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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            ope ſolius regulæ & </s>
            <s xml:id="echoid-s3941" xml:space="preserve">circini peracta, hanc in his non ſolum
              <lb/>
            eſſe impoſſibilem ſed etiam in omnibus problematis quæ ad
              <lb/>
            æquationem quadratic
              <unsure/>
            am reduci non poſſunt, ſicut facile
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            demonſtrari poſſet; </s>
            <s xml:id="echoid-s3942" xml:space="preserve">& </s>
            <s xml:id="echoid-s3943" xml:space="preserve">ſi per geometricum intelligatur redu-
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            ctio problematis ad æquationem analyticam, omnia hæc
              <lb/>
            problemata ſunt geometrice impoſſibilia, cum ex hic demon-
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            ſtratis, manifeſtum ſit talem reductionem fieri non poſſe:
              <lb/>
            </s>
            <s xml:id="echoid-s3944" xml:space="preserve">ſi verò per geometricum intelligatur methodus omnium poſ-
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            ſibilium ſimpliciſſima; </s>
            <s xml:id="echoid-s3945" xml:space="preserve">invenietur fortaſſe poſt maturam con-
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            ſiderationem omnia prædicta problemata eſſe geometriciſſi-
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            mè reſoluta, diligenter animadvertendum totam ſerierum
              <lb/>
            convergentium doctrinam poſſe etiam nullo negotio applicari
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            ſeriebus ſimplicibus. </s>
            <s xml:id="echoid-s3946" xml:space="preserve">Sit enim ſeries A, B, C, D, E, &</s>
            <s xml:id="echoid-s3947" xml:space="preserve">c,
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            talis naturæ ut tertius terminus C eodem modo
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                <lb/>
              A
                <lb/>
              B
                <lb/>
              C
                <lb/>
              D
                <lb/>
              E
                <lb/>
              Z
                <lb/>
              </note>
            componatur ex primo & </s>
            <s xml:id="echoid-s3948" xml:space="preserve">ſecundo A, B, quo
              <lb/>
            quartus D componitur ex ſecundo & </s>
            <s xml:id="echoid-s3949" xml:space="preserve">tertio B, C,
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            & </s>
            <s xml:id="echoid-s3950" xml:space="preserve">quintus E ex tertio & </s>
            <s xml:id="echoid-s3951" xml:space="preserve">quarto C, D, & </s>
            <s xml:id="echoid-s3952" xml:space="preserve">ſic dein-
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            ceps in infinitum; </s>
            <s xml:id="echoid-s3953" xml:space="preserve">ſitque differentia anteceden-
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            tium A, B, major ſemper differentia immediatè
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            ſequentium B, C; </s>
            <s xml:id="echoid-s3954" xml:space="preserve">ſupponamus hanc ſeriem ita in infinitum
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            continuari donec duorum terminorum immediate ſe invicem
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            ſequentium nulla ſit differentia, ſitque unus ex illis terminis
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            z, quem ſeriei terminationem appellamus: </s>
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            modo componi ex A & </s>
            <s xml:id="echoid-s3956" xml:space="preserve">B quo ex B & </s>
            <s xml:id="echoid-s3957" xml:space="preserve">C vel C & </s>
            <s xml:id="echoid-s3958" xml:space="preserve">D; </s>
            <s xml:id="echoid-s3959" xml:space="preserve">de-
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            monſtratio vix differt ab hujus 10 & </s>
            <s xml:id="echoid-s3960" xml:space="preserve">ejus conſectario: </s>
            <s xml:id="echoid-s3961" xml:space="preserve">hac
              <lb/>
            ratione ſi ponatur triangulum, ſectori circulari vel elliptico
              <lb/>
            inſcriptum, vel ſectori hyperbolico circumſcriptum a, & </s>
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              <lb/>
            trapezium, ſectori circulari vel elliptico regulariter in-
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            ſcriptum vel hyperbolico regulariter circumſcriptum b;
              <lb/>
            </s>
            <s xml:id="echoid-s3963" xml:space="preserve">erit hexagonum ſectori circulari vel elliptico regulari-
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            ter inſcriptum vel hyperbolico regulariter circumſcri-
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            ptum Vq {2 b3/a + b;</s>
            <s xml:id="echoid-s3964" xml:space="preserve">} & </s>
            <s xml:id="echoid-s3965" xml:space="preserve">proinde ſector circuli, ellipſeos vel hyperbo-
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            læ eodem modo componitur ex a & </s>
            <s xml:id="echoid-s3966" xml:space="preserve">b quo ex b & </s>
            <s xml:id="echoid-s3967" xml:space="preserve">Vq {2 b3/a + b;</s>
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            atque hinc etiam demonſtrari poteſt, quod ratio inter ſecto-
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            rem & </s>
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