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

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            circumferentiæ portio deſcribatur quæ capiat angulum ipſi
              <lb/>
            B F A æqualem. </s>
            <s xml:id="echoid-s2378" xml:space="preserve">Secabit ea productum latus F A, ut mo-
              <lb/>
            do oſtendetur. </s>
            <s xml:id="echoid-s2379" xml:space="preserve">Itaque ad interſectionis punctum C ducatur
              <lb/>
            B C. </s>
            <s xml:id="echoid-s2380" xml:space="preserve">Dico hujus partem interceptam D C lineæ datæ K æ-
              <lb/>
            qualem eſſe. </s>
            <s xml:id="echoid-s2381" xml:space="preserve">Quod autem circumferentia deſcripta latus F A
              <lb/>
            productum ſecabit, ſic primùm oſtenditur. </s>
            <s xml:id="echoid-s2382" xml:space="preserve">Ducatur A N
              <lb/>
            ita ut ſit angulus B A N angulo B F A vel B E A æqualis.
              <lb/>
            </s>
            <s xml:id="echoid-s2383" xml:space="preserve">Itaque triangulus B A N triangulo B E A ſimilis eſt, ac
              <lb/>
            proinde iſoſceles quoque. </s>
            <s xml:id="echoid-s2384" xml:space="preserve">Quare ſi ſuper B N circumferen-
              <lb/>
            tia deſcribatur quæ capiat angulum B F A, ea continget
              <lb/>
            latus F A in A puncto. </s>
            <s xml:id="echoid-s2385" xml:space="preserve">Sed B G major eſt quam B N: </s>
            <s xml:id="echoid-s2386" xml:space="preserve">
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            nam quadratum A G majus eſt quadrato A N vel A B, cum
              <lb/>
            ſit æquale quadratis ex K & </s>
            <s xml:id="echoid-s2387" xml:space="preserve">A B. </s>
            <s xml:id="echoid-s2388" xml:space="preserve">Quare A G cadet extra
              <lb/>
            triangulum iſoſcelem B A N. </s>
            <s xml:id="echoid-s2389" xml:space="preserve">Itaque manifeſtum eſt cir-
              <lb/>
            cumferentiam ſuper B G deſcriptam capientemque angulum
              <lb/>
            ipſi B F A vel B A N æqualem ſecare lineam F A C. </s>
            <s xml:id="echoid-s2390" xml:space="preserve">Eſto
              <lb/>
            alterum interſectionis punctum M & </s>
            <s xml:id="echoid-s2391" xml:space="preserve">jungantur B M, G C,
              <lb/>
            & </s>
            <s xml:id="echoid-s2392" xml:space="preserve">cadat in B E ex A perpendicularis A L.</s>
            <s xml:id="echoid-s2393" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2394" xml:space="preserve">Quia igitur quadratum A G æquale eſt quadratis ex K & </s>
            <s xml:id="echoid-s2395" xml:space="preserve">
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            A B: </s>
            <s xml:id="echoid-s2396" xml:space="preserve">atque idem quadratum A G æquale quadratis A B & </s>
            <s xml:id="echoid-s2397" xml:space="preserve">
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            B G minus duplo rectangulo G B L, hoc eſt, minus rectan-
              <lb/>
            gulo G B N; </s>
            <s xml:id="echoid-s2398" xml:space="preserve">erit K quadratum æquale quadrato B G mi-
              <lb/>
            nùs rectangulo G B N, hoc eſt, rectangulo B G N. </s>
            <s xml:id="echoid-s2399" xml:space="preserve">Eſt
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            autem ut rectangulum B G N ad rectang. </s>
            <s xml:id="echoid-s2400" xml:space="preserve">B E, G N, ita
              <lb/>
            B G ad B E. </s>
            <s xml:id="echoid-s2401" xml:space="preserve">Ergo ut B G ad B E ita quoque quadratum
              <lb/>
            K ad rectangulum G N, B E, hoc eſt, rectangulum G B E
              <lb/>
            minùs rectangulo N B E. </s>
            <s xml:id="echoid-s2402" xml:space="preserve">Eſt autem rectangulo G B E æ-
              <lb/>
            quale rectang. </s>
            <s xml:id="echoid-s2403" xml:space="preserve">C B D, quoniam G B ad B C ut D B ad B E
              <lb/>
            propter triangulos ſimiles G B C, D B E; </s>
            <s xml:id="echoid-s2404" xml:space="preserve">habent enim an-
              <lb/>
            gulum ad B communem, & </s>
            <s xml:id="echoid-s2405" xml:space="preserve">angulus B C G ipſi B E D eſt
              <lb/>
            æqualis. </s>
            <s xml:id="echoid-s2406" xml:space="preserve">Item rectangulo N B E æquale eſt quadratum A B
              <lb/>
            quia propter triangulos ſimiles eſt N B ad B A ut A B ad
              <lb/>
            B E. </s>
            <s xml:id="echoid-s2407" xml:space="preserve">Ergo erit G B ad B E ut quadratum K ad rectangu-
              <lb/>
            lum C B D minùs quadrato A B. </s>
            <s xml:id="echoid-s2408" xml:space="preserve">Eſt autem rectangulo
              <lb/>
            C B D minùs quadr. </s>
            <s xml:id="echoid-s2409" xml:space="preserve">A B æquale rectangulum D A, A C;
              <lb/>
            </s>
            <s xml:id="echoid-s2410" xml:space="preserve">quod ſic oſtenditur. </s>
            <s xml:id="echoid-s2411" xml:space="preserve">Etenim quia quadrilaterum C G B </s>
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