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

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        <div xml:id="echoid-div208" type="section" level="1" n="101">
          <p>
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              <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>
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              <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
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            proportionalium inter triangulum ſibi inſcriptum & </s>
            <s xml:id="echoid-s3775" xml:space="preserve">trapezium
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            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-
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            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-
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            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
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            ſinu, dantur etiam ex vulgata ſectionum angularium doctri-
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            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-
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            de non latet ſinus arcus in initio propoſiti, cum ſit ad arcum
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            A E in data ratione multiplici, quem invenire oportuit.</s>
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        <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-
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          tento à curva hyperbolica, uno aſymptoto & dua-
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          bus rectis alteri aſymptoto parallelis; quod
            <lb/>
          ſpatium æquale eſt ſectori hyperbolico
            <lb/>
          cujus baſis eſt eadem curva.</head>
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            <s xml:id="echoid-s3784" xml:space="preserve">Sit hyperpola D I L, cujus aſymptota A O, A K, ſibioc-
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              <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-
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            bolæ ſpatium I L M K, contentum à curva hyperbolica I L,
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            aſymptoto K M & </s>
            <s xml:id="echoid-s3786" xml:space="preserve">duabus rectis I K, L M, alteri aſymptoto
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            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-
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            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-
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            ſtum eſt rectangulum L N K M eſſe 9000000000000000000-
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            0000000 & </s>
            <s xml:id="echoid-s3792" xml:space="preserve">Q I K M 9000000000000000000000000 & </s>
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