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

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          <pb o="284" file="0384" n="419" rhead="PHYSICES ELEMENTA"/>
        </div>
        <div xml:id="echoid-div1441" type="section" level="1" n="352">
          <head xml:id="echoid-head483" xml:space="preserve">TC, VM:: AC, LM.</head>
          <p>
            <s xml:id="echoid-s10209" xml:space="preserve">Id eſt ordinatæ ſunt inter ſe, ut harum ſingularum differentiæ cum aliis or dina-
              <lb/>
              <note position="left" xlink:label="note-0384-01" xlink:href="note-0384-01a" xml:space="preserve">983.</note>
            tis æqualiter ab his diſtantibus.</s>
            <s xml:id="echoid-s10210" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10211" xml:space="preserve">In puncto quocunque C logarithmicæ CM, ductâ tangente CT, quæ a-
              <lb/>
              <note position="left" xlink:label="note-0384-02" xlink:href="note-0384-02a" xml:space="preserve">TAB. XXXVII.
                <lb/>
              fig. 2.</note>
            ſymtoton ſecat in T, habetur ſubtangens AT; </s>
            <s xml:id="echoid-s10212" xml:space="preserve">& </s>
            <s xml:id="echoid-s10213" xml:space="preserve">eſt hæc conſtans in omnibus
              <lb/>
            curvæ punctis, ductâque in M tangente MV, erunt æquales AT, LV.
              <lb/>
            </s>
            <s xml:id="echoid-s10214" xml:space="preserve">
              <note position="left" xlink:label="note-0384-03" xlink:href="note-0384-03a" xml:space="preserve">984.</note>
            Ut hoc pateat ſint AD, LN infinitæ exiguæ & </s>
            <s xml:id="echoid-s10215" xml:space="preserve">æquales, ductiſque ordina-
              <lb/>
            tis DE, NO, ſint E c, O m, ipſi AB parallelæ. </s>
            <s xml:id="echoid-s10216" xml:space="preserve">Triangula C c E, CAT,
              <lb/>
            ſunt ſimilia, ut & </s>
            <s xml:id="echoid-s10217" xml:space="preserve">M m O & </s>
            <s xml:id="echoid-s10218" xml:space="preserve">MLV; </s>
            <s xml:id="echoid-s10219" xml:space="preserve">ergo</s>
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        </div>
        <div xml:id="echoid-div1444" type="section" level="1" n="353">
          <head xml:id="echoid-head484" xml:space="preserve">C c, c E:: CA, AT, &
            <lb/>
          M m, m O :: ML, LV.</head>
          <p>
            <s xml:id="echoid-s10220" xml:space="preserve">Sunt autem proportionalia antecedentia, in hiſce proportionibus
              <lb/>
            Cc, M m :</s>
            <s xml:id="echoid-s10221" xml:space="preserve">: CA, ML ; </s>
            <s xml:id="echoid-s10222" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s10223" xml:space="preserve">conſequentia c E, m O :</s>
            <s xml:id="echoid-s10224" xml:space="preserve">: AT, LV:</s>
            <s xml:id="echoid-s10225" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0384-04" xlink:href="note-0384-04a" xml:space="preserve">983.</note>
            ſed ſunt æquales c E, m O; </s>
            <s xml:id="echoid-s10226" xml:space="preserve">idcirco & </s>
            <s xml:id="echoid-s10227" xml:space="preserve">AT, LV.</s>
            <s xml:id="echoid-s10228" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10229" xml:space="preserve">Si ſervatis ordinatis AC, DE, FG, HI &</s>
            <s xml:id="echoid-s10230" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10231" xml:space="preserve">ſervataque æqualitate di-
              <lb/>
              <note position="left" xlink:label="note-0384-05" xlink:href="note-0384-05a" xml:space="preserve">985.</note>
            ſtantiarum AD, DF, FH, &</s>
            <s xml:id="echoid-s10232" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10233" xml:space="preserve">diſtantiæ hæ augeantur, aut minuantur,
              <lb/>
              <note position="left" xlink:label="note-0384-06" xlink:href="note-0384-06a" xml:space="preserve">TAB. XXXVII.
                <lb/>
              fig. 1.</note>
            manifeſtum eſt logarithmicam mutari, ſubtangentemque etiam mutari in
              <lb/>
            eadem ratione in qua diſtantiæ hæ mutantur; </s>
            <s xml:id="echoid-s10234" xml:space="preserve">nam in triangulo C c E, ſervato
              <lb/>
              <note position="left" xlink:label="note-0384-07" xlink:href="note-0384-07a" xml:space="preserve">TAB. XXXVII.
