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

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            <s xml:id="echoid-s4523" xml:space="preserve">
              <pb o="486" file="0206" n="216" rhead="CHRIST. HUGENII"/>
            rallela A B. </s>
            <s xml:id="echoid-s4524" xml:space="preserve">Si verò non habeatur omnino l, recta I K in
              <lb/>
            A B incidere intelligenda eſt.</s>
            <s xml:id="echoid-s4525" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4526" xml:space="preserve">Deinde ſicut z ad n, quæ ratio data, ita ſit I K ad libi-
              <lb/>
            tum ſumpta, ad K L; </s>
            <s xml:id="echoid-s4527" xml:space="preserve">quæ ipſi A I parallela ducendaeſt, ſu-
              <lb/>
            mendaque hoc pacto, ut puncta K L ſita ſint quo ordinc
              <lb/>
            A I, ſi habeatur + {nx/z}, at contrà ſi habeatur - {nx/z}, & </s>
            <s xml:id="echoid-s4528" xml:space="preserve">du-
              <lb/>
            catur recta per IL; </s>
            <s xml:id="echoid-s4529" xml:space="preserve">ſi verò deſit {nx/z}, eadem eſt I L & </s>
            <s xml:id="echoid-s4530" xml:space="preserve">I K.</s>
            <s xml:id="echoid-s4531" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4532" xml:space="preserve">Porro ut p ad g, ita ſit {1/2}o ad ſingulas IX, I Y ſumendas
              <lb/>
            in recta A I; </s>
            <s xml:id="echoid-s4533" xml:space="preserve">atque ita quoque I X ad I V ſumendam in I K
              <lb/>
            ad partes A B ſi habeatur - o x, aut in contrarias ſi habea-
              <lb/>
            tur + ox; </s>
            <s xml:id="echoid-s4534" xml:space="preserve">& </s>
            <s xml:id="echoid-s4535" xml:space="preserve">ſit V M parallela A I, occurratque rectæ I L
              <lb/>
            in M: </s>
            <s xml:id="echoid-s4536" xml:space="preserve">erit jam M centrum hyperbolæ quæſitæ aſymptoti
              <lb/>
            vero, rectæ per M X, M Y ductæ.</s>
            <s xml:id="echoid-s4537" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4538" xml:space="preserve">Si vero non habeatur o x in æquatione, erit I centrum hy-
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            perbolæ; </s>
            <s xml:id="echoid-s4539" xml:space="preserve">ſumptisque I X, I Y ad libitum ſed inter ſe æqua-
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            libus, inventiſque inde punctis V & </s>
            <s xml:id="echoid-s4540" xml:space="preserve">M, ut ante, ducentur
              <lb/>
            aſymptoti per I parallelæ ipſis M X, M Y.</s>
            <s xml:id="echoid-s4541" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4542" xml:space="preserve">Jam porro ſi habeatur + mm, puncta S & </s>
            <s xml:id="echoid-s4543" xml:space="preserve">R, per quæ
              <lb/>
            hyperbola vel oppoſitæ ſectiones tranſire debent, invenien-
              <lb/>
            tur ſumendo in recta A I à puncto I, ſingulas I S, I R æqua-
              <lb/>
            les m: </s>
            <s xml:id="echoid-s4544" xml:space="preserve">unde jam hyperbola data erit ac deſcribi poterit, in
              <lb/>
            qua B C erit ordinatim applicata ad diametrum, ſi {{1/2}og/z} ma-
              <lb/>
            jor quam m; </s>
            <s xml:id="echoid-s4545" xml:space="preserve">ſin verò {{1/2}og/p} minor quam m, erit B C paralle-
              <lb/>
            la diametro hyperbolæ ad quam eſt C punctum, ut hic caſu
              <lb/>
            ſecundo. </s>
            <s xml:id="echoid-s4546" xml:space="preserve">Quod ſi forte punctum S incidat in X, locus
              <lb/>
            puncti C, erunt ipſæ aſymptoti. </s>
            <s xml:id="echoid-s4547" xml:space="preserve">Si verò non habeatur mm,
              <lb/>
            erit ipſum I punctum in hyperbola quæſita.</s>
            <s xml:id="echoid-s4548" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4549" xml:space="preserve">At ſi habeatur — mm, accommodanda eſt intra angu-
              <lb/>
            lum X M I recta G N parallela I X, quæque poſſit quadrata
              <lb/>
            @b I X & </s>
            <s xml:id="echoid-s4550" xml:space="preserve">I S, vel tantum ipſi I S æqualis, ſi non </s>
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