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-s1491" xml:space="preserve">
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            mentum annuli ex ſegmento intermedio ſemihy-
              <lb/>
            perbolæ Q X H I.</s>
            <s xml:id="echoid-s1492" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1493" xml:space="preserve">Ex ſchol prim. </s>
            <s xml:id="echoid-s1494" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s1495" xml:space="preserve">13. </s>
            <s xml:id="echoid-s1496" xml:space="preserve">agnoſcet rationem
              <lb/>
            tubi ex parallelogrammo S C, ad portionem annuli
              <lb/>
            ex portione maiori hyperbolæ I H B C.</s>
            <s xml:id="echoid-s1497" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1498" xml:space="preserve">Ex ſchol. </s>
            <s xml:id="echoid-s1499" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s1500" xml:space="preserve">14. </s>
            <s xml:id="echoid-s1501" xml:space="preserve">agnoſcet rationem, quam
              <lb/>
            habet tubus cylindricus ex parallelogrammo S Y,
              <lb/>
            ad ſegmentum annuli ex ſegmento intermedio
              <lb/>
            I H B Z Y, intercipiente axim B N.</s>
            <s xml:id="echoid-s1502" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1503" xml:space="preserve">Sed portioni minori hyperbolæ A H I, intellecto
              <lb/>
            circumſcripto parallelogrammo H A, agnoſcet ex
              <lb/>
            propoſit. </s>
            <s xml:id="echoid-s1504" xml:space="preserve">15. </s>
            <s xml:id="echoid-s1505" xml:space="preserve">tubum cylindricum ex parallelogram-
              <lb/>
            mo H A, eſſe ad portionem annuli ex portione
              <lb/>
            A H I, vt tripla A N, cum tripla N I, ad duplam
              <lb/>
            A N, cum vnica N I. </s>
            <s xml:id="echoid-s1506" xml:space="preserve">Imo ex ſchol. </s>
            <s xml:id="echoid-s1507" xml:space="preserve">eiuſdem pro-
              <lb/>
            poſit. </s>
            <s xml:id="echoid-s1508" xml:space="preserve">agnoſcet, tubum prædictum eſſe ad prædictam
              <lb/>
            annuli portionem, vt I C ad dimidiam I C, cum
              <lb/>
            ſexta parte I A.</s>
            <s xml:id="echoid-s1509" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1510" xml:space="preserve">Ex ſcholio propoſit. </s>
            <s xml:id="echoid-s1511" xml:space="preserve">17. </s>
            <s xml:id="echoid-s1512" xml:space="preserve">agnoſcet rationem tubi
              <lb/>
            cylindrici ex parallelogrammo H C, ad portionem
              <lb/>
            annuli ex portione maiori I H B C. </s>
            <s xml:id="echoid-s1513" xml:space="preserve">Ex eodem ſchol.
              <lb/>
            </s>
            <s xml:id="echoid-s1514" xml:space="preserve">etiam agnoſcet talem rationem eſſe, vt eſt A I, ad
              <lb/>
            dimidiam A I, cum ſexta parte I C. </s>
            <s xml:id="echoid-s1515" xml:space="preserve">Quare agno-
              <lb/>
            ſcet vniuerſaliter, quod tubus cylindricus ex altero
              <lb/>
            parallelogrammorum H A, H C, ad portionem an-
              <lb/>
            nuli ſibi correſpondentem eſſe, vt baſis reliquæ por-
              <lb/>
            tionis hyperbolæ, ad ſui dimidiam, cum ſexta parte
              <lb/>
            baſis portionis reuolutæ.</s>
            <s xml:id="echoid-s1516" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1517" xml:space="preserve">Ex propoſit, 18. </s>
            <s xml:id="echoid-s1518" xml:space="preserve">aguoſect rationem tubi ex </s>
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