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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        <div xml:id="echoid-div208" type="section" level="1" n="101">
          <p>
            <s xml:id="echoid-s3768" xml:space="preserve">
              <pb o="449" file="0167" n="176" rhead="ET HYPERBOLÆ QUADRATURA."/>
            cogniti A B E, cujus arcus A E etiam innoteſcit, datur radius
              <lb/>
            B A: </s>
            <s xml:id="echoid-s3769" xml:space="preserve">ſit ejus ſinus A D, z; </s>
            <s xml:id="echoid-s3770" xml:space="preserve">& </s>
            <s xml:id="echoid-s3771" xml:space="preserve">proinde è dato ſinu & </s>
            <s xml:id="echoid-s3772" xml:space="preserve">radio, da-
              <lb/>
            bitur ut in antecedente triangulum ſectori inſcriptum A B E & </s>
            <s xml:id="echoid-s3773" xml:space="preserve">
              <lb/>
            eidem trapezium circumſcriptum A B E C; </s>
            <s xml:id="echoid-s3774" xml:space="preserve">atque ipſe ſector
              <lb/>
            datus, eſt ſecunda duarum mediarum arithmeticè continuè
              <lb/>
            proportionalium inter triangulum ſibi inſcriptum & </s>
            <s xml:id="echoid-s3775" xml:space="preserve">trapezium
              <lb/>
            circumſcriptum; </s>
            <s xml:id="echoid-s3776" xml:space="preserve">& </s>
            <s xml:id="echoid-s3777" xml:space="preserve">proinde datur æquatio inter duplum tra-
              <lb/>
            pezii A B E C unà cum triangulo A B E & </s>
            <s xml:id="echoid-s3778" xml:space="preserve">triplum ſectoris
              <lb/>
            cogniti A B E, cujus reſolutio manifeſtat valorem quantita-
              <lb/>
            tis ignotæ z, hoc eſt ſinum A D: </s>
            <s xml:id="echoid-s3779" xml:space="preserve">at dato arcu A E & </s>
            <s xml:id="echoid-s3780" xml:space="preserve">ejus
              <lb/>
            ſinu, dantur etiam ex vulgata ſectionum angularium doctri-
              <lb/>
            na ſinus omnium multiplicium ejuſdem arcus A E; </s>
            <s xml:id="echoid-s3781" xml:space="preserve">& </s>
            <s xml:id="echoid-s3782" xml:space="preserve">proin-
              <lb/>
            de non latet ſinus arcus in initio propoſiti, cum ſit ad arcum
              <lb/>
            A E in data ratione multiplici, quem invenire oportuit.</s>
            <s xml:id="echoid-s3783" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div210" type="section" level="1" n="102">
          <head xml:id="echoid-head140" xml:space="preserve">PROP. XXXII. PROBLEMA.</head>
          <head xml:id="echoid-head141" style="it" xml:space="preserve">Invenire quadratum æquale ſpatio hyperbolico con-
            <lb/>
          tento à curva hyperbolica, uno aſymptoto & dua-
            <lb/>
          bus rectis alteri aſymptoto parallelis; quod
            <lb/>
          ſpatium æquale eſt ſectori hyperbolico
            <lb/>
          cujus baſis eſt eadem curva.</head>
          <p>
            <s xml:id="echoid-s3784" xml:space="preserve">Sit hyperpola D I L, cujus aſymptota A O, A K, ſibioc-
              <lb/>
              <note position="right" xlink:label="note-0167-01" xlink:href="note-0167-01a" xml:space="preserve">TAB. XLIV.
                <lb/>
              fig. 1.</note>
            currunt in angulo recto O A K. </s>
            <s xml:id="echoid-s3785" xml:space="preserve">proponitur hujus hyper-
              <lb/>
            bolæ ſpatium I L M K, contentum à curva hyperbolica I L,
              <lb/>
            aſymptoto K M & </s>
            <s xml:id="echoid-s3786" xml:space="preserve">duabus rectis I K, L M, alteri aſymptoto
              <lb/>
            A O parallelis. </s>
            <s xml:id="echoid-s3787" xml:space="preserve">oportet è datis recti I K 10 000000000000,
              <lb/>
            L M 10000000000000, A M 1000000000000, & </s>
            <s xml:id="echoid-s3788" xml:space="preserve">proinde
              <lb/>
            recta quoque K M 9000000000000, invenire menſuram ſpa-
              <lb/>
            tii I L M K. </s>
            <s xml:id="echoid-s3789" xml:space="preserve">Producantur rectæ I K, O L, & </s>
            <s xml:id="echoid-s3790" xml:space="preserve">ducatur recta
              <lb/>
            I P, ut compleantur rectangula L N K M, Q I K M; </s>
            <s xml:id="echoid-s3791" xml:space="preserve">manife-
              <lb/>
            ſtum eſt rectangulum L N K M eſſe 9000000000000000000-
              <lb/>
            0000000 & </s>
            <s xml:id="echoid-s3792" xml:space="preserve">Q I K M 9000000000000000000000000 & </s>
            <s xml:id="echoid-s3793" xml:space="preserve"/>
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