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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            C, G; </s>
            <s xml:id="echoid-s3575" xml:space="preserve">& </s>
            <s xml:id="echoid-s3576" xml:space="preserve">ideo terminatio ſeriei A, C, E, nempe Z, major
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            erit terminatione ſeriei A, C, G, nempè X; </s>
            <s xml:id="echoid-s3577" xml:space="preserve">at ex Archime-
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            dis quadratura parabolæ conſtat X æqualem eſſe ipſi C dem-
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            pto triente exceſſus A ſupra C, & </s>
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            eſt, quod demonſtrare oportuit.</s>
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          <head xml:id="echoid-head130" xml:space="preserve">PROP. XXIV. THEOREMA.</head>
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            <s xml:id="echoid-s3580" xml:space="preserve">IIsdem poſitis; </s>
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              A B # A B
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              C D # G H
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              E F # M N
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              K L # O P
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              Z # X
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            ctorem hyperbolæ minorem eſ-
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            ſe quam minor duarum mediarum
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            arithmeticè continuè proportio-
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            nalium inter A & </s>
            <s xml:id="echoid-s3582" xml:space="preserve">B. </s>
            <s xml:id="echoid-s3583" xml:space="preserve">Inter A & </s>
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            B ſit media arithmetica G, & </s>
            <s xml:id="echoid-s3585" xml:space="preserve">in-
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            ter G & </s>
            <s xml:id="echoid-s3586" xml:space="preserve">B ſit media Arithmetica
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            H, Item inter G & </s>
            <s xml:id="echoid-s3587" xml:space="preserve">H ſit media Arithmetica M, & </s>
            <s xml:id="echoid-s3588" xml:space="preserve">inter M
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            & </s>
            <s xml:id="echoid-s3589" xml:space="preserve">H ſit media Arithmetica N: </s>
            <s xml:id="echoid-s3590" xml:space="preserve">continueturque hæc ſeries con-
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            vergens A B, G H, M N, O P, in infinitum, ut fiat ejus termi-
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            natio X. </s>
            <s xml:id="echoid-s3591" xml:space="preserve">ſatis patet ex prædictis G majorem eſſe quam C;
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            <s xml:id="echoid-s3592" xml:space="preserve">atque H media arithmetica inter G & </s>
            <s xml:id="echoid-s3593" xml:space="preserve">B major eſt media har-
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            monica inter easdem G & </s>
            <s xml:id="echoid-s3594" xml:space="preserve">B; </s>
            <s xml:id="echoid-s3595" xml:space="preserve">media autem harmonica inter
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            G & </s>
            <s xml:id="echoid-s3596" xml:space="preserve">B; </s>
            <s xml:id="echoid-s3597" xml:space="preserve">major eſt media harmonica inter C & </s>
            <s xml:id="echoid-s3598" xml:space="preserve">B, nempe D, quo-
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            niam G major eſt quam C; </s>
            <s xml:id="echoid-s3599" xml:space="preserve">& </s>
            <s xml:id="echoid-s3600" xml:space="preserve">ideo media Arithmetica inter G
              <lb/>
            & </s>
            <s xml:id="echoid-s3601" xml:space="preserve">B nempe H major eſt quam D media harmonica inter C & </s>
            <s xml:id="echoid-s3602" xml:space="preserve">B
              <lb/>
            eodem modo M media Arithmetica inter G & </s>
            <s xml:id="echoid-s3603" xml:space="preserve">H major eſt me-
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            dia geometrica inter eaſdem G & </s>
            <s xml:id="echoid-s3604" xml:space="preserve">H; </s>
            <s xml:id="echoid-s3605" xml:space="preserve">& </s>
            <s xml:id="echoid-s3606" xml:space="preserve">quoniam G eſt ma-
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            jor quam C & </s>
            <s xml:id="echoid-s3607" xml:space="preserve">H quam D, media geometrica inter G & </s>
            <s xml:id="echoid-s3608" xml:space="preserve">H
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            major eſt quam E media geometrica inter C & </s>
            <s xml:id="echoid-s3609" xml:space="preserve">D; </s>
            <s xml:id="echoid-s3610" xml:space="preserve">& </s>
            <s xml:id="echoid-s3611" xml:space="preserve">proin-
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            de M major eſt quam E. </s>
            <s xml:id="echoid-s3612" xml:space="preserve">Deinde N media Arithmetica in-
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            ter M & </s>
            <s xml:id="echoid-s3613" xml:space="preserve">H major eſt media harmonica inter easdem; </s>
            <s xml:id="echoid-s3614" xml:space="preserve">& </s>
            <s xml:id="echoid-s3615" xml:space="preserve">quo-
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            inter M & </s>
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            D; </s>
            <s xml:id="echoid-s3619" xml:space="preserve">& </s>
            <s xml:id="echoid-s3620" xml:space="preserve">ideo N eadem F major eſt. </s>
            <s xml:id="echoid-s3621" xml:space="preserve">eodem modo utramque
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            minum quemlibet ſeriei A B, C D, minorem eſſe quam idem
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            numero terminum ſeriei A B, G H; </s>
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            riei A B, C D, nempe Z, minor erit terminatione ſeriei A </s>
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