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

Table of contents

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[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)
[151.] II. Excerpta ex literis D. Hugenii, Academiæ regiæ ſcien-tiarum ſocii, ad auctorem Diarii Eruditorum de figura Planetæ Saturni.
Page: 397 (638)
[152.] FINIS.
Page: 399 (640)
[153.] CHRISTIANI HUGENII ΚΟΣΜΟΘΕΩΡΟΣ, SIVE De Terris Cœleſtibus, earumque ornatu, CONJECTURÆ AD CONTANTINUM HUGENIUM, Fratrem: CULIELMO III. MAGNÆ BRITANNIÆ REGI, A SECRETIS.
Page: 400
[154.] Horat. Epiſt. 6. lib. 1.
Page: 401
[155.] BENEVOLO LECTORI SALUTEM.
Page: 402 (643)
[156.] CHRISTIANI HUGENII COSMOTHEOROS, SIVE De Terris Cœleſtibus, earumque ornatu, Conjecturæ. AD CONSTANTINUM HUGENIUM, Fratrem. LIBER I.
Page: 404 (645)
[157.] CHRISTIANI HUGENII COSMOTHEOROS, SIVE De Terris Cœleſtibus, earumque ornatu, Conjecturæ. AD CONSTANTINUM HUGENIUM, Fratrem. LIBER II.
Page: 450 (691)
[158.] FINIS.
Page: 486 (722)
[159.] CHRISTIANI HUGENII OPERA MISCELLANEA. Tomus Quartus.
Page: 487
[160.] Tomi quarti contenta.
Page: 488
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              <pb o="429" file="0147" n="156" rhead="ET HYPERBOLÆ QUADRATURA."/>
            omnes ſeriei convergentis terminationem eodem modo eſſe
              <lb/>
            compoſitam ex terminis convergentibus primis quo ex termi-
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            nis convergentibus ſecundis, tertiis, vel quartis, &</s>
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            <s xml:id="echoid-s3152" xml:space="preserve"/>
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        <div xml:id="echoid-div166" type="section" level="1" n="78">
          <head xml:id="echoid-head114" xml:space="preserve">PROP. XI. THEOREMA.</head>
          <p style="it">
            <s xml:id="echoid-s3153" xml:space="preserve">Dico ſectorem circuli, ellipſeos vel hyperbolæ A B I P
              <lb/>
              <note position="right" xlink:label="note-0147-01" xlink:href="note-0147-01a" xml:space="preserve">TAB. XLIII.
                <lb/>
              Fig. 1. 2. 3.</note>
            non eſſe compoſitum analyticè à triangulo
              <lb/>
            A B P & </s>
            <s xml:id="echoid-s3154" xml:space="preserve">trapezio A B F P.</s>
            <s xml:id="echoid-s3155" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3156" xml:space="preserve">Ponatur triangulum A B P
              <emph style="super">a</emph>
            & </s>
            <s xml:id="echoid-s3157" xml:space="preserve">trapezium A B F P
              <emph style="super">b</emph>
            : </s>
            <s xml:id="echoid-s3158" xml:space="preserve">ma-
              <lb/>
            nifeſtum eſt ex prædictis trapezium A B I P eſſe Vqab & </s>
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              <lb/>
            polygonum A B D L P {2 ab/a + Vqab}, item ſectorem A B I P eſſe
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            hujus ſeriei convergentis terminationem. </s>
            <s xml:id="echoid-s3160" xml:space="preserve">ut ex ſeriei termi-
              <lb/>
            nis auferantur ſigna radicis & </s>
            <s xml:id="echoid-s3161" xml:space="preserve">fractionis, pro
              <emph style="super">a</emph>
            & </s>
            <s xml:id="echoid-s3162" xml:space="preserve">
              <emph style="super">b</emph>
            primis
              <lb/>
            ſeriei terminis convergentibus, hoc eſt pro triangulo A B P
              <lb/>
            & </s>
            <s xml:id="echoid-s3163" xml:space="preserve">trapezio A B F P ponantur a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b & </s>
            <s xml:id="echoid-s3164" xml:space="preserve">ab
              <emph style="super">2</emph>
            + b
              <emph style="super">3</emph>
            ; </s>
            <s xml:id="echoid-s3165" xml:space="preserve">erunt-
              <lb/>
            que ſecundi ſeriei termini convergentes, hoc eſt trapezium
              <lb/>
            A B I P & </s>
            <s xml:id="echoid-s3166" xml:space="preserve">polygonum A B D L P, ba
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            a & </s>
            <s xml:id="echoid-s3167" xml:space="preserve">2 b
              <emph style="super">2</emph>
            a, di-
              <lb/>
            co ſeriei convergentis (cujus primi termini convergentes ſunt
              <lb/>
            a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b, ab
              <emph style="super">2</emph>
            + b
              <emph style="super">3</emph>
            & </s>
            <s xml:id="echoid-s3168" xml:space="preserve">ſecundi ſunt ba
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            a, 2 b
              <emph style="super">2</emph>
            a) termina-
              <lb/>
            tionem non eſſe compoſitam analyticè a terminis a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b,
              <lb/>
            ab
              <emph style="super">2</emph>
            + b
              <emph style="super">3</emph>
            : </s>
            <s xml:id="echoid-s3169" xml:space="preserve">ſi enim componatur prædicta terminatio analyticè a
              <lb/>
            terminis convergentibus a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b, ab
              <emph style="super">2</emph>
            + b
              <emph style="super">3</emph>
            ; </s>
            <s xml:id="echoid-s3170" xml:space="preserve">componetur etiam
              <lb/>
            eadem terminatio analyticè & </s>
            <s xml:id="echoid-s3171" xml:space="preserve">eodem omnino modo à termi-
              <lb/>
            nis convergentibus ba
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            a, 2b
              <emph style="super">2</emph>
            a; </s>
            <s xml:id="echoid-s3172" xml:space="preserve">& </s>
            <s xml:id="echoid-s3173" xml:space="preserve">proinde eadem quan-
              <lb/>
            titas, nempe prædicta terminatio, eodem modo componitur
              <lb/>
            analyticè ex terminis a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b, ab
              <emph style="super">2</emph>
            + b
              <emph style="super">3</emph>
            , quo componitur ex
              <lb/>
            terminis ba
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            a, 2b
              <emph style="super">2</emph>
            a,
              <lb/>
              <note position="right" xlink:label="note-0147-02" xlink:href="note-0147-02a" xml:space="preserve">
                <lb/>
              a
                <emph style="super">3</emph>
              + a
                <emph style="super">2</emph>
              b # ab
                <emph style="super">2</emph>
              + b
                <emph style="super">3</emph>
              .
                <lb/>
              ba
                <emph style="super">2</emph>
              + b
                <emph style="super">2</emph>
              a # 2b
                <emph style="super">2</emph>
              a
                <lb/>
              </note>
            ſed nulla quantitas poteſt
              <lb/>
            eodem modo analyticè com-
              <lb/>
            poni ex terminis a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b,
              <lb/>
            ab
              <emph style="super">2</emph>
            + b
              <emph style="super">3</emph>
            , quo componitur
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            ex terminis ba
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            a, 2b
              <emph style="super">2</emph>
            a, quod ſic demonſtro. </s>
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            ticè componeretur quantitas ex terminis a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b, ab
              <emph style="super">2</emph>
            + b
              <emph style="super">3</emph>
            </s>
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