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

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            <s xml:id="echoid-s2411" xml:space="preserve">
              <pb o="399" file="0115" n="123" rhead="ILLUST. QUORUND. PROB. CONSTRUCT."/>
            eſt in circulo, ſunt anguli C G B & </s>
            <s xml:id="echoid-s2412" xml:space="preserve">B M C ſimul duobus
              <lb/>
            rectis æquales. </s>
            <s xml:id="echoid-s2413" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s2414" xml:space="preserve">anguli E D B, A D B. </s>
            <s xml:id="echoid-s2415" xml:space="preserve">Quorum E D B
              <lb/>
            æqualis angulo C G B propter ſimilitudinem triangulorum
              <lb/>
            G B C, D B E. </s>
            <s xml:id="echoid-s2416" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s2417" xml:space="preserve">angulus B M C æqualis erit an-
              <lb/>
            gulo A D B. </s>
            <s xml:id="echoid-s2418" xml:space="preserve">Trianguli igitur A B M, A B D angulos M
              <lb/>
            & </s>
            <s xml:id="echoid-s2419" xml:space="preserve">D inter ſe æquales habent. </s>
            <s xml:id="echoid-s2420" xml:space="preserve">Verum & </s>
            <s xml:id="echoid-s2421" xml:space="preserve">angulos ad A, & </s>
            <s xml:id="echoid-s2422" xml:space="preserve">
              <lb/>
            latus A B commune. </s>
            <s xml:id="echoid-s2423" xml:space="preserve">Itaque dicti trianguli ſimiles ſunt & </s>
            <s xml:id="echoid-s2424" xml:space="preserve">
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            æquales. </s>
            <s xml:id="echoid-s2425" xml:space="preserve">Quare A M æqualis A D, & </s>
            <s xml:id="echoid-s2426" xml:space="preserve">M B æqualis B D,
              <lb/>
            & </s>
            <s xml:id="echoid-s2427" xml:space="preserve">angulus M B A æqualis A B D. </s>
            <s xml:id="echoid-s2428" xml:space="preserve">In triangulo igitur M B C
              <lb/>
            angulus B in duo æqualia dividitur à recta B A, ideoque
              <lb/>
            rectang. </s>
            <s xml:id="echoid-s2429" xml:space="preserve">M B C minus quadrato B A æquatur rectangulo
              <lb/>
            M A C. </s>
            <s xml:id="echoid-s2430" xml:space="preserve">Sed rectangulo C B M æquale eſt rectangulum
              <lb/>
            C B D; </s>
            <s xml:id="echoid-s2431" xml:space="preserve">& </s>
            <s xml:id="echoid-s2432" xml:space="preserve">rectangulo M A C æquale rectang. </s>
            <s xml:id="echoid-s2433" xml:space="preserve">D A C. </s>
            <s xml:id="echoid-s2434" xml:space="preserve">Igi-
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            tur rectang. </s>
            <s xml:id="echoid-s2435" xml:space="preserve">C B D minus quadrato B A æquale rectangulo
              <lb/>
            C A D, uti dictum fuit. </s>
            <s xml:id="echoid-s2436" xml:space="preserve">Eſt itaque G B ad B E ut quadr.
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            </s>
            <s xml:id="echoid-s2437" xml:space="preserve">K ad rectangulum D A C. </s>
            <s xml:id="echoid-s2438" xml:space="preserve">Sicut autem G B ad B E ita eſt
              <lb/>
            rectang. </s>
            <s xml:id="echoid-s2439" xml:space="preserve">G B E, hoc eſt, rectang. </s>
            <s xml:id="echoid-s2440" xml:space="preserve">C B D ad quadratum B E. </s>
            <s xml:id="echoid-s2441" xml:space="preserve">
              <lb/>
            Ergo ut quadratum K ad rectang. </s>
            <s xml:id="echoid-s2442" xml:space="preserve">D A C ita rectang. </s>
            <s xml:id="echoid-s2443" xml:space="preserve">C B D
              <lb/>
            ad quadratum B E. </s>
            <s xml:id="echoid-s2444" xml:space="preserve">Ratio autem rectanguli C B D ad quadr. </s>
            <s xml:id="echoid-s2445" xml:space="preserve">
              <lb/>
            B E compoſita eſt ex ratione D B ad B E, hoc eſt, D C
              <lb/>
            ad C A, & </s>
            <s xml:id="echoid-s2446" xml:space="preserve">ex ratione C B ad B E ſive B F, hoc eſt, C D
              <lb/>
            ad D A. </s>
            <s xml:id="echoid-s2447" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s2448" xml:space="preserve">quadr. </s>
            <s xml:id="echoid-s2449" xml:space="preserve">K ad rectang. </s>
            <s xml:id="echoid-s2450" xml:space="preserve">D A C eam habet
              <lb/>
            rationem quæ componitur ex ratione D C ad C A & </s>
            <s xml:id="echoid-s2451" xml:space="preserve">D C
              <lb/>
            ad D A. </s>
            <s xml:id="echoid-s2452" xml:space="preserve">hoc eſt, eam quam quadratum D C ad rectang. </s>
            <s xml:id="echoid-s2453" xml:space="preserve">
              <lb/>
            D A C. </s>
            <s xml:id="echoid-s2454" xml:space="preserve">Quamobrem quadr. </s>
            <s xml:id="echoid-s2455" xml:space="preserve">K. </s>
            <s xml:id="echoid-s2456" xml:space="preserve">quadrato D C æquale eſt: </s>
            <s xml:id="echoid-s2457" xml:space="preserve">
              <lb/>
            Et D C ipſi K longitudine. </s>
            <s xml:id="echoid-s2458" xml:space="preserve">Quod erat demonſtrandum.</s>
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        <div xml:id="echoid-div130" type="section" level="1" n="56">
          <head xml:id="echoid-head85" xml:space="preserve">
            <emph style="sc">Probl.</emph>
          VII.</head>
          <p style="it">
            <s xml:id="echoid-s2460" xml:space="preserve">RHombo dato & </s>
            <s xml:id="echoid-s2461" xml:space="preserve">duobus contiguis lateribus pro-
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            ductis, aptare ſub angulo interiorirectam ma-
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            gnitudine datam quæ per oppoſitum angulum tranſ-
              <lb/>
            eat. </s>
            <s xml:id="echoid-s2462" xml:space="preserve">Oportet autem datam non minorem eſſe quam
              <lb/>
            duplam diametri quæ reliquos duos rhombi angulos
              <lb/>
            conjungit.</s>
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