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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            d@in totum, quam ſecundum partes proportiona-
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            les. </s>
            <s xml:id="echoid-s522" xml:space="preserve">Quod &</s>
            <s xml:id="echoid-s523" xml:space="preserve">c.</s>
            <s xml:id="echoid-s524" xml:space="preserve"/>
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        <div xml:id="echoid-div31" type="section" level="1" n="21">
          <head xml:id="echoid-head31" xml:space="preserve">SCHOLIVM I.</head>
          <p>
            <s xml:id="echoid-s525" xml:space="preserve">Licet hæc propoſitio oſtenſa ſit per indiuiſibilia,
              <lb/>
            poteſt tamen probari modo Archimedeo. </s>
            <s xml:id="echoid-s526" xml:space="preserve">Cum e-
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            nim probatum ſit armillam circularem N R P, æ-
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            qualem eſſe circulo Q T, etiam (ſi inſcribantur)
              <lb/>
            tubus cylindricus N L P, inſcriptus in exceſſu fruſti
              <lb/>
            coni ſupra cylindrum, erit æqualis cylindro Q V,
              <lb/>
            inſcripto in conoide. </s>
            <s xml:id="echoid-s527" xml:space="preserve">Si ergo diuidatur B D, in
              <lb/>
            quibuſcunque punctis, & </s>
            <s xml:id="echoid-s528" xml:space="preserve">per hæc agantur plana vt
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            ſupra, & </s>
            <s xml:id="echoid-s529" xml:space="preserve">fiant tubi, & </s>
            <s xml:id="echoid-s530" xml:space="preserve">cylindri modo antedicto, fa-
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            cile patebit omnes tubos cylindricos inſcriptos in
              <lb/>
            exceſſu fruſti coni ſupra cylindrum, æquales fore
              <lb/>
            omnibus cylindris in conoide inſcriptis. </s>
            <s xml:id="echoid-s531" xml:space="preserve">Quare ſi
              <lb/>
            hæc diuiſio fiat per continuam biſlectionem D B,
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            partiumque eiuſdem; </s>
            <s xml:id="echoid-s532" xml:space="preserve">quia tam in exceſſu fruſti ſu-
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            pra cylindrum, quam in conoide inſcribemus ſolida
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            ab ipſis deficientibus defectu minori quacunque
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            data magnitudine; </s>
            <s xml:id="echoid-s533" xml:space="preserve">tandem concludemus exceſſum
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            prædictum, & </s>
            <s xml:id="echoid-s534" xml:space="preserve">conoides eſſe magnitudines æqua-
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            les. </s>
            <s xml:id="echoid-s535" xml:space="preserve">Hæc autem viris Euclideis, Archimedeiſque
              <lb/>
            ſunt nimis obuia.</s>
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          <head xml:id="echoid-head32" xml:space="preserve">SCHOLIVM II.</head>
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            <s xml:id="echoid-s537" xml:space="preserve">Poteſt ergo conſequenter ad ſuperius ſæpe </s>
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