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

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        <div xml:id="echoid-div671" type="section" level="1" n="187">
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            <s xml:id="echoid-s4614" xml:space="preserve">
              <pb o="111" file="0171" n="186" rhead="MATHEMATICA. LIB. I. CAP. XXII."/>
            do preſſio vim generat non in acceleratione æquales gradus
              <lb/>
            velocitatis æquali actione communicantur; </s>
            <s xml:id="echoid-s4615" xml:space="preserve">ut enim æquales
              <lb/>
              <note position="right" xlink:label="note-0171-01" xlink:href="note-0171-01a" xml:space="preserve">439.</note>
            gradus velocitatis corporibus æqualibus, quorum unum quie-
              <lb/>
            ſcit, alterum movetur, æqualibus actionibus communicentur;
              <lb/>
            </s>
            <s xml:id="echoid-s4616" xml:space="preserve">requiritur ut illud quod in corpora agit reſpectu utriuſque
              <lb/>
            eandem habeat relationem; </s>
            <s xml:id="echoid-s4617" xml:space="preserve">id eſt, deſideratur ut cauſa mo-
              <lb/>
            vens eadem velocitate cum corpore moto feratur, in quod
              <lb/>
            tunc poterit agere ut in corpus quieſcens: </s>
            <s xml:id="echoid-s4618" xml:space="preserve">actio autem qua
              <lb/>
            cauſa movens transfertur ſuper addenda eſt actioni hujus
              <lb/>
            ipſius, ut habeamus actionem integram qua corpus move-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s4619" xml:space="preserve">Unde deducimus difficilius corpus acceler ari quam mo-
              <lb/>
              <note position="right" xlink:label="note-0171-02" xlink:href="note-0171-02a" xml:space="preserve">440.</note>
            veri.</s>
            <s xml:id="echoid-s4620" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4621" xml:space="preserve">Sint elaſtra infinite parva e, e, e, e, &</s>
            <s xml:id="echoid-s4622" xml:space="preserve">c, juncta inter ſe,
              <lb/>
              <note position="right" xlink:label="note-0171-03" xlink:href="note-0171-03a" xml:space="preserve">441.</note>
            & </s>
            <s xml:id="echoid-s4623" xml:space="preserve">flexa, quæ, ſi ad priſtinam redeant figuram, illam ac
              <lb/>
              <note position="right" xlink:label="note-0171-04" xlink:href="note-0171-04a" xml:space="preserve">
                <emph style="sc">TAB. XVI.</emph>
                <lb/>
              fig. 1.</note>
            quirant, quæ in E repræſentatur, & </s>
            <s xml:id="echoid-s4624" xml:space="preserve">per ſpatium infinite
              <lb/>
            exiguum ſeſe expandant. </s>
            <s xml:id="echoid-s4625" xml:space="preserve">Elaſtrorum hæc eſt proprietas,
              <lb/>
            ut, ſi, dum ſe expandunt, in corpus ſibi relictum premant,
              <lb/>
            huic vim integram, cum qua ſe expandunt, communicent,
              <lb/>
            ſi ad partem oppoſitam obſtaculo immobili inſiſtant. </s>
            <s xml:id="echoid-s4626" xml:space="preserve">Ela-
              <lb/>
            ſtrum E communicat corpori P gradum velocitatis infinitè
              <lb/>
            exiguum. </s>
            <s xml:id="echoid-s4627" xml:space="preserve">Ut elaſtrum ſequens corpori æqualem gradum
              <lb/>
            velocitatis communicet, requiritur ut elaſtrum, dum ſeſe
              <lb/>
            expandit, ea velocitate feratur, quam corpus jam acqui-
              <lb/>
            ſivit, aliter non ageret in corpus motum, ut E in corpus
              <lb/>
            quieſcens egit; </s>
            <s xml:id="echoid-s4628" xml:space="preserve">præterea requiritur, ut in hoc motu inſi-
              <lb/>
            ſtat Elaſtrum translatum obſtaculo, quod verſus partem op-
              <lb/>
            poſitam cedere nequeat; </s>
            <s xml:id="echoid-s4629" xml:space="preserve">id eſt propellendum eſt ea vi,
              <lb/>
            qua hoc propellit corpus; </s>
            <s xml:id="echoid-s4630" xml:space="preserve">quod obtinebit, ſi elaſtro ſimili
              <lb/>
            ſeſe expandente propellatur. </s>
            <s xml:id="echoid-s4631" xml:space="preserve">Duo ergo elaſtra eodem mo-
              <lb/>
            mento ſeſe expandentia requiruntur, ut ſecundus gradus
              <lb/>
            celeritatis corpori communicetur, id eſt vis deſidera-
              <lb/>
            tur dupla illius, qua primus gradus corpori communicatur.
              <lb/>
            </s>
            <s xml:id="echoid-s4632" xml:space="preserve">Simili demonſtratione patebit, tria elaſtra, eodem momen-
              <lb/>
            to ſeſe expandentia, aut vim triplam requiri, ut communi-
              <lb/>
            cetur tertius velocitatis gradus & </s>
            <s xml:id="echoid-s4633" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s4634" xml:space="preserve">Poſitis
              <lb/>
            nempe gradibus velocitatis infinitè exiguis ne in </s>
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