Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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            <s xml:id="echoid-s4570" xml:space="preserve">
              <pb o="488" file="0208" n="218" rhead="CHRIST. HUGENII"/>
            torum differentia eſt {{1/4}ggoo/pp} - ox + {ppxx/gg} - yy + 2 ly - ll
              <lb/>
            + {2nxy/z} + {2lnx/z} - {nnxx/zz}. </s>
            <s xml:id="echoid-s4571" xml:space="preserve">Ergo hæc æquatur rectangulo
              <lb/>
            Y S X, hoc eſt quadrato I X minus quadrato I S, hoc eſt
              <lb/>
            {{1/4}ggoo/pp} - mm; </s>
            <s xml:id="echoid-s4572" xml:space="preserve">quia I X = {{1/2}go/p} & </s>
            <s xml:id="echoid-s4573" xml:space="preserve">I S = m. </s>
            <s xml:id="echoid-s4574" xml:space="preserve">In qua æqua-
              <lb/>
            tione deleto utrinque {{1/4}ggoo/pp}, invenietur y = l - {nx/z} +
              <lb/>
            √mm - ox + {ppxx/gg} , ut oportebat.</s>
            <s xml:id="echoid-s4575" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4576" xml:space="preserve">In Secundo calu rectangulum Q C O æquatur quadrato
              <lb/>
              <note position="left" xlink:label="note-0208-01" xlink:href="note-0208-01a" xml:space="preserve">fig. 5.</note>
            L C minus quadrato L O; </s>
            <s xml:id="echoid-s4577" xml:space="preserve">& </s>
            <s xml:id="echoid-s4578" xml:space="preserve">rectangulum Y S X quadrato
              <lb/>
            I S minus quadrato I X. </s>
            <s xml:id="echoid-s4579" xml:space="preserve">Unde rurſus valor Y idem qui ca-
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            ſu primo invenietur.</s>
            <s xml:id="echoid-s4580" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4581" xml:space="preserve">Sit tertius caſus quo habeatur - mm, ſitque æquatio y = l
              <lb/>
            - {nx/z} + √- mm + ox + {ppxx/gg} , producta GN occurrat al-
              <lb/>
            teri aſymptoto in D. </s>
            <s xml:id="echoid-s4582" xml:space="preserve">Hîc jam eadem ratione qua prius, ap-
              <lb/>
            parebit L O vel LQ eſſe {{1/2}go/p} + {px/g}, & </s>
            <s xml:id="echoid-s4583" xml:space="preserve">L C = y + {nx/z} - l.
              <lb/>
            </s>
            <s xml:id="echoid-s4584" xml:space="preserve">Et propter hyperbolam erit rectangulum Q C O = rectan-
              <lb/>
            gulo D N G ſeu quadrato N G, hoc eſt {{1/4}ggoo/pp} + mm, quia
              <lb/>
            X I = {{1/2}go/p}, & </s>
            <s xml:id="echoid-s4585" xml:space="preserve">I S = m, quorum quadratis æquale fecimus
              <lb/>
            quadratum G N. </s>
            <s xml:id="echoid-s4586" xml:space="preserve">Rectangulum autem Q C O æquatur qua-
              <lb/>
            drato L O minus quadrato L C, hoceſt {{1/4}ggoo/pp} + ox + {ppxx/gg}
              <lb/>
            - yy - {2nxy/z} — {nnxx/zz} + 2 ly + {2nlx/z} - ll. </s>
            <s xml:id="echoid-s4587" xml:space="preserve">Ergo hoc
              <lb/>
            æquale {{1/4}ggoo/pp} + mm. </s>
            <s xml:id="echoid-s4588" xml:space="preserve">In qua æquatione deleto rurſus </s>
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