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

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        <div xml:id="echoid-div130" type="section" level="1" n="56">
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              <pb o="401" file="0117" n="125" rhead="ILLUST. QUORUND. PROB. CONSTRUCT."/>
            gulus B S T ipſi E A F æqualis eſt trianguluſque B S T æ-
              <lb/>
            quicruris.</s>
            <s xml:id="echoid-s2505" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2506" xml:space="preserve">Porrò quod C D ipſi K æqualis eſt, ſic demonſtrabitur.
              <lb/>
            </s>
            <s xml:id="echoid-s2507" xml:space="preserve">Quia quadratum A G æquale eſt quadratis ex K & </s>
            <s xml:id="echoid-s2508" xml:space="preserve">A B: </s>
            <s xml:id="echoid-s2509" xml:space="preserve">
              <lb/>
            idemque quadratum A G æquale quadratis A B, B G cum
              <lb/>
            duplo rectangulo G B L. </s>
            <s xml:id="echoid-s2510" xml:space="preserve">Erit propterea quadratum K æ-
              <lb/>
            quale quadrato B G cum duplo rectangulo G B L. </s>
            <s xml:id="echoid-s2511" xml:space="preserve">Sicut
              <lb/>
            autem B G ad B E ita eſt quadratum B G cum duplo re-
              <lb/>
            ctangulo G B L ad rectangulum G B E cum duplo rectan-
              <lb/>
            ctulo E B L; </s>
            <s xml:id="echoid-s2512" xml:space="preserve">ſingula enim ad ſingula eam habent rationem. </s>
            <s xml:id="echoid-s2513" xml:space="preserve">
              <lb/>
            Ergo & </s>
            <s xml:id="echoid-s2514" xml:space="preserve">quadratum K ad rectangulum G B E cum duplo re-
              <lb/>
            ctangulo E B L ut B G ad B E. </s>
            <s xml:id="echoid-s2515" xml:space="preserve">Eſt autem rectangulo G B E
              <lb/>
            æquale rectangulum C B D, quoniam C B ad B G ut E B
              <lb/>
            ad B D, propter triangulos ſimiles C B G, E B D; </s>
            <s xml:id="echoid-s2516" xml:space="preserve">habent
              <lb/>
            enim angulos ad B æquales & </s>
            <s xml:id="echoid-s2517" xml:space="preserve">angulum B C G angulo B E D. </s>
            <s xml:id="echoid-s2518" xml:space="preserve">
              <lb/>
            Item duplo rectangulo E B L æquale eſt quadratum A B,
              <lb/>
            quia propter triangulos ſimiles ut S A, hoc eſt, dupla B E
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            ad A B ita A B ad B L. </s>
            <s xml:id="echoid-s2519" xml:space="preserve">Igitur ut B G ad B E ita erit
              <lb/>
            quadratum K ad rectangulum C B D cum quadrato A B. </s>
            <s xml:id="echoid-s2520" xml:space="preserve">
              <lb/>
            Sed hiſce duobus æquale eſt rectangulum C A D; </s>
            <s xml:id="echoid-s2521" xml:space="preserve">quoniam
              <lb/>
            in triangulo C A D angulus A bifariam dividitur à linea A B. </s>
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            Ergo ut B G ad B E ita eſt quadr. </s>
            <s xml:id="echoid-s2523" xml:space="preserve">K ad rectangulum C A D. </s>
            <s xml:id="echoid-s2524" xml:space="preserve">
              <lb/>
            Atque hinc porrò eodem modo ut in caſu præcedenti con-
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            cludemus lineam D C ipſi K æqualem eſſe, repetendo iſta: </s>
            <s xml:id="echoid-s2525" xml:space="preserve">
              <lb/>
            Sicut autem G B ad B E, &</s>
            <s xml:id="echoid-s2526" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2527" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div132" type="section" level="1" n="57">
          <head xml:id="echoid-head86" style="it" xml:space="preserve">Utrumque præcedentium Aliter.</head>
          <p>
            <s xml:id="echoid-s2528" xml:space="preserve">SIt datus rhombus A D B C cujus productum latus
              <lb/>
              <note position="right" xlink:label="note-0117-01" xlink:href="note-0117-01a" xml:space="preserve">TAB. XLII.
                <lb/>
              Fig. 3.</note>
            D B. </s>
            <s xml:id="echoid-s2529" xml:space="preserve">Et data ſit linea G. </s>
            <s xml:id="echoid-s2530" xml:space="preserve">Oportet ducere rectam A N F,
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            ut pars intercepta N F ſit datæ G æqualis.</s>
            <s xml:id="echoid-s2531" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2532" xml:space="preserve">Ducatur diameter A B, & </s>
            <s xml:id="echoid-s2533" xml:space="preserve">quadratis ex G & </s>
            <s xml:id="echoid-s2534" xml:space="preserve">A B ſit æ-
              <lb/>
            quale quadratum A H, & </s>
            <s xml:id="echoid-s2535" xml:space="preserve">ducatur H E ipſi B A parallela.
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            </s>
            <s xml:id="echoid-s2536" xml:space="preserve">Et A E ipſi G ponatur æqualis, eademque producatur ad
              <lb/>
            F. </s>
            <s xml:id="echoid-s2537" xml:space="preserve">Dico N F ipſi G æqualem eſſe.</s>
            <s xml:id="echoid-s2538" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2539" xml:space="preserve">Quod autem ad H E poni poteſt A E ipſi G </s>
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