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

Table of contents

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[121.] II. DEMONSTRATIO REGULÆ DE MAXIMIS ET MINIMIS.
Page: 220 (490)
[122.] Tom. II. Qqq
Page: 224 (491)
[123.] III. REGULA Ad inveniendas Tangentes linearum curvarum.
Page: 231 (498)
[124.] Tom. II. Rrr
Page: 232 (499)
[125.] IV. CHRISTIANI HUGENII EPISTOLA DE CURVIS QUIBUSDAM PECULIARIBUS.
Page: 243 (507)
[126.] V. PROBLEMA AB ERUDITIS SOLVENDUM: A JOHANNE BERNOULLIO IN ACTIS LIPSIENSIBUS ANNI MDCXCIII. PROPOSITUM.
Page: 251 (515)
[127.] Tom. II. Ttt
Page: 251 (515)
[128.] VI. C. H. Z. DE PROBLEMATE BERNOULLIANO IN ACTIS LIPSIENSIBUS PROPOSITO.
Page: 252 (516)
[129.] VII. C. H. Z. CONSTRUCTIO UNIVERSALIS PROBLEMATIS A CLARISSIMO VIRO JOH. BERNOULLIO PROPOSITI.
Page: 254 (518)
[130.] FINIS.
Page: 256 (520)
[131.] CHRISTIANI HUGENII OPERA ASTRONOMICA. Tomus Tertius.
Page: 260
[132.] Tomi tertii contenta.
Page: 261
[133.] CHRISTIANI HUGENII DE SATURNILUNA OBSERVATIO NOVA. Tom. III. Ttt
Page: 262
[134.] CHRISTIANI HUGENII DE SATURNI LUNA OBSERVATIO NOVA.
Page: 264 (523)
[135.] Tom. III. Vvv.
Page: 264 (523)
[136.] CHRISTIANI HUGENII ZULICHEMII, CONST. F. SYSTEMA SATURNIUM, SIVE DE CAUSIS MIRANDORUM SATURNI PHÆNOMENON; ET COMITE EJUS PLANETA NOVO.
Page: 268
[137.] SERENISSIMO PRINCIPI LEOPOLDO AB HETRURIA Chriſtianus Hugenius S.D.
Page: 270 (529)
[138.] Tom. III. Xxx
Page: 272 (531)
[139.] NICOLAUS HEINSIUS, D. F. AD AUCTOREM SYSTEMATIS.
Page: 273 (532)
[140.] CHRISTIANI HUGENII Zulichemii, Cθnst. F. SYSTEMA SATURNIUM.
Page: 276 (535)
[141.] Tabul@ motus æqualis Lunæ Saturniæ in orbita ſua reſpectu fixarum.
Page: 299 (552)
[142.] In Menſibus anni @uli@-ni ineuntibus.
Page: 299 (552)
[143.] FINIS.
Page: 348 (595)
[144.] Eustachii De Divinis Septempedani BREVIS ANNOTATIO IN SYSTEMA SATURNIUM CHRISTIANI HUGENII. A D SERENISSIMUM PRINCIPEM LEOPOLDUM Magni Ducis HETRVRIÆ Fratrem.
Page: 350
[145.] Eustachii De Divinis Septempedani BREVIS ANNOTATIO IN SYSTEMA SATURNIUM CRISTIANI HUGENII. SERENISSIME PRINCEPS
Page: 352 (599)
[146.] FINIS.
Page: 371 (618)
[147.] Christiani Hugenii Zulichemii BREVIS ASSERTIO SYSTEMATIS SATURNII S U I, Ad Serenissimum Principem LEOPOLDUM AB HETRURIA.
Page: 372
[148.] Christiani Hugenii Zulichemii BREVIS ASSERTIO SYSTEMATIS SATURNII S U I, Ad Serenissimum Principem LEOPOLDUM AB HETRURIA. SERENISSIME PRINCEPS,
Page: 374 (621)
[149.] CHRISTIANI HUGENII DE SATURNI ANNULO OBSERVATIONES.
Page: 394
[150.] CHRISTIANI HUGENII DE SATURNI ANNULO OBSERVATIONES. I. Obſervationes in Saturnum Pariſiis habitæ in Bi-bliotheca Regia.
Page: 396 (637)
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            G H, nempe X; </s>
            <s xml:id="echoid-s3624" xml:space="preserve">atque ex hujus 7 terminatio ſeriei A B,
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            meticè continuè proportionalium inter A & </s>
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            <s xml:id="echoid-s3626" xml:space="preserve">ideo Z ea-
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          <head xml:id="echoid-head131" xml:space="preserve">PROP. XXV. THEOREMA.</head>
          <p>
            <s xml:id="echoid-s3628" xml:space="preserve">Iisdem poſitis; </s>
            <s xml:id="echoid-s3629" xml:space="preserve">dico Z ſeu ſectorem
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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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            hyperbolæ minorem eſſe quam mi-
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            nor duarum mediarum geometricè con-
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            tinuè proportionalium inter A & </s>
            <s xml:id="echoid-s3630" xml:space="preserve">B.
