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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          <head xml:id="echoid-head33" xml:space="preserve">SCHOLIVM III.</head>
          <p>
            <s xml:id="echoid-s544" xml:space="preserve">Galileus in poſtremis dialogis pag. </s>
            <s xml:id="echoid-s545" xml:space="preserve">apud nos, 28,
              <lb/>
            oſtendit paradoxum quodam; </s>
            <s xml:id="echoid-s546" xml:space="preserve">nimirum, circuli cir-
              <lb/>
            cumferentiam æqualem eſſe puncto. </s>
            <s xml:id="echoid-s547" xml:space="preserve">Vt hoc oſten-
              <lb/>
            dat vtitur exceſſu cylindri ſupra hemiſphærium, & </s>
            <s xml:id="echoid-s548" xml:space="preserve">
              <lb/>
            cono, vt ibidem poteſt conſpici. </s>
            <s xml:id="echoid-s549" xml:space="preserve">Sed ſicuti vſus fuit
              <lb/>
            exceſlu cylindri ſupra hemiſphærium, ſic etiam po-
              <lb/>
            terat vti exceſſu cylindri ſupra hemiſphæroides; </s>
            <s xml:id="echoid-s550" xml:space="preserve">ea-
              <lb/>
            dem enim fuiſſet demonſtratio. </s>
            <s xml:id="echoid-s551" xml:space="preserve">Paradoxum Galilei
              <lb/>
            oſtendimus & </s>
            <s xml:id="echoid-s552" xml:space="preserve">nos in appendice noſtri libelli ſexa-
              <lb/>
            ginta problematum geometricorum, adhibendo ex-
              <lb/>
            ceſſum cylindri ſupra conoides parabolicum, & </s>
            <s xml:id="echoid-s553" xml:space="preserve">ip-
              <lb/>
            ſum conoides. </s>
            <s xml:id="echoid-s554" xml:space="preserve">Hoc idem paradoxum facile ex præ-
              <lb/>
            ſenti propoſit. </s>
            <s xml:id="echoid-s555" xml:space="preserve">patebit confirmari poſſe, adhibendo
              <lb/>
            exceſſum prædictum fruſticoni G I K H, ſupra cy-
              <lb/>
            lindrum I M, & </s>
            <s xml:id="echoid-s556" xml:space="preserve">conoides hyperbolicum A B C.
              <lb/>
            </s>
            <s xml:id="echoid-s557" xml:space="preserve">Probatum eſt enim, vbicunque traiciatur planum
              <lb/>
            N P, plano G H, parallelum, ſemper armillam
              <lb/>
            N R P, æqualem eſſe circulo Q T; </s>
            <s xml:id="echoid-s558" xml:space="preserve">ſicuti quamli-
              <lb/>
            bet partem exceſſus æqualem eſſe proportionali par-
              <lb/>
            ti conoidis. </s>
            <s xml:id="echoid-s559" xml:space="preserve">Cum ergo exceſſus prædictus deſinat
              <lb/>
            in circumferentia circuli cuius diameter l k, ſicuti
              <lb/>
            conoides deſinit in puncto B; </s>
            <s xml:id="echoid-s560" xml:space="preserve">videtur ergo colligi
              <lb/>
            circumferentiam æqualem eſſe vertici B.</s>
            <s xml:id="echoid-s561" xml:space="preserve"/>
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