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

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        <div xml:id="echoid-div924" type="section" level="1" n="235">
          <head xml:id="echoid-head330" xml:space="preserve">CAPUT XXV.</head>
          <head xml:id="echoid-head331" style="it" xml:space="preserve">De motu compoſito.</head>
          <p style="it">
            <s xml:id="echoid-s6510" xml:space="preserve">SI corpus moveatur, & </s>
            <s xml:id="echoid-s6511" xml:space="preserve">hujus celeritas augenda aut minu-
              <lb/>
              <note position="left" xlink:label="note-0236-01" xlink:href="note-0236-01a" xml:space="preserve">598.</note>
            enda ſit, manente directione, evidens eſt, impre ſſionem
              <lb/>
            requiri, quæ proportionalis ſit differentiæ quadratorum ve-
              <lb/>
            locitatis quam corpus ante actionem habuit, & </s>
            <s xml:id="echoid-s6512" xml:space="preserve">illius quam
              <lb/>
            poſt actionem habet, huic enim differentiæ vis communicata
              <lb/>
            aut ſublata proportionalis eſt .</s>
            <s xml:id="echoid-s6513" xml:space="preserve">
              <note position="right" xlink:label="note-0236-02" xlink:href="note-0236-02a" xml:space="preserve">447.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s6514" xml:space="preserve">Ponamus duas actiones eodem tempore in corpus juxta e an-
              <lb/>
              <note position="left" xlink:label="note-0236-03" xlink:href="note-0236-03a" xml:space="preserve">599.</note>
            dem directionem agere. </s>
            <s xml:id="echoid-s6515" xml:space="preserve">Dum augetur velocitas; </s>
            <s xml:id="echoid-s6516" xml:space="preserve">creſcit in
              <lb/>
            ratione duplicata vis corpori inſita ; </s>
            <s xml:id="echoid-s6517" xml:space="preserve">id eſt hujus
              <note position="left" xlink:label="note-0236-04" xlink:href="note-0236-04a" xml:space="preserve">447.</note>
            tum ſequitur proportionem augmenti trianguli quod dum
              <lb/>
            augetur eidem ſimile manet, & </s>
            <s xml:id="echoid-s6518" xml:space="preserve">cujus latus unum velocitatem
              <lb/>
              <note position="left" xlink:label="note-0236-05" xlink:href="note-0236-05a" xml:space="preserve">
                <emph style="sc">TAB. XXIII</emph>
              .
                <lb/>
              fig. 2.</note>
            repræſentat ; </s>
            <s xml:id="echoid-s6519" xml:space="preserve">vis dum velocitas eſt A g, eſt ad vim
              <note symbol="*" position="left" xlink:label="note-0236-06" xlink:href="note-0236-06a" xml:space="preserve">19. El. vi.</note>
            velocitas eſt A l, ut area A g r ad A l s.</s>
            <s xml:id="echoid-s6520" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6521" xml:space="preserve">Concipiamus, actiones alternatim in corpus agere per in-
              <lb/>
            tervalla temporis æqualia; </s>
            <s xml:id="echoid-s6522" xml:space="preserve">actione primâ communicari vim
              <lb/>
            A d o, ſecundâ vim d o p e; </s>
            <s xml:id="echoid-s6523" xml:space="preserve">iterum actione prima commu-
              <lb/>
            nicari vim p e f q, & </s>
            <s xml:id="echoid-s6524" xml:space="preserve">ſecundâ f q r g & </s>
            <s xml:id="echoid-s6525" xml:space="preserve">ſic ulterius; </s>
            <s xml:id="echoid-s6526" xml:space="preserve">ſumma
              <lb/>
            arearum albarum repræſentat vim integram prima actione
              <lb/>
            communicatam, & </s>
            <s xml:id="echoid-s6527" xml:space="preserve">ſumma nigrarum deſignat vim integram
              <lb/>
            ſecundâ actione corpori impreſſam. </s>
            <s xml:id="echoid-s6528" xml:space="preserve">Cum per tempora æ-
              <lb/>
            qualia actiones egerint, vires hæ, id eſt, ſummæ arearum,
              <lb/>
            ſunt ut ipſæ actiones, in qua etiam ratione eſt area. </s>
            <s xml:id="echoid-s6529" xml:space="preserve">quæcun-
              <lb/>
            que alba ad ſuam vicinam nigram: </s>
            <s xml:id="echoid-s6530" xml:space="preserve">ſi momenta temporum
              <lb/>
            fuerint inſinitè exigua, ut ſunt quando actiones ſimul agunt,
              <lb/>
            areæ hæ pro parallelogrammis haberi poſſunt, & </s>
            <s xml:id="echoid-s6531" xml:space="preserve">parallelogram-
              <lb/>
            ma vicina eandem habebunt altitudinem; </s>
            <s xml:id="echoid-s6532" xml:space="preserve">ideoque erunt in-
              <lb/>
            ter ſe ut baſes ; </s>
            <s xml:id="echoid-s6533" xml:space="preserve">ergo baſis albi ad baſim vicini nigri,
              <note position="left" xlink:label="note-0236-07" xlink:href="note-0236-07a" xml:space="preserve">I. El. VI.</note>
            actio prima ad ſecundam, & </s>
            <s xml:id="echoid-s6534" xml:space="preserve">in eadem ratione ſumma ba-
              <lb/>
            ſium parallelogrammorum alborum ad ſummam baſium ni-
              <lb/>
            grorum; </s>
            <s xml:id="echoid-s6535" xml:space="preserve">id eſt, ita ſe habet velocit as quam communicavit
              <lb/>
            actio prima ad velocitatem ex ſecundâ oriundam. </s>
            <s xml:id="echoid-s6536" xml:space="preserve">Quæ </s>
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