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

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        <div xml:id="echoid-div810" type="section" level="1" n="211">
          <pb o="146" file="0214" n="233" rhead="PHYSICES ELEMENTA"/>
          <p>
            <s xml:id="echoid-s5763" xml:space="preserve">Quieſcant corpora A & </s>
            <s xml:id="echoid-s5764" xml:space="preserve">Cin a & </s>
            <s xml:id="echoid-s5765" xml:space="preserve">c, dum ut ante mobilia ſunt circa H. </s>
            <s xml:id="echoid-s5766" xml:space="preserve">Po-
              <lb/>
            namus B aut b in linea recta motum, velociate q directè & </s>
            <s xml:id="echoid-s5767" xml:space="preserve">perpendiculariter
              <lb/>
            ad a H incurrere in a; </s>
            <s xml:id="echoid-s5768" xml:space="preserve">velocitatem poſt ictum detegimus ipſâ formulâ præcedenti.
              <lb/>
            </s>
            <s xml:id="echoid-s5769" xml:space="preserve">Pono enim B cum linea cohærere & </s>
            <s xml:id="echoid-s5770" xml:space="preserve">agitari circa centrum ad diſtantiam quam-
              <lb/>
            cunque b; </s>
            <s xml:id="echoid-s5771" xml:space="preserve">in hac colliſione p & </s>
            <s xml:id="echoid-s5772" xml:space="preserve">D æquales ſunt nihilo, ideo evaneſcunt quan-
              <lb/>
            titates, quæ per has multiplicantur quare memoratâ formula in hanc
              <note symbol="*" position="left" xlink:label="note-0214-01" xlink:href="note-0214-01a" xml:space="preserve">539.</note>
            tatur {Bbbaaq/
              <emph style="ol">Aaa + Ccc</emph>
            x bb + Bbbaa} = {Baaq/Aaa + Ccc + Baa}: </s>
            <s xml:id="echoid-s5773" xml:space="preserve">ex qua
              <lb/>
            banc deducimus regulam. </s>
            <s xml:id="echoid-s5774" xml:space="preserve">Corpus impingens per quadratum diſtantiæ puncti, in
              <lb/>
            quod incurrit, âcextro, & </s>
            <s xml:id="echoid-s5775" xml:space="preserve">per velocitatem ſuam multiplicatur, productumque boc
              <lb/>
            dividitur per ſummam omnium corporum, ſingulorum multiplicatorum per quadrata
              <lb/>
            ſuarum diſtantiarum à centro.</s>
            <s xml:id="echoid-s5776" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5777" xml:space="preserve">Propoſitiones n. </s>
            <s xml:id="echoid-s5778" xml:space="preserve">500. </s>
            <s xml:id="echoid-s5779" xml:space="preserve">510. </s>
            <s xml:id="echoid-s5780" xml:space="preserve">512. </s>
            <s xml:id="echoid-s5781" xml:space="preserve">513. </s>
            <s xml:id="echoid-s5782" xml:space="preserve">516. </s>
            <s xml:id="echoid-s5783" xml:space="preserve">ſunt caſus peculiares propoſi-
              <lb/>
              <note position="left" xlink:label="note-0214-02" xlink:href="note-0214-02a" xml:space="preserve">544.</note>
            tionum in hoc Scholio in n. </s>
            <s xml:id="echoid-s5784" xml:space="preserve">533. </s>
            <s xml:id="echoid-s5785" xml:space="preserve">537. </s>
            <s xml:id="echoid-s5786" xml:space="preserve">538. </s>
            <s xml:id="echoid-s5787" xml:space="preserve">539. </s>
            <s xml:id="echoid-s5788" xml:space="preserve">540. </s>
            <s xml:id="echoid-s5789" xml:space="preserve">demonſtratarum, ut
              <lb/>
            patet, ſi ponamus duo corpora quæ cum lineis, circa centra quæcunque mo-
              <lb/>
            bilibus, cohærent.</s>
            <s xml:id="echoid-s5790" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div828" type="section" level="1" n="212">
