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-s1327" xml:space="preserve">
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            ctis ergo his, tranſeamus ad quadrandam parabolam
              <lb/>
            duobus nouis modis.</s>
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        <div xml:id="echoid-div73" type="section" level="1" n="50">
          <head xml:id="echoid-head61" xml:space="preserve">PROPOSITIO XXIII.</head>
          <p style="it">
            <s xml:id="echoid-s1329" xml:space="preserve">Si ſemihyperbola cum ſibi circumſ ripto parallelogrammo ro-
              <lb/>
            tetur circa ſecundan. </s>
            <s xml:id="echoid-s1330" xml:space="preserve">diametrum. </s>
            <s xml:id="echoid-s1331" xml:space="preserve">Tubus cylindruus
              <lb/>
            ex parallelogrammo, erit ſeſquialter annuli lati ex ſe-
              <lb/>
            mibyperbola.</s>
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            <s xml:id="echoid-s1333" xml:space="preserve">SEmihyperbola A B C, cum ſibi circumſcripto
              <lb/>
            parallogrammo A D, rotetur circa E F, ſe-
              <lb/>
            cundam dametrum. </s>
            <s xml:id="echoid-s1334" xml:space="preserve">Dico tubum cylindricum.
              <lb/>
            </s>
            <s xml:id="echoid-s1335" xml:space="preserve">A D H, eſſe ſeſquialterum annuli lati ex ſemihy-
              <lb/>
            perbola A B C, circa E F, reuoluta. </s>
            <s xml:id="echoid-s1336" xml:space="preserve">Quoniam
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            tubus C B S H, eſt ad cylindrum A L, vt rectan-
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            gulum H B A, ad quadratum E A; </s>
            <s xml:id="echoid-s1337" xml:space="preserve">nempe vt re-
              <lb/>
            ctangulum k A B, ad idem quadratum E A; </s>
            <s xml:id="echoid-s1338" xml:space="preserve">& </s>
            <s xml:id="echoid-s1339" xml:space="preserve">cy-
              <lb/>
            lindrus A L, probatus eſt eſſe in propoſit. </s>
            <s xml:id="echoid-s1340" xml:space="preserve">21. </s>
            <s xml:id="echoid-s1341" xml:space="preserve">ad ſo-
              <lb/>
            lidum C B k L, vt quadratum E A, ad quadratum
              <lb/>
            E B, cum tertia parte rectanguli K A B; </s>
            <s xml:id="echoid-s1342" xml:space="preserve">vnde per
              <lb/>
            conuerſionem rationis, eſt idem cylindrus A L, ad
              <lb/>
            annulum ex ſemihyperbola A B C, circa E F, vt
              <lb/>
            idem quadratum E A, ad exceſſum ipſius ſupra
              <lb/>
            quadratum E B, & </s>
            <s xml:id="echoid-s1343" xml:space="preserve">ſupra tertiam partem rectanguli
              <lb/>
            k A B; </s>
            <s xml:id="echoid-s1344" xml:space="preserve">ergo ex æquali, erit tubus cylindricus A D k L,
              <lb/>
            ad talem annulum latum, vt rect angulum A B H, ad
              <lb/>
            prædictum exceſſum. </s>
            <s xml:id="echoid-s1345" xml:space="preserve">Sed quadratum E A, cum ſit
              <lb/>
            æquale quadrato E B, & </s>
            <s xml:id="echoid-s1346" xml:space="preserve">rectangulo k A B, </s>
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