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="489" file="0209" n="219" rhead="GEOMET. VARIA."/>
            que {{1/4}ggoo/pp}, invenitur y = l - {nx/z} + √- mm + ox + {ppxx/gg}
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            Eademque eſt demonſtrandi ratio in caſu quarto, & </s>
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              <note position="right" xlink:label="note-0209-01" xlink:href="note-0209-01a" xml:space="preserve">fig. 7.</note>
            quibusvis, habita ratione ſignorum + & </s>
            <s xml:id="echoid-s4590" xml:space="preserve">-.</s>
            <s xml:id="echoid-s4591" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4592" xml:space="preserve">Cum non habetur {nx/z} in æquatione, puncta M & </s>
            <s xml:id="echoid-s4593" xml:space="preserve">V unum
              <lb/>
            ſunt, tunc vero ſi p = g, hoc eſt ſi habeatur + xx pro
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            {ppxx/gg}, erunt ſemper aſymptoti ſibi mutuò ad angulos rectos,
              <lb/>
            quia ut p ad g, ita fecimus {1/2}o ad I X & </s>
            <s xml:id="echoid-s4594" xml:space="preserve">ad I Y, & </s>
            <s xml:id="echoid-s4595" xml:space="preserve">ita IX
              <lb/>
            ad I V; </s>
            <s xml:id="echoid-s4596" xml:space="preserve">fiunt enim jam æquales I X, I Y, I V, & </s>
            <s xml:id="echoid-s4597" xml:space="preserve">ſingulæ =
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            {1/2}o, unde punctum V eſt in ſemicirculo ſuper X Y & </s>
            <s xml:id="echoid-s4598" xml:space="preserve">proin-
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            de angulus X V Y rectus. </s>
            <s xml:id="echoid-s4599" xml:space="preserve">Item quia I M = {{1/2}aogg/zpp}, patet
              <lb/>
            quod ſi ag = zp, hoc eſt ſi g ad p ut z ad a, tunc erit
              <lb/>
            I M = {{1/2}og/p}, ac proinde æqualis ipſi IX & </s>
            <s xml:id="echoid-s4600" xml:space="preserve">IY quæ etiam erant
              <lb/>
            {{1/2}og/p}. </s>
            <s xml:id="echoid-s4601" xml:space="preserve">Adeoque hoc caſu erunt aſymptoti ſibi mutuo ad angu-
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            los rectos; </s>
            <s xml:id="echoid-s4602" xml:space="preserve">cum rurſus punctum M ſit futurum in circumfe-
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            rentia circuli deſcripti ſuper X Y centro I.</s>
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