          <head xml:id="echoid-head300" xml:space="preserve">SCHOLIUM 3.</head>
          <head xml:id="echoid-head301" style="it" xml:space="preserve">Examen Experimenti circa corpora in lancem, aut
            <lb/>
          brachium, libræ impingentia.</head>
          <p>
            <s xml:id="echoid-s5791" xml:space="preserve">Merſennus, de Lanis, & </s>
            <s xml:id="echoid-s5792" xml:space="preserve">alii experimentum dedere circa corpora caden-
              <lb/>
              <note position="left" xlink:label="note-0214-03" xlink:href="note-0214-03a" xml:space="preserve">545.</note>
            tia inſtitutum, & </s>
            <s xml:id="echoid-s5793" xml:space="preserve">notarunt corpus in lancem libræ impingens, pondus ma-
              <lb/>
            jus, in lance oppoſitâ, paululum elevare; </s>
            <s xml:id="echoid-s5794" xml:space="preserve">& </s>
            <s xml:id="echoid-s5795" xml:space="preserve">pondera ſic elevari ad exiguam, ſed
              <lb/>
            æqualem (quam tamen circumſtantiam non notat Merſennus) altitudinem,
              <lb/>
            ſi corpus quod impingit cadat ab altitudinibus quæ ſunt ut quadrata pon-
              <lb/>
            derum quæ elevantur.</s>
            <s xml:id="echoid-s5796" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5797" xml:space="preserve">Merſennus tamen notat in quibuſdam circumſtantiis experimentum non pro-
              <lb/>
            ceſſiſſe, quod & </s>
            <s xml:id="echoid-s5798" xml:space="preserve">mihi contigit, experimentum paululum aliter inſtituenti, quod
              <lb/>
            defectui machinæ tribuebam, & </s>
            <s xml:id="echoid-s5799" xml:space="preserve">in illis ſolis altitudinibus, in quibus regulam
              <lb/>
            ſatis exacte obſervari videbam, defectus, qui in machina me non latebant,
              <lb/>
            minus noxios credebam. </s>
            <s xml:id="echoid-s5800" xml:space="preserve">Cum autem attentius rem examinarem me toto
              <lb/>
            cælo erraſſe percepi, & </s>
            <s xml:id="echoid-s5801" xml:space="preserve">ipſis illis principiis Mechanices, de quibus inter omnes
              <lb/>
            convenit, adverſari, memoratam dari inter quadrata ponderum elevatorum
              <lb/>
            proportionem, quæ datur inter altitudines, a quibus cadit corpus, quod in lancem,
              <lb/>
            aut brachium oppoſitum, impingit; </s>
            <s xml:id="echoid-s5802" xml:space="preserve">& </s>
            <s xml:id="echoid-s5803" xml:space="preserve">in dubium vocare non potui ipſi defe-
              <lb/>
            ctui machinæ tribuendum eſſe, ſi aliquando inter certos limites hæc dete-
              <lb/>
            gatur proportio, ut mihi ſemper contigerat. </s>
            <s xml:id="echoid-s5804" xml:space="preserve">Non ſenſibilis fateor dabitur
              <lb/>
            error, ſi corpus cadens, & </s>
            <s xml:id="echoid-s5805" xml:space="preserve">pondustotius libræ, id eſt, jugi & </s>
            <s xml:id="echoid-s5806" xml:space="preserve">lancium, admodum
              <lb/>
            exigua fuerint reſpectu ponderum elevatorum: </s>
            <s xml:id="echoid-s5807" xml:space="preserve">ſed in hoc caſu experimen-
              <lb/>
            tum inſtitui non poterit; </s>
            <s xml:id="echoid-s5808" xml:space="preserve">majus enim pondus ſubtiliori libræ imponi non po-
              <lb/>
            teſt.</s>
            <s xml:id="echoid-s5809" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5810" xml:space="preserve">Ut autem, quæ hoc experimentum ſpectant, clarius paterent, Machinam </s>
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