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-s1216" xml:space="preserve">
              <pb o="57" file="0089" n="93" rhead="HOROLOG. OSCILLATOR."/>
            quadratum A B ad quadratum C D. </s>
            <s xml:id="echoid-s1217" xml:space="preserve">quare neceſſe eſt ut
              <lb/>
              <note position="right" xlink:label="note-0089-01" xlink:href="note-0089-01a" xml:space="preserve">
                <emph style="sc">De de-</emph>
                <lb/>
                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">@RAVIUM</emph>
              .</note>
            eandem habeat. </s>
            <s xml:id="echoid-s1218" xml:space="preserve">Porro cum celeritates in fine temporum A B,
              <lb/>
            C D acquiſitæ ſint inter ſe ſicut ipſamet tempora; </s>
            <s xml:id="echoid-s1219" xml:space="preserve">apparet
              <lb/>
            rationem ſpatiorum E ad F eandem quoque eſſe quæ qua-
              <lb/>
            dratorum temporum A B, C D, quibus transmiſſa ſunt.
              <lb/>
            </s>
            <s xml:id="echoid-s1220" xml:space="preserve">Itaque conſtat propoſitum.</s>
            <s xml:id="echoid-s1221" xml:space="preserve"/>
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        <div xml:id="echoid-div62" type="section" level="1" n="27">
          <head xml:id="echoid-head49" xml:space="preserve">PROPOSITIO IV.</head>
          <p style="it">
            <s xml:id="echoid-s1222" xml:space="preserve">SI grave celeritate ea quam in fine deſcenſus ac-
              <lb/>
            quiſivit ſurſum tendere cœperit, fiet ut paribus
              <lb/>
            temporis partibus, ſpatia quæ prius ſurſum, ea-
              <lb/>
            dem deorſum transeat, adeoque ad eandem unde
              <lb/>
            deſcenderat altitudinem aſcendat. </s>
            <s xml:id="echoid-s1223" xml:space="preserve">Item ut æquali-
              <lb/>
            bus temporis partibus æqualia amittat celeritatis
              <lb/>
            momenta.</s>
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          </p>
          <note position="right" xml:space="preserve">TAB. V.
            <lb/>
          Fig. 1.</note>
          <p>
            <s xml:id="echoid-s1225" xml:space="preserve">Sunto enim ut in propoſitione 2, ſpatia quotlibet, æqua-
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            libus temporis partibus cadendo è quiete peracta, quorum
              <lb/>
            primum A B; </s>
            <s xml:id="echoid-s1226" xml:space="preserve">ſecundum compoſitum ex B D, quod celeri-
              <lb/>
            tate æquabili acquiſita per A B tranſeundum erat, & </s>
            <s xml:id="echoid-s1227" xml:space="preserve">ex D E
              <lb/>
            ipſi A B æquali; </s>
            <s xml:id="echoid-s1228" xml:space="preserve">tertium compoſitum, ex E F, duplo
              <lb/>
            ipſius B D, & </s>
            <s xml:id="echoid-s1229" xml:space="preserve">ex F G, eidem A B æquali; </s>
            <s xml:id="echoid-s1230" xml:space="preserve">quartum com-
              <lb/>
            poſitum ex G H, triplo ipſius B D, & </s>
            <s xml:id="echoid-s1231" xml:space="preserve">ex H K ipſi itidem
              <lb/>
            A B æquali, atque eadem ratione porro creſcentia, ſi plu-
              <lb/>
            ra fuerint. </s>
            <s xml:id="echoid-s1232" xml:space="preserve">Dico totidem æqualibus temporibus eadem ſpatia
              <lb/>
            K G, G E, E B, B A, ſingula ſingulis peragenda eſſe à
              <lb/>
            gravi ſurſum tendente, atque incipiente cum celeritate in
              <lb/>
            fine deſcenſus K acquiſita.</s>
            <s xml:id="echoid-s1233" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1234" xml:space="preserve">Brevitatis autem gratia celeritas quæque deſignetur de-
              <lb/>
            inceps longitudine ſpatii quod grave motu æquabili, cum
              <lb/>
            celeritate illa, atque temporis parte una, quales in deſcen-
              <lb/>
            ſu conſideravimus, tranſmiſſurum eſſet.</s>
            <s xml:id="echoid-s1235" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1236" xml:space="preserve">Itaque ex oſtenſis dicta propoſitione, cum in K grave
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            pervenerit, habet celeritatem G H auctam celeritate B </s>
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