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-s1346" xml:space="preserve">
              <pb o="74" file="0086" n="86"/>
            illa plana duobus tertijs rectanguli k A B. </s>
            <s xml:id="echoid-s1347" xml:space="preserve">Ergo tu-
              <lb/>
            bus cylindricus A D K L, erit ad prædictum annu-
              <lb/>
            lum, vt rectangulum K A B, ad duotertia eiuſdem
              <lb/>
            rectanguli; </s>
            <s xml:id="echoid-s1348" xml:space="preserve">nempe in ratione ſeſquialtera. </s>
            <s xml:id="echoid-s1349" xml:space="preserve">Quod
              <lb/>
            erat oſtendendum.</s>
            <s xml:id="echoid-s1350" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div74" type="section" level="1" n="51">
          <head xml:id="echoid-head62" xml:space="preserve">PROPOSITIO XXIV.</head>
          <p style="it">
            <s xml:id="echoid-s1351" xml:space="preserve">Si recta linea A B, ſecetur in C, bifariam, & </s>
            <s xml:id="echoid-s1352" xml:space="preserve">in D,
              <lb/>
            E, æque remotè à C, eodemque modo in F, G. </s>
            <s xml:id="echoid-s1353" xml:space="preserve">Re-
              <lb/>
            ctangulum A G B, erit exceſſus rectanguli A E B, ſu-
              <lb/>
            pra rectangulum F E G.</s>
            <s xml:id="echoid-s1354" xml:space="preserve"/>
          </p>
          <figure number="36">
            <image file="0086-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/PVNDER1Y/figures/0086-01"/>
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          <p>
            <s xml:id="echoid-s1355" xml:space="preserve">NAm rectangulum A E B, diuiditur in rectan-
              <lb/>
            gulum A E G, & </s>
            <s xml:id="echoid-s1356" xml:space="preserve">in rectangulum A F, G B.
              <lb/>
            </s>
            <s xml:id="echoid-s1357" xml:space="preserve">Pariter rectangulum A E G, diuiditur in rectangu-
              <lb/>
            lum F E G, & </s>
            <s xml:id="echoid-s1358" xml:space="preserve">in rectangulum A F, E G, ſeù B G F,
              <lb/>
            quia A F, @xhypotheſi, @ſt æqualis G B. </s>
            <s xml:id="echoid-s1359" xml:space="preserve">Ergo ex-
              <lb/>
            ceſſus rectanguli A E B, ſupra rectangulum F E G,
              <lb/>
            eſt rectangulum A E, G B, cum rectangulo E G B; </s>
            <s xml:id="echoid-s1360" xml:space="preserve">
              <lb/>
            quæ duo rectangula ſunt æqualia rectangulo A G B. </s>
            <s xml:id="echoid-s1361" xml:space="preserve">
              <lb/>
            Quare patet propoſitum.</s>
            <s xml:id="echoid-s1362" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div75" type="section" level="1" n="52">
          <head xml:id="echoid-head63" xml:space="preserve">PROPOSITIO XXV.</head>
          <p style="it">
            <s xml:id="echoid-s1363" xml:space="preserve">Si in oppoſitis ſection bus, quæ hyperb læ appellantur du-
              <lb/>
            cantur lineæ lateri tranſuerſo parallelæ, </s>
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