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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        <div xml:id="echoid-div79" type="section" level="1" n="54">
          <p>
            <s xml:id="echoid-s1443" xml:space="preserve">
              <pb o="81" file="0093" n="93"/>
            cylindrici ex G C, eſſe ad omnes tubos ex paralle-
              <lb/>
            logrammis inſcriptis in hyperbola, qui tubi inſcri-
              <lb/>
            buntur in annulo ex hyperbola, vt partes parallelo-
              <lb/>
            grammi P C, ad omnia parallelogramma inſcripta
              <lb/>
            in parabola. </s>
            <s xml:id="echoid-s1444" xml:space="preserve">Cumque, tubi inſcripti in annulo ex
              <lb/>
            hyperbola, ſicuti parallelogramma inſcripta in pa-
              <lb/>
            rabola, per continuatam talem biſſectionem poſſint
              <lb/>
            tandem deficere à magnitudinibus in quibus inſcri-
              <lb/>
            buntur, defectu, quacunque data magnitudine mi-
              <lb/>
            nori: </s>
            <s xml:id="echoid-s1445" xml:space="preserve">ſequitur tandem modo archimedeo per dedu-
              <lb/>
            ctionem ad impoſſibile poſſe concludi, tubum cy-
              <lb/>
            lindricum ex parallelogrammo eſſe ad annulum la-
              <lb/>
            tum ex hyperbola, vt parallelogrammum ad para-
              <lb/>
            bolam.</s>
            <s xml:id="echoid-s1446" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1447" xml:space="preserve">Patet ergo ex dictis haberi nouo modo parabo-
              <lb/>
            læ quadraticæ quadraturam; </s>
            <s xml:id="echoid-s1448" xml:space="preserve">nimirum parallelo-
              <lb/>
            grammum ei circumſcriptum, eſſe ipſius ſeſquial-
              <lb/>
            terum. </s>
            <s xml:id="echoid-s1449" xml:space="preserve">Probatum fuit enim in anteced. </s>
            <s xml:id="echoid-s1450" xml:space="preserve">propoſit.
              <lb/>
            </s>
            <s xml:id="echoid-s1451" xml:space="preserve">tubum cylindricum ex parallelogrammo G C, cir-
              <lb/>
            ca k M, eſſe ſeſquialterum annuli lati ex hyperbola
              <lb/>
            circa eandem k M. </s>
            <s xml:id="echoid-s1452" xml:space="preserve">Sed infra adhibendo aliud ſoli-
              <lb/>
            dum hyperbolicum, parabolam alio nouo modo
              <lb/>
            quadrabimus; </s>
            <s xml:id="echoid-s1453" xml:space="preserve">nunc ſuggerendæ ſunt lectori quam-
              <lb/>
            plurimæ nouæ notitiæ geometricæ, quæ ex hac pro-
              <lb/>
            poſitione, & </s>
            <s xml:id="echoid-s1454" xml:space="preserve">ex dictis in lib. </s>
            <s xml:id="echoid-s1455" xml:space="preserve">de Infin. </s>
            <s xml:id="echoid-s1456" xml:space="preserve">Par. </s>
            <s xml:id="echoid-s1457" xml:space="preserve">deducuntur.</s>
            <s xml:id="echoid-s1458" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div81" type="section" level="1" n="55">
          <head xml:id="echoid-head66" xml:space="preserve">SCHOLIVM II.</head>
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            <s xml:id="echoid-s1459" xml:space="preserve">Dedu@itur ergo ex dictis, & </s>
            <s xml:id="echoid-s1460" xml:space="preserve">ad modum </s>
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