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            </s>
            <s xml:id="echoid-s3631" xml:space="preserve">Inter A & </s>
            <s xml:id="echoid-s3632" xml:space="preserve">B ſit media geometrica G,
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            & </s>
            <s xml:id="echoid-s3633" xml:space="preserve">inter G & </s>
            <s xml:id="echoid-s3634" xml:space="preserve">B media geometrica H; </s>
            <s xml:id="echoid-s3635" xml:space="preserve">
              <lb/>
            Item inter G & </s>
            <s xml:id="echoid-s3636" xml:space="preserve">H media geometrica M, & </s>
            <s xml:id="echoid-s3637" xml:space="preserve">inter M & </s>
            <s xml:id="echoid-s3638" xml:space="preserve">H media
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            geometriea N; </s>
            <s xml:id="echoid-s3639" xml:space="preserve">continueturque hæc ſeries convergens AB, GH,
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            MN, OP, &</s>
            <s xml:id="echoid-s3640" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3641" xml:space="preserve">in infinitum ut fiat ejus terminatio X. </s>
            <s xml:id="echoid-s3642" xml:space="preserve">ſatis patet
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            ex prædictis C & </s>
            <s xml:id="echoid-s3643" xml:space="preserve">G eſſe inter ſe æquales, & </s>
            <s xml:id="echoid-s3644" xml:space="preserve">H majorem eſſe
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            quam D; </s>
            <s xml:id="echoid-s3645" xml:space="preserve">atque ob hanc rationem M media geometrica inter G
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            & </s>
            <s xml:id="echoid-s3646" xml:space="preserve">H major eſt quam E media geometrica inter C & </s>
            <s xml:id="echoid-s3647" xml:space="preserve">D. </s>
            <s xml:id="echoid-s3648" xml:space="preserve">Deinde
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            N media geometrica inter M & </s>
            <s xml:id="echoid-s3649" xml:space="preserve">H major eſt media harmonica
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            inter eaſdem; </s>
            <s xml:id="echoid-s3650" xml:space="preserve">& </s>
            <s xml:id="echoid-s3651" xml:space="preserve">quoniam M major eſt quam E & </s>
            <s xml:id="echoid-s3652" xml:space="preserve">H quam D, erit
              <lb/>
            media harmonica inter M & </s>
            <s xml:id="echoid-s3653" xml:space="preserve">H major quam F media harmo-
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            nica inter E & </s>
            <s xml:id="echoid-s3654" xml:space="preserve">D; </s>
            <s xml:id="echoid-s3655" xml:space="preserve">proinde N media geometrica inter M & </s>
            <s xml:id="echoid-s3656" xml:space="preserve">H
              <lb/>
            major eritquam F. </s>
            <s xml:id="echoid-s3657" xml:space="preserve">eadem methodo utramque ſeriem in in-
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            finitum continuando, ſemper demonſtratur terminum quem-
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            libet ſeriei A B, C D, minorem eſſe quam idem numero ter-
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            minus ſeriei A B, G H; </s>
            <s xml:id="echoid-s3658" xml:space="preserve">& </s>
            <s xml:id="echoid-s3659" xml:space="preserve">igitur terminatio ſeriei A B, C D,
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            nempe Z minor erit quam terminatio ſeriei A B, G H, nem-
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            pe X; </s>
            <s xml:id="echoid-s3660" xml:space="preserve">atque ex hujus 9 terminatio ſeriei A B, G H, ſeu X, æqua-
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            lis eſt minori duarum mediarum geometricè continuè propor-
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            tionalium inter A & </s>
            <s xml:id="echoid-s3661" xml:space="preserve">B; </s>
            <s xml:id="echoid-s3662" xml:space="preserve">& </s>
            <s xml:id="echoid-s3663" xml:space="preserve">ideo Z eadem minor eſt, quod
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            demonſtrare oportuit.</s>
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            <s xml:id="echoid-s3665" xml:space="preserve">Ex dictis manifeſtum eſt hanc approximationem exactio-
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            rem eſſe illa, in antecedenti propoſitione, demonſtrata, et-
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            iamſi hæc ſit paulò laborioſior. </s>
            <s xml:id="echoid-s3666" xml:space="preserve">ſed non diſſimulandum
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            eſt duas poſſe eſſe ſeries æquales terminationes habentes, </s>
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