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

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        <div xml:id="echoid-div132" type="section" level="1" n="57">
          <pb o="403" file="0119" n="127" rhead="ILLUST. QUORUND. PROB. CONSTRUCT."/>
          <p>
            <s xml:id="echoid-s2594" xml:space="preserve">Illud autem hic aliter eſt oſtendendum, quod ad lineam
              <lb/>
            H E poni poteſt A E ipſi G æqualis. </s>
            <s xml:id="echoid-s2595" xml:space="preserve">Sit R S æqualis R B,
              <lb/>
            & </s>
            <s xml:id="echoid-s2596" xml:space="preserve">jungatur A S. </s>
            <s xml:id="echoid-s2597" xml:space="preserve">Quoniam igitur in triangulo B A S à ver-
              <lb/>
            tice ad mediam baſin ducta eſt A R, erunt quadrata B R
              <lb/>
            & </s>
            <s xml:id="echoid-s2598" xml:space="preserve">R A ſimul ſumpta, hoc eſt, quadratum B A cum duplo
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0119-01" xlink:href="note-0119-01a" xml:space="preserve">per 122.
                <lb/>
              lib.7. Pappi.</note>
            quadrato A R, ſubdupla quadratorum B A, A S . </s>
            <s xml:id="echoid-s2599" xml:space="preserve">Itaque quadratum A B duplum cum quadruplo quadrato A R, hoc
              <lb/>
            eſt, cum quadrato R L, æquabitur quadratis B A, A S.
              <lb/>
            </s>
            <s xml:id="echoid-s2600" xml:space="preserve">Quare ablato utrimque quadrato B A, erit quadratum A S
              <lb/>
            æquale quadratis B A & </s>
            <s xml:id="echoid-s2601" xml:space="preserve">R L, ac proinde minus quam quadr. </s>
            <s xml:id="echoid-s2602" xml:space="preserve">
              <lb/>
            A H; </s>
            <s xml:id="echoid-s2603" xml:space="preserve">nam hoc æquale eſt quadratis A B & </s>
            <s xml:id="echoid-s2604" xml:space="preserve">G. </s>
            <s xml:id="echoid-s2605" xml:space="preserve">Eſt igitur
              <lb/>
            A S minor quam A H. </s>
            <s xml:id="echoid-s2606" xml:space="preserve">Sed major eſt quam A R. </s>
            <s xml:id="echoid-s2607" xml:space="preserve">Ergo pun-
              <lb/>
            ctum S cadit inter R & </s>
            <s xml:id="echoid-s2608" xml:space="preserve">H; </s>
            <s xml:id="echoid-s2609" xml:space="preserve">angulus enim A R H obtuſus
              <lb/>
            eſt. </s>
            <s xml:id="echoid-s2610" xml:space="preserve">Major itaque eſt R H quam R S vel R B. </s>
            <s xml:id="echoid-s2611" xml:space="preserve">Et quum
              <lb/>
            propter triangulos ſimiles ſit R H ad H P ut R B ad B A,
              <lb/>
            erit quoque H P major quam B A; </s>
            <s xml:id="echoid-s2612" xml:space="preserve">& </s>
            <s xml:id="echoid-s2613" xml:space="preserve">quadratum H P ma-
              <lb/>
            jus quadrato A B. </s>
            <s xml:id="echoid-s2614" xml:space="preserve">At quadratum H P cum quadrato P A
              <lb/>
            æquatur quadrato A H, hoc eſt, quadratis B A & </s>
            <s xml:id="echoid-s2615" xml:space="preserve">G. </s>
            <s xml:id="echoid-s2616" xml:space="preserve">Er-
              <lb/>
            go cum quadratum H P ſit majus quadrato A B, erit invi-
              <lb/>
            cem quadr. </s>
            <s xml:id="echoid-s2617" xml:space="preserve">P A minus quam quadr. </s>
            <s xml:id="echoid-s2618" xml:space="preserve">G. </s>
            <s xml:id="echoid-s2619" xml:space="preserve">Patet igitur quod
              <lb/>
            ſi centro A circumferentia deſcribatur radio A E ipſi G æ-
              <lb/>
            quali, ea lineam H E ſecabit.</s>
            <s xml:id="echoid-s2620" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div137" type="section" level="1" n="58">
          <head xml:id="echoid-head87" xml:space="preserve">
            <emph style="sc">Probl.</emph>
          VIII.</head>
          <head xml:id="echoid-head88" style="it" xml:space="preserve">In Conchoide linea invenire confinia
            <lb/>
          flexus contrarii.</head>
          <p>
            <s xml:id="echoid-s2621" xml:space="preserve">Conchoidem intelligimus quam Nicomedes excogitavit;
              <lb/>
            </s>
            <s xml:id="echoid-s2622" xml:space="preserve">
              <note position="right" xlink:label="note-0119-02" xlink:href="note-0119-02a" xml:space="preserve">TAB. XLII.
                <lb/>
              Fig. 5.</note>
            quâ & </s>
            <s xml:id="echoid-s2623" xml:space="preserve">angulum diviſit trifariam, & </s>
            <s xml:id="echoid-s2624" xml:space="preserve">duas medias invenit
              <lb/>
            proportionales: </s>
            <s xml:id="echoid-s2625" xml:space="preserve">Eſto ea C Q D, polus G, regula autem
              <lb/>
            A B cujus ope deſcripta eſt; </s>
            <s xml:id="echoid-s2626" xml:space="preserve">quam ſecet G Q ad angulos
              <lb/>
            rectos. </s>
            <s xml:id="echoid-s2627" xml:space="preserve">Hæc igitur lineæ proprietas eſt, ut ductâ ad ipſam
              <lb/>
            rectâ qualibet ex G puncto, pars hujus inter conchoidem & </s>
            <s xml:id="echoid-s2628" xml:space="preserve">
              <lb/>
            rectam A B intercepta ſit ipſi A Q æqualis.</s>
            <s xml:id="echoid-s2629" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2630" xml:space="preserve">Quum autem appareat partem quandam Conchoidis ut in
              <lb/>
            ſchemate ſubjecto C Q D verſus polum G cavam eſſe, </s>
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