Gravesande, Willem Jacob 's, Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1

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          <p>
            <s xml:id="echoid-s10086" xml:space="preserve">
              <pb o="280" file="0380" n="415" rhead="PHYSICES ELEMENTA"/>
            & </s>
            <s xml:id="echoid-s10087" xml:space="preserve">adſcenſum motum ultra punctum hoc; </s>
            <s xml:id="echoid-s10088" xml:space="preserve">agam enim depen-
              <lb/>
            dulis a parte A deſcendentibus.</s>
            <s xml:id="echoid-s10089" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10090" xml:space="preserve">Ut autem demonſtremus quæ obtinent, quando pendulum
              <lb/>
              <note position="left" xlink:label="note-0380-01" xlink:href="note-0380-01a" xml:space="preserve">970.</note>
            etiam reſiſtentiâ ex ſecunda cauſa retardatur, fingam re-
              <lb/>
            ſiſtentiam quæ retardationem generat in ratione velocitatis,
              <lb/>
            quaſdamque, hac poſitâ, propoſitiones demonſtrabo, qui-
              <lb/>
            bus expoſitis facilius patebunt quæ locum habent quando
              <lb/>
            retardatio eſt ut quadratum velocitatis.</s>
            <s xml:id="echoid-s10091" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10092" xml:space="preserve">Poſitâ nunc retardatione in ratione ipſius velocitatis, & </s>
            <s xml:id="echoid-s10093" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0380-02" xlink:href="note-0380-02a" xml:space="preserve">971.</note>
            pendula duo, omnino ſimilia, in cycloide oſcillata, inæquales
              <lb/>
            peragant vibrationes, eodemque momento cadere incipiant;
              <lb/>
            </s>
            <s xml:id="echoid-s10094" xml:space="preserve">moveri inchoant velocitatibus quæ ſunt ut arcus deſcenſu
              <lb/>
            deſcribendi ; </s>
            <s xml:id="echoid-s10095" xml:space="preserve">ſi hæ impreſſiones primi momenti ſolæ
              <note symbol="*" position="left" xlink:label="note-0380-03" xlink:href="note-0380-03a" xml:space="preserve">287.</note>
            ſiderantur, poſt tempus quodcunque celeritates erunt in
              <lb/>
            eadem ratione ac in principio; </s>
            <s xml:id="echoid-s10096" xml:space="preserve">nam retardationes, quæ
              <lb/>
            ſunt ut ipſæ velocitates, harum proportionem immutare
              <lb/>
            nequeunt; </s>
            <s xml:id="echoid-s10097" xml:space="preserve">ratio enim inter quantitates non mutatur, addi-
              <lb/>
            tione, aut ſubtractione, quantitatum in eadem ratione. </s>
            <s xml:id="echoid-s10098" xml:space="preserve">Tem-
              <lb/>
            poribus igitur æqualibus, utcunque inter movendum ex
              <lb/>
            reſiſtentia mutetur corporis celeritas, ſpatia percurruntur
              <lb/>
            quæ ſunt ut velocitates in principio , id eſt, ut arcus
              <note symbol="*" position="left" xlink:label="note-0380-04" xlink:href="note-0380-04a" xml:space="preserve">94.</note>
            ſcenſu deſcribendi; </s>
            <s xml:id="echoid-s10099" xml:space="preserve">idcirco poſt tempus quodcunque cor-
              <lb/>
            pora ſunt in horum arcuum punctis reſpondentibus. </s>
            <s xml:id="echoid-s10100" xml:space="preserve">In
              <lb/>
            hiſce autem punctis accelerationes ſunt in eadem ratione
              <lb/>
            quàm in principio ; </s>
            <s xml:id="echoid-s10101" xml:space="preserve">& </s>
            <s xml:id="echoid-s10102" xml:space="preserve">ratio inter celeritates, quæ
              <note symbol="*" position="left" xlink:label="note-0380-05" xlink:href="note-0380-05a" xml:space="preserve">287.</note>
            reſiſtentia non variatur, ex acceleratione etiam nullam muta-
              <lb/>
            tionem patitur. </s>
            <s xml:id="echoid-s10103" xml:space="preserve">In adſcenſu motus corporum retardatur, ſed in
              <lb/>
            punctis reſpondentibus retardationes ſunt in eadem ratione in
              <lb/>
            qua ſunt in deſcenſu accelerationes. </s>
            <s xml:id="echoid-s10104" xml:space="preserve">Ubique ergo in punctis re-
              <lb/>
            ſpondentibus celeritates ſunt in eadem ratione. </s>
            <s xml:id="echoid-s10105" xml:space="preserve">Cum autem
              <lb/>
            iiſdem momentis corpora ſint in hiſce punctis reſpon-
              <lb/>
            dentibus, ſequitur motum amborum eodem momento de-
              <lb/>
            ſtrui, id eſt, iiſdem temporibus vibrationes abſolvi. </s>
            <s xml:id="echoid-s10106" xml:space="preserve">Spa-
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            tia in integris vibrationibus percurſa, cum æqualibus tem-
              <lb/>
            poribus percurrantur, & </s>
            <s xml:id="echoid-s10107" xml:space="preserve">cum in ſingulis momentis veloci-
              <lb/>
            tates ſint inter ſe eadem ratione, ſunt quoque in hac </s>
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