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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          <head xml:id="echoid-head175" xml:space="preserve">VI.
            <lb/>
          C. H. Z. DE PROBLEMATE
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          BERNOULLIANO
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          IN
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          ACTIS LIPSIENSIBUS
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          PROPOSITO.</head>
          <p>
            <s xml:id="echoid-s5146" xml:space="preserve">ELegans inprimis eſſe hoc Problema, cum ex iis
              <lb/>
            quæ Clariſſimus inventor de eo prodidit, tum
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            ex ſolutione & </s>
            <s xml:id="echoid-s5147" xml:space="preserve">commentatione fraterna mani-
              <lb/>
            feſtum eſt. </s>
            <s xml:id="echoid-s5148" xml:space="preserve">A quo inveſtigando cum propter
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            inſignem difficultatem, quæ ſtatim ſeſe offerebat, abſtinere
              <lb/>
            ſtatuerim (neque enim omnibus perquirendis, quæ à Viris
              <lb/>
            eruditis exercitii gratia proponuntur, incumbere neceſſe exi-
              <lb/>
            ſtimo, aut aſſequendis parem me profiteor) non deſiit
              <lb/>
            tamen quaſi invitum compellere recurrens identidem quæ-
              <lb/>
            ſiti non vulgaris idea, donec tandem quod deſiderabam
              <lb/>
            obtinui. </s>
            <s xml:id="echoid-s5149" xml:space="preserve">Inventa nimirum æquatione differentiali, in qua
              <lb/>
            ex altera parte erat elementum trapezii hyperbolici, ab
              <lb/>
            aſymptoto perpendicularibus intercepti; </s>
            <s xml:id="echoid-s5150" xml:space="preserve">ab altera elemen-
              <lb/>
            tum ſpatii curvilinei, quod itidem ad trapezium hyper-
              <lb/>
            bolicum reduci poſſet. </s>
            <s xml:id="echoid-s5151" xml:space="preserve">Quod apertius exponerem, niſi
              <lb/>
            relinquendam etiamnum aliis putarem inquirendi volupta-
              <lb/>
            tem. </s>
            <s xml:id="echoid-s5152" xml:space="preserve">Inde eo rem deducebam, ut trapezium ejuſmodi
              <lb/>
            hyperbolicum ſecandum eſſet aut augendum ſecundum ra-
              <lb/>
            tionem datam. </s>
            <s xml:id="echoid-s5153" xml:space="preserve">Quod cum per medias aut continue </s>
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