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

Table of Notes

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            <s xml:id="echoid-s2883" xml:space="preserve">
              <pb o="127" file="0185" n="202" rhead="HOROLOG. OSCILLATOR."/>
            cto deinceps communi vinculo, ſingula intelligantur acqui-
              <lb/>
              <note position="right" xlink:label="note-0185-01" xlink:href="note-0185-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS.</emph>
              </note>
            ſitas celeritates ſurſum convertere, (quod impingendo in pla-
              <lb/>
            na quædam inclinata, fieri poterit,) & </s>
            <s xml:id="echoid-s2884" xml:space="preserve">quouſque poſſunt
              <lb/>
            aſcendere, nempe in L, M, N. </s>
            <s xml:id="echoid-s2885" xml:space="preserve">Quo ubi pervenerint, ſit
              <lb/>
            centrum gravitatis omnium punctum P. </s>
            <s xml:id="echoid-s2886" xml:space="preserve">Dico hoc pari alti-
              <lb/>
            tudine eſſe cum puncto E.</s>
            <s xml:id="echoid-s2887" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2888" xml:space="preserve">Nam primum quidem, conſtat P non altius eſſe quam E,
              <lb/>
            ex prima ſumptarum hypotheſium. </s>
            <s xml:id="echoid-s2889" xml:space="preserve">Sed nec humilius fore ſic
              <lb/>
            oſtendemus. </s>
            <s xml:id="echoid-s2890" xml:space="preserve">Sit enim, ſi poteſt, P humilius quam E, & </s>
            <s xml:id="echoid-s2891" xml:space="preserve">
              <lb/>
            intelligantur pondera ex iiſdem, ad quas aſcenderunt, alti-
              <lb/>
            tudinibus recidere, quæ ſunt L G, M H, N K. </s>
            <s xml:id="echoid-s2892" xml:space="preserve">Unde
              <lb/>
            quidem eaſdem celeritates ipſis acquiri conſtat, quas habe-
              <lb/>
            bant ad aſcendendum ad iſtas altitudines , hoc eſt, eas
              <note symbol="*" position="right" xlink:label="note-0185-02" xlink:href="note-0185-02a" xml:space="preserve">Propoſ. 4.
                <lb/>
              part. 2.</note>
            pſas quas acquiſierant motu penduli ex C B A D in
              <lb/>
            K H G D. </s>
            <s xml:id="echoid-s2893" xml:space="preserve">Quare, ſi cum dictis celeritatibus ad virgam ſu-
              <lb/>
            perficiemve, cui innexa fuere, nunc referantur, eique ſi-
              <lb/>
            mul adhæreſcant, motumque ſecundum inceptos arcus con-
              <lb/>
            tinuent; </s>
            <s xml:id="echoid-s2894" xml:space="preserve">quod fiet, ſi priuſquam virgam attingant, à planis
              <lb/>
            inclinatis Q Q repercuſſa intelligantur; </s>
            <s xml:id="echoid-s2895" xml:space="preserve">abſolvet, hoc modo
              <lb/>
            reſtitutum pendulum, oſcillationis partem reliquam, æquè
              <lb/>
            ac ſi abſque ulla interruptione motum continuaſſet. </s>
            <s xml:id="echoid-s2896" xml:space="preserve">Ita ut
              <lb/>
            centrum gravitatis penduli, E, arcus æquales E F, F R,
              <lb/>
            deſcendendo ac aſcendendo percurrat, ac proinde in R ea-
              <lb/>
            dem ac in E altitudine reperiatur. </s>
            <s xml:id="echoid-s2897" xml:space="preserve">Ponebatur autem E eſſe
              <lb/>
            altius quam P centrum gravitatis ponderum in L, M, N,
              <lb/>
            poſitorum. </s>
            <s xml:id="echoid-s2898" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s2899" xml:space="preserve">R altius erit quam P: </s>
            <s xml:id="echoid-s2900" xml:space="preserve">adeoque ponde-
              <lb/>
            rum ex L, M, N, delapſorum centrum gravitatis, altius,
              <lb/>
            quam unde deſcenderat, aſcendiſſet. </s>
            <s xml:id="echoid-s2901" xml:space="preserve">quod eſt abſurdum .</s>
            <s xml:id="echoid-s2902" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0185-03" xlink:href="note-0185-03a" xml:space="preserve">Hypoth. @
                <lb/>
              huj.</note>
            Non igitur centrum gravitatis P humilius eſt quam E. </s>
            <s xml:id="echoid-s2903" xml:space="preserve">Sed
              <lb/>
            nec altius erat. </s>
            <s xml:id="echoid-s2904" xml:space="preserve">Ergo æque altum ſit neceſſe eſt. </s>
            <s xml:id="echoid-s2905" xml:space="preserve">quod erat
              <lb/>
            demonſtrandum.</s>
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          <head xml:id="echoid-head119" xml:space="preserve">PROPOSITIO V.</head>
          <p style="it">
            <s xml:id="echoid-s2907" xml:space="preserve">DAto pendulo ex ponderibus quotlibet compoſito,
              <lb/>
            ſi ſingula ducantur in quadrata </s>
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