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

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            <s xml:id="echoid-s2539" xml:space="preserve">
              <pb o="402" file="0118" n="126" rhead="CHRISTIANI HUGENII"/>
            hinc manifeſtum eſt. </s>
            <s xml:id="echoid-s2540" xml:space="preserve">Etenim quadratum A H majus eſt
              <lb/>
            quadratis A X & </s>
            <s xml:id="echoid-s2541" xml:space="preserve">X H, quum ſit angulus A X H obtuſus.
              <lb/>
            </s>
            <s xml:id="echoid-s2542" xml:space="preserve">Sed idem quadratum A H æquale ponitur quadratis A B ſeu
              <lb/>
            H X & </s>
            <s xml:id="echoid-s2543" xml:space="preserve">G. </s>
            <s xml:id="echoid-s2544" xml:space="preserve">Itaque quadratum G ſeu A E majus eſt quadrato
              <lb/>
            A X. </s>
            <s xml:id="echoid-s2545" xml:space="preserve">Unde apparet interſectionem E accidere inter puncta
              <lb/>
            H & </s>
            <s xml:id="echoid-s2546" xml:space="preserve">X.</s>
            <s xml:id="echoid-s2547" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2548" xml:space="preserve">Producatur B D & </s>
            <s xml:id="echoid-s2549" xml:space="preserve">ponatur ipſi æqualis D R. </s>
            <s xml:id="echoid-s2550" xml:space="preserve">& </s>
            <s xml:id="echoid-s2551" xml:space="preserve">ſit R K
              <lb/>
            parallela D A vel B C, eique occurrant productæ F A,
              <lb/>
            B A, H E, in punctis M, Q, K: </s>
            <s xml:id="echoid-s2552" xml:space="preserve">& </s>
            <s xml:id="echoid-s2553" xml:space="preserve">jungatur R A, & </s>
            <s xml:id="echoid-s2554" xml:space="preserve">
              <lb/>
            producatur ad P.</s>
            <s xml:id="echoid-s2555" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2556" xml:space="preserve">Quoniam igitur D R æqualis eſt D B, & </s>
            <s xml:id="echoid-s2557" xml:space="preserve">R Q K paral-
              <lb/>
            lela D A, erit & </s>
            <s xml:id="echoid-s2558" xml:space="preserve">M A æqualis A N, & </s>
            <s xml:id="echoid-s2559" xml:space="preserve">Q A æqualis A B;
              <lb/>
            </s>
            <s xml:id="echoid-s2560" xml:space="preserve">angulus autem B A R rectus, quum ſit in ſemicirculo,
              <lb/>
            nam tres hæ æquales ſunt D B, D A, D R. </s>
            <s xml:id="echoid-s2561" xml:space="preserve">Parallelæ au-
              <lb/>
            tem ſunt B Q, H E K, ergo & </s>
            <s xml:id="echoid-s2562" xml:space="preserve">anguli ad P recti, & </s>
            <s xml:id="echoid-s2563" xml:space="preserve">erit
              <lb/>
            H P æqualis P K. </s>
            <s xml:id="echoid-s2564" xml:space="preserve">Eſt itaque quadratum A H æquale qua-
              <lb/>
            drato A E unà cum rectangulo H E K . </s>
            <s xml:id="echoid-s2565" xml:space="preserve">Sed idem
              <note symbol="*" position="left" xlink:label="note-0118-01" xlink:href="note-0118-01a" xml:space="preserve">12.2 Elem.</note>
            tum A H æquale eſt etiam quadratis ex G ſeu A E, & </s>
            <s xml:id="echoid-s2566" xml:space="preserve">ex
              <lb/>
            A B. </s>
            <s xml:id="echoid-s2567" xml:space="preserve">Itaque quadr. </s>
            <s xml:id="echoid-s2568" xml:space="preserve">A B æquale erit rectangulo K E H.
              <lb/>
            </s>
            <s xml:id="echoid-s2569" xml:space="preserve">Ac propterea K E ad A B ut A B ad E H. </s>
            <s xml:id="echoid-s2570" xml:space="preserve">Verum ut K E
              <lb/>
            ad A B ſeu Q A ita eſt E M ad M A: </s>
            <s xml:id="echoid-s2571" xml:space="preserve">& </s>
            <s xml:id="echoid-s2572" xml:space="preserve">ut A B ad E H
              <lb/>
            ita A F ad F E. </s>
            <s xml:id="echoid-s2573" xml:space="preserve">Igitur E M ad M A ut A F ad F E: </s>
            <s xml:id="echoid-s2574" xml:space="preserve">Et
              <lb/>
            proinde E A ad A M ut E A ad E F. </s>
            <s xml:id="echoid-s2575" xml:space="preserve">Æqualis eſt igi-
              <lb/>
            tur E F ipſi A M; </s>
            <s xml:id="echoid-s2576" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s2577" xml:space="preserve">ipſi A N. </s>
            <s xml:id="echoid-s2578" xml:space="preserve">Ideoque & </s>
            <s xml:id="echoid-s2579" xml:space="preserve">F N
              <lb/>
            ipſi A E, hoc eſt, datæ G. </s>
            <s xml:id="echoid-s2580" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s2581" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2582" xml:space="preserve">Sit denuo datus rhomdus A D B C, cujus producta la-
              <lb/>
              <note position="left" xlink:label="note-0118-02" xlink:href="note-0118-02a" xml:space="preserve">TAB. XLII.
                <lb/>
              Fig. 4.</note>
            tera B D, B C; </s>
            <s xml:id="echoid-s2583" xml:space="preserve">& </s>
            <s xml:id="echoid-s2584" xml:space="preserve">data ſit linea G. </s>
            <s xml:id="echoid-s2585" xml:space="preserve">Oportet ducere re-
              <lb/>
            ctam N F tranſeuntem per angulum A, quæque æqualis ſit
              <lb/>
            ipſi G.</s>
            <s xml:id="echoid-s2586" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2587" xml:space="preserve">Ducatur diameter B A, eique ad angulos rectos R A L.
              <lb/>
            </s>
            <s xml:id="echoid-s2588" xml:space="preserve">Si igitur G minor detur quam R L, problema conſtrui ne-
              <lb/>
            quit, uti ſupra quoque dictum fuit. </s>
            <s xml:id="echoid-s2589" xml:space="preserve">Si vero æqualis, jam fa-
              <lb/>
            ctum eſt quod quærebatur. </s>
            <s xml:id="echoid-s2590" xml:space="preserve">Sit igitur G major quam R L. </s>
            <s xml:id="echoid-s2591" xml:space="preserve">
              <lb/>
            Erit in ſchemate adjecto, ſicut propoſitum eſt, conſtru-
              <lb/>
            ctio & </s>
            <s xml:id="echoid-s2592" xml:space="preserve">demonſtratio eadem quæ in caſu præcedenti.</s>
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