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

Table of figures

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[61] Fig. 5.G L B H D O A E C K
[62] Fig. 7.K F A C D B E H G
[63] Pag. 404.TAB. XLII.Fig. 1.K F M A C D B L E N G
[64] Fig. 3.G R D B H F E N A X C M P Q K
[65] Fig. 2.K A F c S C L E B T G D R d
[66] Fig. 4.K e G P E m B D f R F S H M C A N L Q n
[67] Fig. 5.B C R E G A F M Q D O
[68] Fig. 6.B C H G E A M Q P K D
[69] Fig. 7.B C E G A M P Q K H D
[Figure 70]
[71] Pag. 450.TAB.XLIII.Fig. 4.B A F R P C D E G H I K S L M N O
[72] Fig. 1.F G I K D L E S T O C N H M V R B Q P A
[73] Fig. 2.F G I K D L E S T O C N V R B Q P A
[74] Fig. 5.A C B D E
[75] Fig. 3.A F G I K D L S T E O C N H M V R B Q P
[Figure 76]
[Figure 77]
[Figure 78]
[Figure 79]
[Figure 80]
[Figure 81]
[Figure 82]
[83] TAB. XLIV.Fig. 2.D H A B E F G
[84] Fig. 1.E G N L O I Q P D K M H F A
[85] Fig. 3.B E F A D G C
[86] I. CasusFig. 4.Y Q R C A B M L I K V C O S X
[87] II. CasusFig. 5.R C Y Q A B I L M K V O X S C
[88] III. CasusFig. 6.Q C D Y K L I N M S V B X C A G O
[89] Fig. 7.IV. CasusQ D C A B S L N X M I V Y K C G O
[Figure 90]
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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-
              <lb/>
            perbolæ; </s>
            <s xml:id="echoid-s4539" xml:space="preserve">ſumptisque I X, I Y ad libitum ſed inter ſe æqua-
              <lb/>
            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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