Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

Table of contents

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[91.] PROP. XXII. THEOREMA.
[92.] SCHOLIUM.
[93.] PROP. XXIII. THEOREMA.
[94.] PROP. XXIV. THEOREMA.
[95.] PROP. XXV. THEOREMA.
[96.] PROP. XXVI. THEOREMA.
[97.] PROP. XXVII. THEOREMA.
[98.] PROP. XXVIII. THEOREMA.
[99.] PROP. XXIX. PROBLEMA. Dato circulo æquale invenire quadratum.
[100.] PROP. XXX. PROBLEMA. Ex dato ſinu invenire arcum.
[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.
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            metricum inter parallelogramma P D M L, F D M K, quod de-
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            monſtrare oportuit.</s>
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        <div xml:id="echoid-div203" type="section" level="1" n="98">
          <head xml:id="echoid-head134" xml:space="preserve">PROP. XXVIII. THEOREMA.</head>
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            <s xml:id="echoid-s3715" xml:space="preserve">Iisdem poſitis ducantur rectæ F E, L E, hyperbolam tan-
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              <note position="left" xlink:label="note-0164-01" xlink:href="note-0164-01a" xml:space="preserve">TAB. XLIII.
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              fig. 4.</note>
            gentes in punctis F, L, ut compleatur trapezium A F E L,
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            quod dico eſſe medium harmonicum inter parallelogramma
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            P D M L, F D M K. </s>
            <s xml:id="echoid-s3716" xml:space="preserve">triangulum A F L, trapezium A F G L,
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            & </s>
            <s xml:id="echoid-s3717" xml:space="preserve">medium harmonicum inter parallelogramma P D M L,
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            F D M K, ſunt continuè proportionalia, quoniam triangu-
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            lum A F L eſt medium arithmeticum & </s>
            <s xml:id="echoid-s3718" xml:space="preserve">trapezium A F G L
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            medium geometricum inter eadem parallelogramma, ut pa-
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            tet ex hujus 13; </s>
            <s xml:id="echoid-s3719" xml:space="preserve">ſed triangulum A F L, trapezium A F G L,
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            & </s>
            <s xml:id="echoid-s3720" xml:space="preserve">trapezium A F E L ſunt continuè proportionalia ex hujus
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            1; </s>
            <s xml:id="echoid-s3721" xml:space="preserve">& </s>
            <s xml:id="echoid-s3722" xml:space="preserve">proinde trapezium A F E L eſt medium harmonicum
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            inter parallelogramma P D M L, F D M K, quod demon-
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            ftrare oportuit.</s>
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          <head xml:id="echoid-head135" xml:space="preserve">PROP. XXIX. PROBLEMA.
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          Dato circulo æquale invenire quadratum.</head>
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            <s xml:id="echoid-s3724" xml:space="preserve">Sit quadratum circulo circumſcriptum 4000000000000000;
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            </s>
            <s xml:id="echoid-s3725" xml:space="preserve">erit ergo eidem inſcriptum 2000000000000000, inter quæ
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            quadrata ſit medium geometricum 2828427124746190
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            octagonum nempe intra circulum: </s>
            <s xml:id="echoid-s3726" xml:space="preserve">deinde inter octago-
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            num intra circulum & </s>
            <s xml:id="echoid-s3727" xml:space="preserve">quadratum extra ſit medium har-
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            monicum, quod levi labore invenitur dividendoduplum
              <lb/>
            quadrati octagoni intra circulum ſeu duplum rectanguli à
              <lb/>
            quadratis intra & </s>
            <s xml:id="echoid-s3728" xml:space="preserve">extra circulum per ſummam quadrati & </s>
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            octagoni intra; </s>
            <s xml:id="echoid-s3730" xml:space="preserve">eritque inventum medium harmonicum, octa-
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            gonum circumſcriptum, nempe 3313708498984760. </s>
            <s xml:id="echoid-s3731" xml:space="preserve">conti-
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            nuetur hæc ſeries convergens polygonorum complicatorum
              <lb/>
            donec prima medietas notarum ſit eadem in utroque </s>
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