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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              <pb o="401" file="0117" n="125" rhead="ILLUST. QUORUND. PROB. CONSTRUCT."/>
            gulus B S T ipſi E A F æqualis eſt trianguluſque B S T æ-
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            quicruris.</s>
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          <p>
            <s xml:id="echoid-s2506" xml:space="preserve">Porrò quod C D ipſi K æqualis eſt, ſic demonſtrabitur.
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            </s>
            <s xml:id="echoid-s2507" xml:space="preserve">Quia quadratum A G æquale eſt quadratis ex K & </s>
            <s xml:id="echoid-s2508" xml:space="preserve">A B: </s>
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            idemque quadratum A G æquale quadratis A B, B G cum
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            duplo rectangulo G B L. </s>
            <s xml:id="echoid-s2510" xml:space="preserve">Erit propterea quadratum K æ-
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            quale quadrato B G cum duplo rectangulo G B L. </s>
            <s xml:id="echoid-s2511" xml:space="preserve">Sicut
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            autem B G ad B E ita eſt quadratum B G cum duplo re-
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            ctangulo G B L ad rectangulum G B E cum duplo rectan-
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            ctulo E B L; </s>
            <s xml:id="echoid-s2512" xml:space="preserve">ſingula enim ad ſingula eam habent rationem. </s>
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            Ergo & </s>
            <s xml:id="echoid-s2514" xml:space="preserve">quadratum K ad rectangulum G B E cum duplo re-
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            ctangulo E B L ut B G ad B E. </s>
            <s xml:id="echoid-s2515" xml:space="preserve">Eſt autem rectangulo G B E
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            æquale rectangulum C B D, quoniam C B ad B G ut E B
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            ad B D, propter triangulos ſimiles C B G, E B D; </s>
            <s xml:id="echoid-s2516" xml:space="preserve">habent
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            enim angulos ad B æquales & </s>
            <s xml:id="echoid-s2517" xml:space="preserve">angulum B C G angulo B E D. </s>
            <s xml:id="echoid-s2518" xml:space="preserve">
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            Item duplo rectangulo E B L æquale eſt quadratum A B,
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            quia propter triangulos ſimiles ut S A, hoc eſt, dupla B E
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            ad A B ita A B ad B L. </s>
            <s xml:id="echoid-s2519" xml:space="preserve">Igitur ut B G ad B E ita erit
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            quadratum K ad rectangulum C B D cum quadrato A B. </s>
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            Sed hiſce duobus æquale eſt rectangulum C A D; </s>
            <s xml:id="echoid-s2521" xml:space="preserve">quoniam
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            in triangulo C A D angulus A bifariam dividitur à linea A B. </s>
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            Ergo ut B G ad B E ita eſt quadr. </s>
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            Atque hinc porrò eodem modo ut in caſu præcedenti con-
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            cludemus lineam D C ipſi K æqualem eſſe, repetendo iſta: </s>
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            Sicut autem G B ad B E, &</s>
            <s xml:id="echoid-s2526" xml:space="preserve">c.</s>
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          <head xml:id="echoid-head86" style="it" xml:space="preserve">Utrumque præcedentium Aliter.</head>
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            <s xml:id="echoid-s2528" xml:space="preserve">SIt datus rhombus A D B C cujus productum latus
              <lb/>
              <note position="right" xlink:label="note-0117-01" xlink:href="note-0117-01a" xml:space="preserve">TAB. XLII.
                <lb/>
              Fig. 3.</note>
            D B. </s>
            <s xml:id="echoid-s2529" xml:space="preserve">Et data ſit linea G. </s>
            <s xml:id="echoid-s2530" xml:space="preserve">Oportet ducere rectam A N F,
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            ut pars intercepta N F ſit datæ G æqualis.</s>
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            <s xml:id="echoid-s2532" xml:space="preserve">Ducatur diameter A B, & </s>
            <s xml:id="echoid-s2533" xml:space="preserve">quadratis ex G & </s>
            <s xml:id="echoid-s2534" xml:space="preserve">A B ſit æ-
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            quale quadratum A H, & </s>
            <s xml:id="echoid-s2535" xml:space="preserve">ducatur H E ipſi B A parallela.
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            </s>
            <s xml:id="echoid-s2536" xml:space="preserve">Et A E ipſi G ponatur æqualis, eademque producatur ad
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            F. </s>
            <s xml:id="echoid-s2537" xml:space="preserve">Dico N F ipſi G æqualem eſſe.</s>
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          <p>
            <s xml:id="echoid-s2539" xml:space="preserve">Quod autem ad H E poni poteſt A E ipſi G </s>
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