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

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            <s xml:id="echoid-s2355" xml:space="preserve">
              <pb o="53" file="0099" n="107" rhead="MATHEMATICA. LIB. I. CAP. XV."/>
            rum directiones ſunt parallelæ lateribus trianguli AED; </s>
            <s xml:id="echoid-s2356" xml:space="preserve">& </s>
            <s xml:id="echoid-s2357" xml:space="preserve">
              <lb/>
            quæ ergo, ut detur æquilibrium, ſunt inter ſe ut iſta latera.</s>
            <s xml:id="echoid-s2358" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2359" xml:space="preserve">Punctum A, ob æqualitatem diſtantiarum punctorum A
              <lb/>
            & </s>
            <s xml:id="echoid-s2360" xml:space="preserve">B a fulcro, juxta
              <emph style="sc">Ea</emph>
            continuatam, trahitur eadem vi
              <lb/>
            qua pondus P deſcendit, id eſt, pondere duarum librarum;
              <lb/>
            </s>
            <s xml:id="echoid-s2361" xml:space="preserve">vis ergo per AD requiritur trium librarum, quia latera AD
              <lb/>
            & </s>
            <s xml:id="echoid-s2362" xml:space="preserve">AE ſunt inter ſe ut tria ad duo. </s>
            <s xml:id="echoid-s2363" xml:space="preserve">Latus DE exprimit
              <lb/>
            quid fulcrum patiatur vi qua punctum A in fig. </s>
            <s xml:id="echoid-s2364" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2365" xml:space="preserve">premitur
              <lb/>
            B verſus, & </s>
            <s xml:id="echoid-s2366" xml:space="preserve">in fig. </s>
            <s xml:id="echoid-s2367" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2368" xml:space="preserve">à B retrahitur.</s>
            <s xml:id="echoid-s2369" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2370" xml:space="preserve">Idem omnino dicendum de potentia obliqua axi in peri-
              <lb/>
            trochio applicata.</s>
            <s xml:id="echoid-s2371" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div378" type="section" level="1" n="128">
          <head xml:id="echoid-head185" xml:space="preserve">
            <emph style="sc">Experimentum</emph>
          5.</head>
          <p>
            <s xml:id="echoid-s2372" xml:space="preserve">Pondus P, trochleæ annexum, ſuſtinetur potentiis ab u-
              <lb/>
              <note position="right" xlink:label="note-0099-01" xlink:href="note-0099-01a" xml:space="preserve">232.</note>
            traque parte funi ductario applicatis, ſed oblique trahenti-
              <lb/>
              <note position="right" xlink:label="note-0099-02" xlink:href="note-0099-02a" xml:space="preserve">TAB. IX.
                <lb/>
              fig. 4.</note>
            bus per CA & </s>
            <s xml:id="echoid-s2373" xml:space="preserve">CB; </s>
            <s xml:id="echoid-s2374" xml:space="preserve">hæ potentiæ ſunt æquales inter ſe, quia
              <lb/>
            omnis funis trochleam circumdans non quieſcit, niſi ab u-
              <lb/>
            traque parte æqualiter trahatur ; </s>
            <s xml:id="echoid-s2375" xml:space="preserve">ipſum pondus P eſt
              <note symbol="*" position="right" xlink:label="note-0099-03" xlink:href="note-0099-03a" xml:space="preserve">124.</note>
            ſi tertia potentia, & </s>
            <s xml:id="echoid-s2376" xml:space="preserve">ita punctum C tribus potentiis trahi-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s2377" xml:space="preserve">Concipiatur linea CE ad horizontem perpendicularis,
              <lb/>
            & </s>
            <s xml:id="echoid-s2378" xml:space="preserve">linea AE parallela lineæ CB: </s>
            <s xml:id="echoid-s2379" xml:space="preserve">ſi CE ſit ad AE aut AC,
              <lb/>
            (hæ enim duæ lineæ ſunt æquales, propter memoratam æ-
              <lb/>
            qualitatem potentiarum trahentium per CB, CA ,)
              <note symbol="*" position="right" xlink:label="note-0099-04" xlink:href="note-0099-04a" xml:space="preserve">220.</note>
            ſex ad quinque, pondus P ſex librarum a ponderibus Q & </s>
            <s xml:id="echoid-s2380" xml:space="preserve">
              <lb/>
            Q quinque librarum ſuſtinetur; </s>
            <s xml:id="echoid-s2381" xml:space="preserve">cujus ratio patet ex n. </s>
            <s xml:id="echoid-s2382" xml:space="preserve">220.</s>
            <s xml:id="echoid-s2383" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2384" xml:space="preserve">Si extremitas una funis ductarii annectatur clavo, unico
              <lb/>
            pondere ut Q, pondus P ſuſtinetur.</s>
            <s xml:id="echoid-s2385" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div380" type="section" level="1" n="129">
          <head xml:id="echoid-head186" xml:space="preserve">
            <emph style="sc">Experimentum</emph>
          6.</head>
          <p>
            <s xml:id="echoid-s2386" xml:space="preserve">Si pondus P Trochleæ non conjungatur, ſed funibus
              <emph style="sc">Ca</emph>
              <lb/>
              <note position="right" xlink:label="note-0099-05" xlink:href="note-0099-05a" xml:space="preserve">233.</note>
            & </s>
            <s xml:id="echoid-s2387" xml:space="preserve">CB, ei annexis, ſuſtineatur, poterit ſuſtineri poten-
              <lb/>
              <note position="right" xlink:label="note-0099-06" xlink:href="note-0099-06a" xml:space="preserve">TAB. IX.
                <lb/>
              fig. 5.</note>
            tiis duabus inæqualibus; </s>
            <s xml:id="echoid-s2388" xml:space="preserve">formetur ut in Experimento præ-
              <lb/>
            cedenti triangulum
              <emph style="sc">Ca</emph>
            E, & </s>
            <s xml:id="echoid-s2389" xml:space="preserve">ſit AE undecim,
              <emph style="sc">Ca</emph>
            duo-
              <lb/>
            decim cum ſemiſſe, & </s>
            <s xml:id="echoid-s2390" xml:space="preserve">CE duodecim; </s>
            <s xml:id="echoid-s2391" xml:space="preserve">dabitur æquilibri-
              <lb/>
            um, ſi pondera Q & </s>
            <s xml:id="echoid-s2392" xml:space="preserve">Q ſint ad P ut primi numeri ad ulti-
              <lb/>
            mum; </s>
            <s xml:id="echoid-s2393" xml:space="preserve">cujus Experimenti ratio iterum patet ex n. </s>
            <s xml:id="echoid-s2394" xml:space="preserve">220.</s>
            <s xml:id="echoid-s2395" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2396" xml:space="preserve">Hic in tranſitu obſervandum, ex datis inclinationibus fi-
              <lb/>
              <note position="right" xlink:label="note-0099-07" xlink:href="note-0099-07a" xml:space="preserve">234.</note>
            lorum
              <emph style="sc">Ca</emph>
            & </s>
            <s xml:id="echoid-s2397" xml:space="preserve">CB ad horizontem, proportionem </s>
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