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

Table of contents

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[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.
[121.] II. DEMONSTRATIO REGULÆ DE MAXIMIS ET MINIMIS.
[122.] Tom. II. Qqq
[123.] III. REGULA Ad inveniendas Tangentes linearum curvarum.
[124.] Tom. II. Rrr
[125.] IV. CHRISTIANI HUGENII EPISTOLA DE CURVIS QUIBUSDAM PECULIARIBUS.
[126.] V. PROBLEMA AB ERUDITIS SOLVENDUM: A JOHANNE BERNOULLIO IN ACTIS LIPSIENSIBUS ANNI MDCXCIII. PROPOSITUM.
[127.] Tom. II. Ttt
[128.] VI. C. H. Z. DE PROBLEMATE BERNOULLIANO IN ACTIS LIPSIENSIBUS PROPOSITO.
[129.] VII. C. H. Z. CONSTRUCTIO UNIVERSALIS PROBLEMATIS A CLARISSIMO VIRO JOH. BERNOULLIO PROPOSITI.
[130.] FINIS.
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              <pb o="456" file="0176" n="186" rhead="VERA CIRCULI"/>
            ut lectori compendium patefiat) ſeu logorithmus numeri 1{24/1000}
              <lb/>
            poſito logorithmo denarii arbitrario 23025850929940456-
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            240178700; </s>
            <s xml:id="echoid-s3871" xml:space="preserve">deinde eodem ſuppoſito logorithmo arbitrario
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            denarii, addatur logorithmus numeri 1000, ſeu triplus logo-
              <lb/>
            rithmi denarii, logorithmo numeri 1{24/1000}, eritque ſumma
              <lb/>
            logorithmus numeri 1024, cujus pars decima erit logorithmus
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            numeri binarii, pro eodem logorithmo denarii arbitrario,
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            nempe 6931471805599452914171917: </s>
            <s xml:id="echoid-s3872" xml:space="preserve">fiatque ut logorith-
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            mus numerii denarii 23025850929940456240178700 ad lo-
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            gorithmum numeri binarii correſpondentem 69314718055-
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            99452914171917, ita logorithmus numeri denarii arbitrarius
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            propoſitus nempe 100000000000000000000000000 ad lo-
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            gorithmum numeri binarii quæſitum 3010299956639811952-
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            405804, quem invenire oportuit: </s>
            <s xml:id="echoid-s3873" xml:space="preserve">eodem modo invenitur lo-
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            gorithmus ternarii 4771212547196624373502993, &</s>
            <s xml:id="echoid-s3874" xml:space="preserve">c.</s>
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          <p>
            <s xml:id="echoid-s3876" xml:space="preserve">Ut in promptu habeantur numeri illi compoſiti parum in-
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            ter ſe differentes pro unoquoque numero primo, hic tabel-
              <lb/>
            lam exhibeo pro numeris primis uſque ad 100, & </s>
            <s xml:id="echoid-s3877" xml:space="preserve">unam re-
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            gulam pro numeris primis inter 100 & </s>
            <s xml:id="echoid-s3878" xml:space="preserve">1000 & </s>
            <s xml:id="echoid-s3879" xml:space="preserve">alteram pro
              <lb/>
            numeris primis ſupra 1000; </s>
            <s xml:id="echoid-s3880" xml:space="preserve">quæ omnia ita excogitata ſunt,
              <lb/>
            ut verus cujuscunque numeri primi logorithmus inveniri
              <lb/>
            poſſit correſpondens logorithmo arbitrario denarii 100000-
              <lb/>
            00000000000000000000 ex una ſola multiplicatione, dua-
              <lb/>
            bus diviſionibus & </s>
            <s xml:id="echoid-s3881" xml:space="preserve">una radicis quadratæ extractione, ultra
              <lb/>
            inconſiderabiles aliquot operatiunculas.</s>
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            <lb/>
          2 # 1000(
            <emph style="super">3</emph>
          )10
            <lb/>
          " # 1024(
            <emph style="super">10</emph>
          )2
            <lb/>
          3 # 32805 factus ex 5 & 6561(
            <emph style="super">8</emph>
          )3
            <lb/>
          " # 32768(
            <emph style="super">15</emph>
          ) 2
            <lb/>
          7 # 2400 factus ex 3 & 32(
            <emph style="super">5</emph>
          )2 & 25(
            <emph style="super">2</emph>
          )5
            <lb/>
          " # 2401(
            <emph style="super">4</emph>
          )7
            <lb/>
          11 # 9800 factus ex 2, 49(
            <emph style="super">2</emph>
          )7 & 100(
            <emph style="super">2</emph>
          )10
            <lb/>
          " # 9801 factus ex 121(
            <emph style="super">2</emph>
          )11 & 81(
            <emph style="super">4</emph>
          )3
            <lb/>
          </note>
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