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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            gitudine minus diſtet quam partibus 85; </s>
            <s xml:id="echoid-s1954" xml:space="preserve">(Eſt enim arcus
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            A B, per ea quæ ſupra oſtendimus, major quam 7853981)
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            partes autem 85 efficiant minus quam duos ſcrupulos ſecun-
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            dos, hoc eſt, quam {2/1296600} circumferentiæ, nam tota earun-
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            dem plures habet quam 60000000: </s>
            <s xml:id="echoid-s1955" xml:space="preserve">Hinc manifeſtum eſt, ſi
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            trianguli rectanguli angulos quæramus ex datis lateribus, eo
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            modo quo majorem iſtum terminum paulò antè, nunquam
              <lb/>
            duobus ſcrupulis ſecundis aberraturos; </s>
            <s xml:id="echoid-s1956" xml:space="preserve">etiamſi æqualia inter
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            ſe fuerint latera circa angulum rectum, veluti hic erant in
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            triangulo D A M.</s>
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          <p>
            <s xml:id="echoid-s1958" xml:space="preserve">Si vero ea ſit ratio lateris D M ad M A, ut angulus A D M
              <lb/>
            non excedat {1/4} recti; </s>
            <s xml:id="echoid-s1959" xml:space="preserve">non unius tertii ſcrupuli error erit. </s>
            <s xml:id="echoid-s1960" xml:space="preserve">Po-
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            ſito enim arcu A B {1/16} circumferentiæ, erit A M ſemiſſis la-
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            teris octanguli æquilateri circulo inſcripti partium 382683433,
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            non unâ minus. </s>
            <s xml:id="echoid-s1961" xml:space="preserve">A B vero latus ſexdecanguli 390180644
              <lb/>
            non unâ amplius, qualium radius D B 1000000000. </s>
            <s xml:id="echoid-s1962" xml:space="preserve">Unde
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            primus minor terminus longitudinis arcus A B invenitur par-
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            tium 392679714. </s>
            <s xml:id="echoid-s1963" xml:space="preserve">Terminus autem major 392699148. </s>
            <s xml:id="echoid-s1964" xml:space="preserve">Et ex
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            his minor rurſus 392699010. </s>
            <s xml:id="echoid-s1965" xml:space="preserve">Conſtat autem ex ſupra demon-
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            ſtratis arcum A B {1/16} peripheriæ, majorem eſſe quam
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            392699081, quas terminus major ſuperat partibus 67. </s>
            <s xml:id="echoid-s1966" xml:space="preserve">Hæ
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            autem minus efficiunt uno ſcrupulo tertio, hoc eſt, {1/77760000} to-
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            tius circumferentiæ, quoniam ea major eſt utique quam
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            6000000000.</s>
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            <s xml:id="echoid-s1968" xml:space="preserve">Porro ex noviſſimis terminis inventis orietur ratio circum-
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            ferentiæ ad diametrum minor quam 3141593 {1/5}, major autem
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            quam 3141592 ad 1000000.</s>
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            <s xml:id="echoid-s1970" xml:space="preserve">Quod ſi {1/60} circumferentiæ ponatur arcus A B, ſeu par-
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            tium 6 qualium tota 360: </s>
            <s xml:id="echoid-s1971" xml:space="preserve">Erit A M ſemiſſis lateris trigin-
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            tanguli inſcripti partium 10452846326766, non unâ minus,
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            qualium radius 100000000000000. </s>
            <s xml:id="echoid-s1972" xml:space="preserve">Et A B latus ſexagintan-
              <lb/>
            guli inſcripti 10467191248588 non unâ amplius. </s>
            <s xml:id="echoid-s1973" xml:space="preserve">Invenietur-
              <lb/>
            que ex his arcus A B ſecundum primum minorem terminum
              <lb/>
            10471972889195. </s>
            <s xml:id="echoid-s1974" xml:space="preserve">Secundum majorem 10471975512584.
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            </s>
            <s xml:id="echoid-s1975" xml:space="preserve">Et ex his minor alter terminus 10471975511302. </s>
            <s xml:id="echoid-s1976" xml:space="preserve">Unde
              <lb/>
            efficitur peripheriæ ad diametrum ratio minor </s>
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