid-s1915" xml:space="preserve">Ratio eſt quia ſic di-
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            uidit B D, centrum grauitatis prædictæ figuræ re-
              <lb/>
            uolutæ. </s>
            <s xml:id="echoid-s1916" xml:space="preserve">Nam cum ex Torricellio de dimenſione cy-
              <lb/>
            cloidis, & </s>
            <s xml:id="echoid-s1917" xml:space="preserve">ex Tacquet in diſlertatione de circulorum
              <lb/>
            volutationibus propoſit. </s>
            <s xml:id="echoid-s1918" xml:space="preserve">20. </s>
            <s xml:id="echoid-s1919" xml:space="preserve">demonſtratione nun-
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            quam ſatis laudata, conſtet, A E B F C, eſſe tertiam
              <lb/>
            partem cycloidis A B C; </s>
            <s xml:id="echoid-s1920" xml:space="preserve">& </s>
            <s xml:id="echoid-s1921" xml:space="preserve">cum ex eodem Torri-
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            cellio ſupra citato, ſupponamus centrum grauitatis
              <lb/>
            cycloidis ſic ſecare B D, vt pars terminata ad B, ſit
              <lb/>
            ad partem terminatam ad D, vt 7. </s>
            <s xml:id="echoid-s1922" xml:space="preserve">ad 5; </s>
            <s xml:id="echoid-s1923" xml:space="preserve">& </s>
            <s xml:id="echoid-s1924" xml:space="preserve">pariter
              <lb/>
            cum medium punctum B D, ſit centrum grauitatis
              <lb/>
            torius parallelogrammi E C, nempe centrum gra-
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            uitatis parallelogramn irelinquat hinc inde 6, par-
              <lb/>
            tes, quarum B D, ſupponitur 12; </s>
            <s xml:id="echoid-s1925" xml:space="preserve">lector in doctri-
              <lb/>
            nis A chimed s exercitatus facile agnoſcet, centrum
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            grauitatis prædicti exceſſus ſic ſecare B D, vt </s>
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