Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

Table of contents

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[11.] CHRISTIANI HUGENII A ZULICHEM, Const, F. HOROLOGIUM.
[12.] ILLUSTRISSIMIS AC POTENTISSIMIS HOLLANDIAE Et WESTFRISIAE ORDINIBUS Dominis ſuis, Christianus Hugenius à Zulighem Felicitatem omnem.
[13.] CHRISTIANI HUGENII A ZULICHEM, Const. F. HOROLOGIUM.
[14.] FINIS.
[15.] CHRISTIANI HUGENII ZULICHEMII, CONST. F. HOROLOGIUM OSCILLATORIUM. SIVE DE MOTU PENDULORUM AD HOROLOGIA APTATO DEMONSTRATIONES GEOMETRICÆ
[16.] Dividitur liber hic in partes quinque, quarum
[17.] LUDOVICO XIV, FRANCIÆ ET NAVARRÆ REGI INCLYTO.
[18.] HADRIANI VALLII DAPHNIS, ECLOGA.
[19.] CHRISTIANI HUGENII ZULICHEMII, CONST. F. HOROLOGIUM OSCILLATORIUM, SIVE DE MOTU PENDULORUM AD HOROLOGIA APTATO Demonſtrationes Geometricæ.
[20.] HOROLOGII OSCILLATORII PARS PRIMA, Deſcriptionem ejus continens.
[21.] HOROLOGII OSCILLATORII PARS SECUNDA. De deſcenſu Gravium & motu eorum in Cycloide. HYPOTHESES. I.
[22.] II.
[23.] III.
[24.] PROPOSITIO I.
[25.] PROPOSITIO II.
[26.] PROPOSITIO III.
[27.] PROPOSITIO IV.
[28.] PROPOSITIO V.
[29.] PROPOSITIO VI.
[30.] PROPOSITIO VII.
[31.] PROPOSITIO VIII.
[32.] PROPOSITIO IX.
[33.] PROPOSITIO X.
[34.] PROPOSITIO XI.
[35.] PROPOSITIO XII.
[36.] PROPOSITIO XIII.
[37.] PROPOSITIO XIV.
[38.] PROPOSITIO XV.
[39.] PROPOSITIO XVI.
[40.] PROPOSITIO XVII.
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            <s xml:id="echoid-s1418" xml:space="preserve">
              <pb o="67" file="0101" n="106" rhead="HOROLOG. OSCILLATOR."/>
            dem ſuperficiem vel aliam ſimilem ſimiliter que po-
              <lb/>
              <note position="right" xlink:label="note-0101-01" xlink:href="note-0101-01a" xml:space="preserve">
                <emph style="sc">De de-</emph>
                <lb/>
                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">GRAVIUM</emph>
              .</note>
            ſitam feratur, æqualibus temporibus per idem ſpa-
              <lb/>
            tium deſcendet atque aſcendet.</s>
            <s xml:id="echoid-s1419" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1420" xml:space="preserve">Velut ſi per ſuperficiem A B deſcendat mobile, atque, ubi
              <lb/>
              <note position="right" xlink:label="note-0101-02" xlink:href="note-0101-02a" xml:space="preserve">TAB. VI.
                <lb/>
              Fig. 4.</note>
            ad B pervenerit, converſo motu ſurſum per eandem A B, vel
              <lb/>
            ei ſimilem & </s>
            <s xml:id="echoid-s1421" xml:space="preserve">reſpectu plani horizontalis ſimiliter poſitam
              <lb/>
            B C, aſcendat, conſtat ex ante demonſtratis, perventurum
              <lb/>
            ad eandem ex qua venit altitudinem. </s>
            <s xml:id="echoid-s1422" xml:space="preserve">Cum autem perpetuo,
              <lb/>
            in punctis quorum eadem altitudo, eandem velocitatem ha-
              <lb/>
            beat aſcendendo ac deſcendendo ; </s>
            <s xml:id="echoid-s1423" xml:space="preserve">apparet eandem
              <note symbol="*" position="right" xlink:label="note-0101-03" xlink:href="note-0101-03a" xml:space="preserve">Prop.
                <lb/>
              præced.</note>
            bis eadem velocitate ſingulis ſui partibus percurri: </s>
            <s xml:id="echoid-s1424" xml:space="preserve">unde & </s>
            <s xml:id="echoid-s1425" xml:space="preserve">
              <lb/>
            tempora utriusque motus æqualia eſſe neceſſe eſt; </s>
            <s xml:id="echoid-s1426" xml:space="preserve">quod erat
              <lb/>
            demonſtrandum.</s>
            <s xml:id="echoid-s1427" xml:space="preserve"/>
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        <div xml:id="echoid-div86" type="section" level="1" n="35">
          <head xml:id="echoid-head57" xml:space="preserve">PROPOSITIO XII.</head>
          <p style="it">
            <s xml:id="echoid-s1428" xml:space="preserve">ESto circulus A B C, diametro A C, cui ad an-
              <lb/>
              <note position="right" xlink:label="note-0101-04" xlink:href="note-0101-04a" xml:space="preserve">TAB. VI.
                <lb/>
              Fig. 5.</note>
            gulos rectos ſit F G; </s>
            <s xml:id="echoid-s1429" xml:space="preserve">huic vero occurrat à ter-
              <lb/>
            mino diametri A educta A F extra circulum, quæ
              <lb/>
            quidem neceſſario ſecabit circumferentiam, puta
              <lb/>
            in B. </s>
            <s xml:id="echoid-s1430" xml:space="preserve">Dico arcum B D, lineis G F, A F inter-
              <lb/>
            ceptum, minorem eſſe recta D F.</s>
            <s xml:id="echoid-s1431" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1432" xml:space="preserve">Jungatur enim B C, & </s>
            <s xml:id="echoid-s1433" xml:space="preserve">ducatur ex B puncto tangens cir-
              <lb/>
            cumferentiam recta B E, quæ neceſſario occurret rectæ F G
              <lb/>
            inter F & </s>
            <s xml:id="echoid-s1434" xml:space="preserve">D. </s>
            <s xml:id="echoid-s1435" xml:space="preserve">Eſt igitur angulus B A C in circulo æqualis
              <lb/>
            angulo E B C . </s>
            <s xml:id="echoid-s1436" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s1437" xml:space="preserve">angulus F B E, qui una
              <note symbol="*" position="right" xlink:label="note-0101-05" xlink:href="note-0101-05a" xml:space="preserve">Prop. 32.
                <lb/>
              Lib. 3. Eucl.</note>
            E B C conſtituit angulum rectum F B C, erit æqualis B C A.
              <lb/>
            </s>
            <s xml:id="echoid-s1438" xml:space="preserve">Quia autem ſimilia ſunt triangula A B C, A G F, erit & </s>
            <s xml:id="echoid-s1439" xml:space="preserve">
              <lb/>
            angulus F æqualis angulo A C B. </s>
            <s xml:id="echoid-s1440" xml:space="preserve">Ergo idem angulus F æ-
              <lb/>
            qualis angulo F B E. </s>
            <s xml:id="echoid-s1441" xml:space="preserve">Itaque iſoſceles eſt triangulus F E B,
              <lb/>
            habens crura æqualia F E, E B. </s>
            <s xml:id="echoid-s1442" xml:space="preserve">Addita ergo utrique eo-
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            rum recta E D, fiet F D, æqualis duabus B E, E D. </s>
            <s xml:id="echoid-s1443" xml:space="preserve">Has-
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            ce vero duas majores eſſe conſtat arcu B D, iisdem </s>
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