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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          <p>
            <s xml:id="echoid-s1976" xml:space="preserve">
              <pb o="387" file="0101" n="108" rhead="DE CIRCULI MAGNIT. INVENTA."/>
            31415926538, major autem quam 31415926533 ad
              <lb/>
            10000000000.</s>
            <s xml:id="echoid-s1977" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1978" xml:space="preserve">Quos terminos ſi ex additis inſcriptorum & </s>
            <s xml:id="echoid-s1979" xml:space="preserve">circumſcripto-
              <lb/>
            rum polygonorum lateribus inquirendum eſſet ferè ad late-
              <lb/>
            rum quadringenta millia deveniendum. </s>
            <s xml:id="echoid-s1980" xml:space="preserve">Nam ex ſexagintan-
              <lb/>
            gulo inſcripto circumſcriptoque hoc tantum probatur, mi-
              <lb/>
            norem eſſe rationem peripheriæ ad diametrum quam 3145 ad
              <lb/>
            1000, majorem autem quam 3140. </s>
            <s xml:id="echoid-s1981" xml:space="preserve">Adeo ut triplum & </s>
            <s xml:id="echoid-s1982" xml:space="preserve">am-
              <lb/>
            plius verarum notarum numerum noſtro ratiocinio produ-
              <lb/>
            ctum appareat. </s>
            <s xml:id="echoid-s1983" xml:space="preserve">Idem vero in ulterioribus polygonis ſi quis
              <lb/>
            experiatur ſemper evenire cernet: </s>
            <s xml:id="echoid-s1984" xml:space="preserve">non ignota nobis ratione,
              <lb/>
            ſed quæ longiori explicatione indigeret.</s>
            <s xml:id="echoid-s1985" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1986" xml:space="preserve">Porro autem quomodo, datis quibuſcunque aliis inſcriptis,
              <lb/>
            arcuum quibus ſubtenduntur longitudo per hæc inveniri que-
              <lb/>
            at ſatis puto manifeſtum. </s>
            <s xml:id="echoid-s1987" xml:space="preserve">Si enim quadrati inſcripti latere
              <lb/>
            majores ſunt, longitudo arcus ad ſemicircumferentiam reli-
              <lb/>
            qui inquirenda eſt, cujus tum quoque ſubtenſa datur. </s>
            <s xml:id="echoid-s1988" xml:space="preserve">Sci-
              <lb/>
            endum autem & </s>
            <s xml:id="echoid-s1989" xml:space="preserve">dimidiorum arcuum ſubtenſas inveniri cum
              <lb/>
            totius arcus ſubtenſa data eſt. </s>
            <s xml:id="echoid-s1990" xml:space="preserve">Atque hâc ratione ſi biſectioni-
              <lb/>
            bus uti placebit, poterimus ad omnem ſubtenſam, arcus i-
              <lb/>
            pſius longitudinem quamlibet veræ propinquam non difficul-
              <lb/>
            ter cognoſcere. </s>
            <s xml:id="echoid-s1991" xml:space="preserve">Utile hoc ad ſinuum tabulas examinandas.
              <lb/>
            </s>
            <s xml:id="echoid-s1992" xml:space="preserve">Imo ad componendas quoque: </s>
            <s xml:id="echoid-s1993" xml:space="preserve">quia cognitâ arcus alicujus
              <lb/>
            ſubtenſâ, etiam ejus qui paulò major minorve ſit ſatis accu-
              <lb/>
            ratè definiri poteſt.</s>
            <s xml:id="echoid-s1994" xml:space="preserve"/>
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