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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        <div xml:id="echoid-div240" type="section" level="1" n="119">
          <head xml:id="echoid-head164" xml:space="preserve">I.
            <lb/>
          CONSTRUCTIO LOCI
            <lb/>
          AD HYPERBOLAM
            <lb/>
          PER ASYMPTOTOS.</head>
          <p>
            <s xml:id="echoid-s4504" xml:space="preserve">In æquatione loci ad hyperbolam, ſi neutra indeter-
              <lb/>
              <note position="right" xlink:label="note-0205-01" xlink:href="note-0205-01a" xml:space="preserve">TAB. XLIV.
                <lb/>
              fig. 4. 5. 6. 7.</note>
            minatarum linearum in ſeipſam ducta inveniatur,
              <lb/>
            velut ſi ſit xy = bb; </s>
            <s xml:id="echoid-s4505" xml:space="preserve">vel xy = cx. </s>
            <s xml:id="echoid-s4506" xml:space="preserve">bb; </s>
            <s xml:id="echoid-s4507" xml:space="preserve">(literis x & </s>
            <s xml:id="echoid-s4508" xml:space="preserve">y
              <lb/>
            lineas indeterminatas A B, B C ſignificantibus,
              <lb/>
            quæ in dato angulo ſibi mutuò ſint applicatæ, quarumque al-
              <lb/>
            tera, ut A B, poſitione data intelligitur, & </s>
            <s xml:id="echoid-s4509" xml:space="preserve">in ea datum pun-
              <lb/>
            ctum A) conſtructio per aſymptotorum inventionem facilè
              <lb/>
            abſolvitur, ut oſtenſum eſt à Fl. </s>
            <s xml:id="echoid-s4510" xml:space="preserve">de Beaune in Notis ad Geo-
              <lb/>
            metriam Carteſii. </s>
            <s xml:id="echoid-s4511" xml:space="preserve">Cum verò habetur x x vel y y in æquatio-
              <lb/>
            ne, vel utrumque nihilominus ad aſymptotos rem deduci
              <lb/>
            poſſe, & </s>
            <s xml:id="echoid-s4512" xml:space="preserve">quidem brevius quàm ad diametri laterumque re-
              <lb/>
            cti & </s>
            <s xml:id="echoid-s4513" xml:space="preserve">transverſi inventionem, oſtendemus hoc modo.</s>
            <s xml:id="echoid-s4514" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4515" xml:space="preserve">Sit æquatio ejuſmodi reducta, y = l. </s>
            <s xml:id="echoid-s4516" xml:space="preserve">{nx/z} √mm.</s>
            <s xml:id="echoid-s4517" xml:space="preserve">ox + {ppxx;</s>
            <s xml:id="echoid-s4518" xml:space="preserve">/gg}
              <lb/>
            ſemper enim ad hos terminos reduci poteſt, nempe ut y al-
              <lb/>
            tera linearum indeterminatarum, quæ applicata eſt ad poſi-
              <lb/>
            tionem datam, ſola ab una parte æquationis habeatur, ab alte-
              <lb/>
            ra verò non plures termini quàm hîc inveniantur; </s>
            <s xml:id="echoid-s4519" xml:space="preserve">nam ſæ-
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            pe pauciores etiam eſſe poſſunt, cum ſoli neceſſarii ſint
              <lb/>
            + {ppxx/gg} cum alterutro horum mm vel ox.</s>
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          <p>
            <s xml:id="echoid-s4521" xml:space="preserve">Quum angulus A B C datus ſit, ducatur per A punctum
              <lb/>
            linea X Y quæ ſit rectæ B C parallela, & </s>
            <s xml:id="echoid-s4522" xml:space="preserve">in ea accipiatur AI
              <lb/>
            æqualis l, idque ad partes B C, ſi habeatur + l in æquatio-
              <lb/>
            ne, in contrarias verò ſi habeatur — l, & </s>
            <s xml:id="echoid-s4523" xml:space="preserve">agatur I K </s>
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