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

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            <s xml:id="echoid-s5914" xml:space="preserve">
              <pb o="149" file="0217" n="236" rhead="MATHEMATICA. LIB. I. CAP. XXIII."/>
            cium ut & </s>
            <s xml:id="echoid-s5915" xml:space="preserve">P, Q, & </s>
            <s xml:id="echoid-s5916" xml:space="preserve">G, dicimus c, & </s>
            <s xml:id="echoid-s5917" xml:space="preserve">velocitas puncti A poſt ictum erit
              <lb/>
            {AC
              <emph style="super">q</emph>
            x Gva/b x AC
              <emph style="super">q</emph>
            + c x AC
              <emph style="super">q</emph>
            } = {Gva /b + c}.</s>
            <s xml:id="echoid-s5918" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0217-01" xlink:href="note-0217-01a" xml:space="preserve">543.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s5919" xml:space="preserve">Ut, data hac velocitate, altitudinem ad quam elevatur punctum A cumal-
              <lb/>
            titudine a conferamus, determinandum eſt centrum oſcillationis, quod mo-
              <lb/>
            vetur ut corpus in quod gravitas tantum agit , diſtantia autem centri
              <note symbol="*" position="right" xlink:label="note-0217-02" xlink:href="note-0217-02a" xml:space="preserve">296.</note>
            lationis a centro motus eſt {b x AC
              <emph style="super">q</emph>
            + c x AC
              <emph style="super">q</emph>
            /P x AC } = {b x AC + c x AC/P}.</s>
            <s xml:id="echoid-s5920" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0217-03" xlink:href="note-0217-03a" xml:space="preserve">3127</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s5921" xml:space="preserve">Diſtantia autem AC ſe habet ad diſtantiam hanc centri oſcillationis, id eſt
              <lb/>
            (multiplicando utramque diſtantiam per P, & </s>
            <s xml:id="echoid-s5922" xml:space="preserve">dividendo per AC) P ad
              <lb/>
            b + c, ut velocitas puncti A ad velocitatem centri oſcillationis; </s>
            <s xml:id="echoid-s5923" xml:space="preserve">& </s>
            <s xml:id="echoid-s5924" xml:space="preserve">in eadem
              <lb/>
            ratione altitudo ad quam adſcendit A, quam dicimus d, ad altitudinem ad
              <lb/>
            quam adſcendit centrum oſcillationis; </s>
            <s xml:id="echoid-s5925" xml:space="preserve">ergo
              <lb/>
            P, b + c:</s>
            <s xml:id="echoid-s5926" xml:space="preserve">: {Gva/b + c}, {Gva/P} = velocitati centri oſcillationis. </s>
            <s xml:id="echoid-s5927" xml:space="preserve">Et
              <lb/>
            P, b + c:</s>
            <s xml:id="echoid-s5928" xml:space="preserve">: d {db + dc/P} = altitudini, ad quam centrum oſcillationis adſcendit.</s>
            <s xml:id="echoid-s5929" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5930" xml:space="preserve">Altitudo hæc etiam quadrato velocitatis hujus centri exprimitur, cum a ex-
              <lb/>
            primat altitudinem ad quam corpus velociate √ a pertingit .</s>
            <s xml:id="echoid-s5931" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0217-04" xlink:href="note-0217-04a" xml:space="preserve">255. 261.</note>
            Habemus ergo hanc æquationem {G
              <emph style="super">q</emph>
            x a/P
              <emph style="super">q</emph>
            } = {db + dc/P} id eſt G
              <emph style="super">q</emph>
            x a = db
              <lb/>
            x P + dc x P: </s>
            <s xml:id="echoid-s5932" xml:space="preserve">& </s>
            <s xml:id="echoid-s5933" xml:space="preserve">a = {
              <emph style="ol">b + c</emph>
            x d x P/G
              <emph style="super">q</emph>
            }</s>
          </p>
          <p>
            <s xml:id="echoid-s5934" xml:space="preserve">Pro litteris ut numeri ſubſtituantur, conſiderandum, b æquale eſſe {2/3} GC
              <lb/>
              <note position="right" xlink:label="note-0217-05" xlink:href="note-0217-05a" xml:space="preserve">550.</note>
            x AC + {1/6}-GF x AC, dum ipſa figura ADFHB, id eſt
              <emph style="super">2</emph>
            GC x AC +
              <lb/>
            GF x AC , Jugi pondus repræſentat; </s>
            <s xml:id="echoid-s5935" xml:space="preserve">quare hoc pondus jugi ad b,
              <note symbol="*" position="right" xlink:label="note-0217-06" xlink:href="note-0217-06a" xml:space="preserve">34. El. 1.</note>
              <emph style="super">2</emph>
            GC + GF ad {2/3} GC + {1/6} GF.</s>
            <s xml:id="echoid-s5936" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5937" xml:space="preserve">In noſtra machina eſt GC ad GF ut 3 ad 4. </s>
            <s xml:id="echoid-s5938" xml:space="preserve">& </s>
            <s xml:id="echoid-s5939" xml:space="preserve">jugi pondus novemdecim
              <lb/>
            unciarum cum dragmis duabus & </s>
            <s xml:id="echoid-s5940" xml:space="preserve">ſcrupulo uno, id eſt ſcrupulorum 463,
              <lb/>
            Ergo 15, 4:</s>
            <s xml:id="echoid-s5941" xml:space="preserve">: 463, b = 123 {1/2}. </s>
            <s xml:id="echoid-s5942" xml:space="preserve">ſcrup.</s>
            <s xml:id="echoid-s5943" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5944" xml:space="preserve">Pondera lancium additis Q & </s>
            <s xml:id="echoid-s5945" xml:space="preserve">G id eſt c-P valent 1320. </s>
            <s xml:id="echoid-s5946" xml:space="preserve">ſcrupula; </s>
            <s xml:id="echoid-s5947" xml:space="preserve">Globus
              <lb/>
            G, ponderat ſcrupula 67; </s>
            <s xml:id="echoid-s5948" xml:space="preserve">altitudo d æqualis eſto, 21. </s>
            <s xml:id="echoid-s5949" xml:space="preserve">poll. </s>
            <s xml:id="echoid-s5950" xml:space="preserve">id eſt, excedit paulu-
              <lb/>
            lum quintam pollicis partem.</s>
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