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

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[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.
[131.] CHRISTIANI HUGENII OPERA ASTRONOMICA. Tomus Tertius.
[132.] Tomi tertii contenta.
[133.] CHRISTIANI HUGENII DE SATURNILUNA OBSERVATIO NOVA. Tom. III. Ttt
[134.] CHRISTIANI HUGENII DE SATURNI LUNA OBSERVATIO NOVA.
[135.] Tom. III. Vvv.
[136.] CHRISTIANI HUGENII ZULICHEMII, CONST. F. SYSTEMA SATURNIUM, SIVE DE CAUSIS MIRANDORUM SATURNI PHÆNOMENON; ET COMITE EJUS PLANETA NOVO.
[137.] SERENISSIMO PRINCIPI LEOPOLDO AB HETRURIA Chriſtianus Hugenius S.D.
[138.] Tom. III. Xxx
[139.] NICOLAUS HEINSIUS, D. F. AD AUCTOREM SYSTEMATIS.
[140.] CHRISTIANI HUGENII Zulichemii, Cθnst. F. SYSTEMA SATURNIUM.
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            jecta eſt linea C F, erit rectangulum A F C cum quadrato
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            E C æquale quadrato E F. </s>
            <s xml:id="echoid-s2205" xml:space="preserve">Quadratum autem E F æquale
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            eſt quadrato E G. </s>
            <s xml:id="echoid-s2206" xml:space="preserve">Erit igitur rectangulum A F C cum qua-
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            drato C E, æquale rectangulo A G B cum quadrato B E.
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            </s>
            <s xml:id="echoid-s2207" xml:space="preserve">Atqui quadratum C E ſeu E A æquale eſt quadrato E B. </s>
            <s xml:id="echoid-s2208" xml:space="preserve">
              <lb/>
            Ergo & </s>
            <s xml:id="echoid-s2209" xml:space="preserve">reliquum rectangulum A F C æquale rectangulo
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            A G B. </s>
            <s xml:id="echoid-s2210" xml:space="preserve">Quare ſicut F A ad A G ita B G ad C F. </s>
            <s xml:id="echoid-s2211" xml:space="preserve">Ut au-
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            tem F A ad A G ita eſt D B ad B G, & </s>
            <s xml:id="echoid-s2212" xml:space="preserve">ita quoque F C ad
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            C D. </s>
            <s xml:id="echoid-s2213" xml:space="preserve">Igitur ut D B, hoc eſt, A C ad B G ita B G ad
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            F C, & </s>
            <s xml:id="echoid-s2214" xml:space="preserve">F C ad C D, hoc eſt, A B. </s>
            <s xml:id="echoid-s2215" xml:space="preserve">Quod erat dem. </s>
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            Quod autem dictum eſt, etiam deſcriptâ hyperbole inveni-
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            ri quomodo linea F D G ducenda ſit, hinc conſtabit: </s>
            <s xml:id="echoid-s2217" xml:space="preserve">Fa-
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            ctum enim ſit, ut E F, E G ſint æquales, & </s>
            <s xml:id="echoid-s2218" xml:space="preserve">ſumatur G N
              <lb/>
            æqualis D F. </s>
            <s xml:id="echoid-s2219" xml:space="preserve">Itaque punctum N eſt ad hyperbolem quæ
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            deſcribetur per D punctum circa aſymptotos F A, A G .</s>
            <s xml:id="echoid-s2220" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0108-01" xlink:href="note-0108-01a" xml:space="preserve">8. 2. Conic.</note>
            Sed idem punctum N eſt quoque ad circuli circumferentiam
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            cujus centrum E radius E D: </s>
            <s xml:id="echoid-s2221" xml:space="preserve">(Hoc enim facile intelligitur
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            quia triangulus F E G eſt æquicruris, & </s>
            <s xml:id="echoid-s2222" xml:space="preserve">N G æqualis D F)
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            Itaque datum eſt punctum N ad interſectionem hyperboles
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            & </s>
            <s xml:id="echoid-s2223" xml:space="preserve">circumferentiæ dictæ. </s>
            <s xml:id="echoid-s2224" xml:space="preserve">Sed & </s>
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            <s xml:id="echoid-s2226" xml:space="preserve">Datur igitur
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            poſitione linea F G ducenda per puncta N, D. </s>
            <s xml:id="echoid-s2227" xml:space="preserve">Et compo-
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            ſitio manifeſta eſt.</s>
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          <head xml:id="echoid-head80" xml:space="preserve">ALITER.</head>
          <p>
            <s xml:id="echoid-s2229" xml:space="preserve">CIrca diametrum A C majori datarum linearum æqualem
              <lb/>
              <note position="left" xlink:label="note-0108-02" xlink:href="note-0108-02a" xml:space="preserve">TAB. XLI.
                <lb/>
              Fig. 5.</note>
            circulus deſcribatur & </s>
            <s xml:id="echoid-s2230" xml:space="preserve">ponatur A B minori datarum æqua-
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            lis, & </s>
            <s xml:id="echoid-s2231" xml:space="preserve">perficiatur parallelogrammum A D: </s>
            <s xml:id="echoid-s2232" xml:space="preserve">productâque A B,
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            ducatur ex centro E recta E H G eâ ratione ut H D, H G
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            ſint inter ſe æquales. </s>
            <s xml:id="echoid-s2233" xml:space="preserve">Secet autem circumferentiam in L.
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            </s>
            <s xml:id="echoid-s2234" xml:space="preserve">Dico duabus A C, A B duas medias inventas eſſe B G,
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            G L.</s>
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            <s xml:id="echoid-s2236" xml:space="preserve">Producatur enim G E uſque ad circumferentiam in K, & </s>
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            jungatur A K, eique parrallela ducatur B O. </s>
            <s xml:id="echoid-s2238" xml:space="preserve">Similes ita-
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            que ſunt trianguli A E K, B H O; </s>
            <s xml:id="echoid-s2239" xml:space="preserve">& </s>
            <s xml:id="echoid-s2240" xml:space="preserve">quia A E æqualis
              <lb/>
            E K, etiam B H, H O æquales erunt. </s>
            <s xml:id="echoid-s2241" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s2242" xml:space="preserve">H G, H D
              <lb/>
            inter ſe æquales ſunt. </s>
            <s xml:id="echoid-s2243" xml:space="preserve">Igitur tota O G æqualis B D, </s>
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