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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              <pb o="62" file="0094" n="98" rhead="CHRISTIANI HUGENII"/>
            P ſuperat triangulum A H L, erit igitur neceſſario figura
              <lb/>
              <note position="left" xlink:label="note-0094-01" xlink:href="note-0094-01a" xml:space="preserve">
                <emph style="sc">De de-</emph>
                <lb/>
                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">GRAVIUM</emph>
              .</note>
            circumſcripta minor plano P. </s>
            <s xml:id="echoid-s1322" xml:space="preserve">Conſtat jam, prima temporis
              <lb/>
            parte A C, minus ſpatium à mobili transmitti quam ſit B C,
              <lb/>
            quia hoc percurreretur eodem tempore A C cum celeritate
              <lb/>
            æquabili C K, quam demum in fine temporis A C mobile
              <lb/>
            adeptum eſt. </s>
            <s xml:id="echoid-s1323" xml:space="preserve">Similiter ſecunda parte temporis C E, minus
              <lb/>
            ſpatium motu accelerato transmittetur quam ſit D E, quia
              <lb/>
            hoc percurreretur eodem tempore C E, cum celeritate æ-
              <lb/>
            quabili E O, quam demum in fine temporis C E mobile aſ-
              <lb/>
            ſequitur. </s>
            <s xml:id="echoid-s1324" xml:space="preserve">Atque ita deinceps, ſingulis partibus temporis
              <lb/>
            A H, minora ſpatia à mobili trajicientur quam ſunt rectan-
              <lb/>
            gula figuræ circumſcriptæ, ipſis partibus adjacentia. </s>
            <s xml:id="echoid-s1325" xml:space="preserve">Quare
              <lb/>
            totum ſpatium motu accelerato peractum, minus erit ipſa fi-
              <lb/>
            gura circumſcripta. </s>
            <s xml:id="echoid-s1326" xml:space="preserve">Spatium vero illud æquale poſitum fuit
              <lb/>
            plano P; </s>
            <s xml:id="echoid-s1327" xml:space="preserve">ergo planum P minus quoque erit figura circum-
              <lb/>
            ſcripta. </s>
            <s xml:id="echoid-s1328" xml:space="preserve">quod eſt abſurdum, cum figura hæc plano P minor
              <lb/>
            oſtenſa fuerit. </s>
            <s xml:id="echoid-s1329" xml:space="preserve">Ergo planum P non majus eſt triangulo A H L,
              <lb/>
            ſed nec minus eſſe jam oſtenſum fuit. </s>
            <s xml:id="echoid-s1330" xml:space="preserve">Ergo æquale ſit neceſ-
              <lb/>
            ſe eſt; </s>
            <s xml:id="echoid-s1331" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1332" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1333" xml:space="preserve">Et hæc quidem omnia quæ hactenus demonſtrata ſunt,
              <lb/>
            gravibus per plana inclinata deſcendentibus atque aſcenden-
              <lb/>
            tibus æque ac perpendiculariter motis convenire ſciendum
              <lb/>
            eſt: </s>
            <s xml:id="echoid-s1334" xml:space="preserve">cum, quæ de effectu gravitatis poſita fuerunt, eadem
              <lb/>
            ratione utrobique ſint admittenda.</s>
            <s xml:id="echoid-s1335" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1336" xml:space="preserve">Hinc vero non difficile jam erit demonſtrare propoſitionem
              <lb/>
            ſequentem quam concedi ſibi, ut quodammodo per ſe ma-
              <lb/>
            nifeſtam, Galileus poſtulavit. </s>
            <s xml:id="echoid-s1337" xml:space="preserve">nam demonſtratio illa quam
              <lb/>
            poſtea adferre conatus eſt, quæque in poſteriori operum
              <lb/>
            ejus editione extat, parum firma meo quidem judicio vide-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s1338" xml:space="preserve">Eſt autem propoſitio hujusmodi.</s>
            <s xml:id="echoid-s1339" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div69" type="section" level="1" n="29">
          <head xml:id="echoid-head51" xml:space="preserve">PROPOSITIO VI.</head>
          <p style="it">
            <s xml:id="echoid-s1340" xml:space="preserve">CEleritates gravium, ſuper diverſis planorum
              <lb/>
            inclinationibus deſcendendo acquiſitæ, æquales
              <lb/>
            ſunt, ſi planorum elevationes fuerint æquales.</s>
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