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

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        <div xml:id="echoid-div243" type="section" level="1" n="120">
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            <s xml:id="echoid-s4588" xml:space="preserve">
              <pb o="489" file="0209" n="219" rhead="GEOMET. VARIA."/>
            que {{1/4}ggoo/pp}, invenitur y = l - {nx/z} + √- mm + ox + {ppxx/gg}
              <lb/>
            Eademque eſt demonſtrandi ratio in caſu quarto, & </s>
            <s xml:id="echoid-s4589" xml:space="preserve">aliis
              <lb/>
              <note position="right" xlink:label="note-0209-01" xlink:href="note-0209-01a" xml:space="preserve">fig. 7.</note>
            quibusvis, habita ratione ſignorum + & </s>
            <s xml:id="echoid-s4590" xml:space="preserve">-.</s>
            <s xml:id="echoid-s4591" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s4592" xml:space="preserve">Cum non habetur {nx/z} in æquatione, puncta M & </s>
            <s xml:id="echoid-s4593" xml:space="preserve">V unum
              <lb/>
            ſunt, tunc vero ſi p = g, hoc eſt ſi habeatur + xx pro
              <lb/>
            {ppxx/gg}, erunt ſemper aſymptoti ſibi mutuò ad angulos rectos,
              <lb/>
            quia ut p ad g, ita fecimus {1/2}o ad I X & </s>
            <s xml:id="echoid-s4594" xml:space="preserve">ad I Y, & </s>
            <s xml:id="echoid-s4595" xml:space="preserve">ita IX
              <lb/>
            ad I V; </s>
            <s xml:id="echoid-s4596" xml:space="preserve">fiunt enim jam æquales I X, I Y, I V, & </s>
            <s xml:id="echoid-s4597" xml:space="preserve">ſingulæ =
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            {1/2}o, unde punctum V eſt in ſemicirculo ſuper X Y & </s>
            <s xml:id="echoid-s4598" xml:space="preserve">proin-
              <lb/>
            de angulus X V Y rectus. </s>
            <s xml:id="echoid-s4599" xml:space="preserve">Item quia I M = {{1/2}aogg/zpp}, patet
              <lb/>
            quod ſi ag = zp, hoc eſt ſi g ad p ut z ad a, tunc erit
              <lb/>
            I M = {{1/2}og/p}, ac proinde æqualis ipſi IX & </s>
            <s xml:id="echoid-s4600" xml:space="preserve">IY quæ etiam erant
              <lb/>
            {{1/2}og/p}. </s>
            <s xml:id="echoid-s4601" xml:space="preserve">Adeoque hoc caſu erunt aſymptoti ſibi mutuo ad angu-
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            los rectos; </s>
            <s xml:id="echoid-s4602" xml:space="preserve">cum rurſus punctum M ſit futurum in circumfe-
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            rentia circuli deſcripti ſuper X Y centro I.</s>
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