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-s1377" xml:space="preserve">
              <pb o="76" file="0088" n="88"/>
            rectangulum E T B, eſt vt quadratum A H, ad qua-
              <lb/>
            dratum N T, ſeù O H; </s>
            <s xml:id="echoid-s1378" xml:space="preserve">& </s>
            <s xml:id="echoid-s1379" xml:space="preserve">rectangulis E H B, E T B,
              <lb/>
            ſunt æqualia rectangula K B H, V B T, quia k E,
              <lb/>
            B H, & </s>
            <s xml:id="echoid-s1380" xml:space="preserve">V E, B T, ſunt æquales; </s>
            <s xml:id="echoid-s1381" xml:space="preserve">ergo erit vt rectan-
              <lb/>
            gulum K B H, ad rectangulum V B T, ſic quadra-
              <lb/>
            tum A H, ad quadratum H O. </s>
            <s xml:id="echoid-s1382" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s1383" xml:space="preserve">per con-
              <lb/>
            uerſionem rationis, erit rectangulum K B H, ad ex-
              <lb/>
            ceſſum ipſius ſupra rectangulum V B T; </s>
            <s xml:id="echoid-s1384" xml:space="preserve">nempe ex
              <lb/>
            propoſit. </s>
            <s xml:id="echoid-s1385" xml:space="preserve">anteced. </s>
            <s xml:id="echoid-s1386" xml:space="preserve">ad rectangulum k T H, ſeù ad ei
              <lb/>
            æquale L N O, vt quadratum A H, ad rectangu-
              <lb/>
            lum A O C. </s>
            <s xml:id="echoid-s1387" xml:space="preserve">Et conuertendo, erit rectangulum.
              <lb/>
            </s>
            <s xml:id="echoid-s1388" xml:space="preserve">A O C, ad quadratum A H, vt rectangulum L N O,
              <lb/>
            ad rectangulum K B H. </s>
            <s xml:id="echoid-s1389" xml:space="preserve">Eodem modo oſtendetur
              <lb/>
            eſſe rectangulum K B H, ad rectangulum P R S,
              <lb/>
            vt quadratum A H, ſeù H C, ad rectangulum. </s>
            <s xml:id="echoid-s1390" xml:space="preserve">
              <lb/>
            A S C. </s>
            <s xml:id="echoid-s1391" xml:space="preserve">Quare ex æquali, erit rectangulum L N O,
              <lb/>
            ad rectangulum P R S, vt rectangulum A O C, ad
              <lb/>
            rectangulum A S C. </s>
            <s xml:id="echoid-s1392" xml:space="preserve">Quod &</s>
            <s xml:id="echoid-s1393" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1394" xml:space="preserve"/>
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        <div xml:id="echoid-div77" type="section" level="1" n="53">
          <head xml:id="echoid-head64" xml:space="preserve">PROPOSITIO XXVI.</head>
          <p style="it">
            <s xml:id="echoid-s1395" xml:space="preserve">Parallelogrammum circum ſcriptum parabolæ quadraticæ, eſt
              <lb/>
            ad ipſam, vt tubus @ylindricus ex gyratione parallelo-
              <lb/>
            gramm@ circurnſcripti hyperbolæ circa ſecundam coniuga-
              <lb/>
            tam diametrum, ad annulum latum ex reuolutione hyper-
              <lb/>
            bo´æ circa eandem diametrum; </s>
            <s xml:id="echoid-s1396" xml:space="preserve">& </s>
            <s xml:id="echoid-s1397" xml:space="preserve">hoc tam ſecundum to-
              <lb/>
            tum, quam ſecundum partes proportionales; </s>
            <s xml:id="echoid-s1398" xml:space="preserve">dummodo ba-
              <lb/>
            ſes pa abolæ, & </s>
            <s xml:id="echoid-s1399" xml:space="preserve">hyperbolæ genitricis annuli proportiona-
              <lb/>
            liter ſecentur.</s>
            <s xml:id="echoid-s1400" xml:space="preserve"/>
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