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-s2770" xml:space="preserve">
              <pb o="151" file="0163" n="163"/>
            uentioni rationis infinitorum cylindrorum R K, ad
              <lb/>
            infinitos annulos E R B Z k, vt luculenter explica-
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            tum fuit in admirabili ſcholio 4. </s>
            <s xml:id="echoid-s2771" xml:space="preserve">citat. </s>
            <s xml:id="echoid-s2772" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s2773" xml:space="preserve">4.
              <lb/>
            </s>
            <s xml:id="echoid-s2774" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2775" xml:space="preserve">4.</s>
            <s xml:id="echoid-s2776" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2777" xml:space="preserve">Inſuper cum in varijs propoſitionibus lib. </s>
            <s xml:id="echoid-s2778" xml:space="preserve">prim.
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            </s>
            <s xml:id="echoid-s2779" xml:space="preserve">aſſignata fuerit ratio, quam habet quælibet pars pa-
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            rallelogrammi A S, ad quamlibet partem parabolæ
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            R B A, quam pars parallelogrammi includit, & </s>
            <s xml:id="echoid-s2780" xml:space="preserve">cum
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            in cit. </s>
            <s xml:id="echoid-s2781" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s2782" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2783" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2784" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2785" xml:space="preserve">& </s>
            <s xml:id="echoid-s2786" xml:space="preserve">in eiuſdem ſcholijs, aſſi-
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            gnata fuerit ratio ex illa ſimplici analogia, quam ha-
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            bet quælibet pars cylindri R C, ad quamlibet par-
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            tem annuli A R B Z C; </s>
            <s xml:id="echoid-s2787" xml:space="preserve">v. </s>
            <s xml:id="echoid-s2788" xml:space="preserve">g. </s>
            <s xml:id="echoid-s2789" xml:space="preserve">oſtenſa ſit ratio, quam
              <lb/>
            habet cylindrus I K, ad partem annuli ex E I T B,
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            circa V B; </s>
            <s xml:id="echoid-s2790" xml:space="preserve">patet ex propoſit. </s>
            <s xml:id="echoid-s2791" xml:space="preserve">antecedentibus, nec-
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            dum dari rationem cuiuslibet partis cylindri R C,
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            v. </s>
            <s xml:id="echoid-s2792" xml:space="preserve">g. </s>
            <s xml:id="echoid-s2793" xml:space="preserve">I k, vel ei æqualis ex I B, circa I E, ad par-
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            tem fuſi ex I T B E, circa I E: </s>
            <s xml:id="echoid-s2794" xml:space="preserve">ſed etiam dari in
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            B E, vel in V I, centrum æquilibrij ſegmenti
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            I T B E, vel grauitatis duplicati ſegmenti ad par-
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            tes B E, vel I V.</s>
            <s xml:id="echoid-s2795" xml:space="preserve"/>
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            <s xml:id="echoid-s2796" xml:space="preserve">In propoſit. </s>
            <s xml:id="echoid-s2797" xml:space="preserve">autem 3. </s>
            <s xml:id="echoid-s2798" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2799" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2800" xml:space="preserve">patuit cylindrum
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            E C, eſſe ad quodlibet conoides parabolicum ABC,
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            cuius exponens ſit numerus par, vt parallelogram-
              <lb/>
            mum E C, ad parabolam A B C, cuius exponens
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            ſit ſubduplus exponentis conoidis. </s>
            <s xml:id="echoid-s2801" xml:space="preserve">Quare, vt ibi-
              <lb/>
            dem patuit, infinitæ parabolæ non inſeruierunt in-
              <lb/>
            uentioni rationi infinitorum cylindrorum ad in finita
              <lb/>
            conoidea, ſed tantum ad ea, quorum exponentes
              <lb/>
            ſunt numeri pares. </s>
            <s xml:id="echoid-s2802" xml:space="preserve">Eliciemus crgo ex </s>
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