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

Table of contents

< >
[91.] PROP. XXII. THEOREMA.
[92.] SCHOLIUM.
[93.] PROP. XXIII. THEOREMA.
[94.] PROP. XXIV. THEOREMA.
[95.] PROP. XXV. THEOREMA.
[96.] PROP. XXVI. THEOREMA.
[97.] PROP. XXVII. THEOREMA.
[98.] PROP. XXVIII. THEOREMA.
[99.] PROP. XXIX. PROBLEMA. Dato circulo æquale invenire quadratum.
[100.] PROP. XXX. PROBLEMA. Ex dato ſinu invenire arcum.
[101.] PROP. XXXI. PROBLEMA. Ex dato arcu invenire ſinum.
[102.] PROP. XXXII. PROBLEMA. Invenire quadratum æquale ſpatio hyperbolico con-tento à curva hyperbolica, uno aſymptoto & dua-bus rectis alteri aſymptoto parallelis; quod ſpatium æquale eſt ſectori hyperbolico cujus baſis eſt eadem curva.
[103.] PROP. XXXIII. PROBLEMA. Propoſiti cujuscunque numeri logorithmum invenire.
[104.] SCHOLIUM.
[105.] PROP. XXXIV. PROBLEMA. Ex dato logorithmo invenire ejus numerum.
[106.] Tom. II. Mmm
[107.] PROP. XXXV. PROBLEMA. Rectâ per datum punctum in diametro ductâ, ſemicirculum in ratione data dividere.
[108.] SCHOLIUM.
[109.] FINIS.
[110.] II. HUGENII OBSERVATIONES IN LIBRUM JACOBI GREGORII, DE VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
[111.] III. DOMINI GREGORII RESPONSUM AD ANIMADVERSIONES DOMINI HUGENII, IN EJUS LIBRUM, DE VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
[112.] PROP. X. PROBLEMA.
[113.] Tom. II. Nnn
[114.] CONSECTARIUM.
[115.] IV. EXCERPTA EX LITERIS Dni. HUGENII DE RESPONSO, QUOD Dnus. GREGORIUS DEDIT AD EXAMEN LIBRI, CUI TITULUS EST, VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
[116.] V. EXCERPTA EX EPISTOLA D. JACOBI GREGORII, CONTINENTE QUASDAM EJUS CONSIDERATIO-NES, SUPER EPISTOLA D. HUGENII, IMPRESSA IN VINDICATIONEM EXAMINIS SUI LIBRI, DE VERA CIRCULI ET HY-PERBOLÆ QUADRATURA.
[117.] FINIS.
[118.] CHRISTIANI HUGENII GEOMETRICA VARIA. Tom. II. Ppp
[119.] I. CONSTRUCTIO LOCI AD HYPERBOLAM PER ASYMPTOTOS.
[120.] DEMONSTRATIO.
< >
page |< < (449) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <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"/>
          </p>
        </div>
      </text>
    </echo>