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

Table of Notes

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              <pb o="49" file="0093" n="100" rhead="MATHEMATICA. LIB. I. CAP. XV."/>
            dus ſuperet, adaugeri debet; </s>
            <s xml:id="echoid-s2213" xml:space="preserve">pontentiâ tamen minimâ pon-
              <lb/>
            dus maximum elevatur. </s>
            <s xml:id="echoid-s2214" xml:space="preserve">Longitudo ſcytalæ ED duplicari,
              <lb/>
            aut etiam ulterius augeri poteſt, quo actio potentiæ dupli-
              <lb/>
            catur, aut magis augetur; </s>
            <s xml:id="echoid-s2215" xml:space="preserve">in hoc caſu capillo tenuiſſimo ho-
              <lb/>
            mo fortis ſuperatur.</s>
            <s xml:id="echoid-s2216" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2217" xml:space="preserve">Innumeræ aliæ Machinæ compoſitæ conſtrui poſſunt,
              <lb/>
            quarum vires eodem modo computatione determinantur,
              <lb/>
            ope regulæ initio hujus capitis memoratæ, aut etiam compa-
              <lb/>
            rando viam percurſam a potentiâ cum viâ à pondere, aut
              <lb/>
            alio quocumque impedimento, percurſâ; </s>
            <s xml:id="echoid-s2218" xml:space="preserve">harum enim ratio
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            eſt ratio inverſa potentiæ & </s>
            <s xml:id="echoid-s2219" xml:space="preserve">ponderis autimpedimenti, quando
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            potentiæ actio cum reſiſtentiâ impedimenti æquè pollet.</s>
            <s xml:id="echoid-s2220" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2221" xml:space="preserve">Preſſiones, quæ contrarie agentes æquè pollent, ſemper
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            ſunt æquales; </s>
            <s xml:id="echoid-s2222" xml:space="preserve">ſi ergo potentia intenſitate minor eſt impe-
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            dimento, reſpectu viæ percurſæ illud ſuperare debet, & </s>
            <s xml:id="echoid-s2223" xml:space="preserve">
              <lb/>
            quidem toties quoties ab illo intenſitate ſuperatur; </s>
            <s xml:id="echoid-s2224" xml:space="preserve">nullo e-
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            nim alio reſpectu preſſionum effectus differre poſſunt, etiam
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            nulla alia compenſatio dari poteſt.</s>
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        <div xml:id="echoid-div359" type="section" level="1" n="122">
          <head xml:id="echoid-head177" xml:space="preserve">CAPUT XV.</head>
          <head xml:id="echoid-head178" xml:space="preserve">De Potentiis obliquis.</head>
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            <s xml:id="echoid-s2226" xml:space="preserve">Detur punctum A, quod tribus potentiis filis applicatis
              <lb/>
              <note position="right" xlink:label="note-0093-01" xlink:href="note-0093-01a" xml:space="preserve">220.</note>
            per AB,
              <emph style="sc">A</emph>
            E, & </s>
            <s xml:id="echoid-s2227" xml:space="preserve">
              <emph style="sc">A</emph>
            D, trabitur, quieſcit, ſi poten-
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              <note position="right" xlink:label="note-0093-02" xlink:href="note-0093-02a" xml:space="preserve">TAB. X.
                <lb/>
              fig. 1.</note>
            tiæ fuerint inter ſe ut latera trianguli formati lineis juxta
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            directiones potentiarum poſitis; </s>
            <s xml:id="echoid-s2228" xml:space="preserve">id eſt, ſi potentiæ fuerint
              <lb/>
            inter ſe ut latera trianguli A Db. </s>
            <s xml:id="echoid-s2229" xml:space="preserve">In quo caſu poſitis AB,
              <lb/>
            AE & </s>
            <s xml:id="echoid-s2230" xml:space="preserve">AD, reſpectivè ut preſſiones per has lineas agentes,
              <lb/>
            ſi duabus ut AD & </s>
            <s xml:id="echoid-s2231" xml:space="preserve">
              <emph style="sc">A</emph>
            E formetur parallelogrammum, pa-
              <lb/>
            tet tertiam
              <emph style="sc">Ba</emph>
            continuatam fore parallelogrammi diagona-
              <lb/>
            lem & </s>
            <s xml:id="echoid-s2232" xml:space="preserve">AB, Ab, æquales eſſe inter ſe.</s>
            <s xml:id="echoid-s2233" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2234" xml:space="preserve">Punctum autem A in hoc caſu quieſcere ut demonſtremus,
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            concipere debemus, ſepoſitâ potentiâ per
              <emph style="sc">A</emph>
            B, preſſiones per
              <lb/>
            AE & </s>
            <s xml:id="echoid-s2235" xml:space="preserve">AD deſtrui, punctumque quieſcere, actione quacunque,
              <lb/>
            & </s>
            <s xml:id="echoid-s2236" xml:space="preserve">in hanc actionem inquirendum eſt. </s>
            <s xml:id="echoid-s2237" xml:space="preserve">Sint lineæ minimæ A d,
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            A e, inter ſe ut A D, AE, id eſt, ut preſſiones juxta haſce lineas
              <lb/>
            agentes;</s>
            <s xml:id="echoid-s2238" xml:space="preserve">æquali tempore punctum A per haſce lineas </s>
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