                <lb/>
              fig. 2.</note>
            latere C c, ſi mutetur c E, in triangulo ſimili CAT, cujus latus CA ſerva-
              <lb/>
            tur, in eadem ratione cum c E mutabitur AT.</s>
            <s xml:id="echoid-s10235" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10236" xml:space="preserve">Etiam in eadem ratione in qua ſingulæ diſtantiæ minores mutantur, mu-
              <lb/>
              <note position="left" xlink:label="note-0384-08" xlink:href="note-0384-08a" xml:space="preserve">TAB. XXXVII.
                <lb/>
              fig 2.</note>
            tantur ſummæ diſtantiarum quatumcunque: </s>
            <s xml:id="echoid-s10237" xml:space="preserve">id eſt ut mutatur AD ſic & </s>
            <s xml:id="echoid-s10238" xml:space="preserve">
              <lb/>
            mutatur AH, log. </s>
            <s xml:id="echoid-s10239" xml:space="preserve">rationis AC ad HI; </s>
            <s xml:id="echoid-s10240" xml:space="preserve">unde ſequitur, in diverſis logari-
              <lb/>
              <note position="left" xlink:label="note-0384-09" xlink:href="note-0384-09a" xml:space="preserve">986.</note>
            tbmicis ſubtangentes eſſe inter ſe, ut ſunt logarithmi ear undem rationum.</s>
            <s xml:id="echoid-s10241" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10242" xml:space="preserve">In Tabulis logarithmorum quas editas habemus, logarithmus rationis u-
              <lb/>
              <note position="left" xlink:label="note-0384-10" xlink:href="note-0384-10a" xml:space="preserve">987.</note>
            nius ad decem eſt ipſa unitas, & </s>
            <s xml:id="echoid-s10243" xml:space="preserve">logarithmi rationum intermediarum per
              <lb/>
            fractiones decimales exprimuntur, eſtque ſubtangens logarithmicæ tabularum
              <lb/>
            o, 43429. </s>
            <s xml:id="echoid-s10244" xml:space="preserve">44819.</s>
            <s xml:id="echoid-s10245" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1449" type="section" level="1" n="354">
          <head xml:id="echoid-head485" xml:space="preserve">SCHOLIUM 2.</head>
          <head xml:id="echoid-head486" style="it" xml:space="preserve">De Retardatione in genere.</head>
          <p>
            <s xml:id="echoid-s10246" xml:space="preserve">REtardatio, & </s>
            <s xml:id="echoid-s10247" xml:space="preserve">acceleratio, menſuratur, poſitis momentis infinitè exiguis æqua-
              <lb/>
              <note position="left" xlink:label="note-0384-11" xlink:href="note-0384-11a" xml:space="preserve">988.</note>
            libus; </s>
            <s xml:id="echoid-s10248" xml:space="preserve">retardatio quæ a prima cauſa pendet æquabilis dicitur, quia di-
              <lb/>
            minutiones velocitatis æqualibus temporibus ſunt æquales . </s>
            <s xml:id="echoid-s10249" xml:space="preserve">Retardatio
              <note symbol="*" position="left" xlink:label="note-0384-12" xlink:href="note-0384-12a" xml:space="preserve">951.</note>
            ſecunda cauſa dicitur ut quadratum velocitatis, quia diminutiones, in mo-
              <lb/>
            mentis infinitè exiguis æqualibus, ſunt ut hæc quadrata. </s>
            <s xml:id="echoid-s10250" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">954.</note>
          <p>
            <s xml:id="echoid-s10251" xml:space="preserve">In ſingulis autem momentis infinitè exiguis retardationes, & </s>
            <s xml:id="echoid-s10252" xml:space="preserve">accelerationes, ſunt
              <lb/>
              <note position="left" xlink:label="note-0384-14" xlink:href="note-0384-14a" xml:space="preserve">989.</note>
            æquabiles, nam in tali momento mutatio in actione reſpectiva pro nulla ha-
              <lb/>
            beri poteſt; </s>
            <s xml:id="echoid-s10253" xml:space="preserve">&</s>
            <s xml:id="echoid-s10254" xml:space="preserve">, durante integro momento eodem modo variat motus relativus
              <lb/>
            fluidi & </s>
            <s xml:id="echoid-s10255" xml:space="preserve">corporis: </s>
            <s xml:id="echoid-s10256" xml:space="preserve">ergo ſi momenta differant erunt retardationes, & </s>
            <s xml:id="echoid-s10257" xml:space="preserve">accelerationes
              <lb/>
              <note position="left" xlink:label="note-0384-15" xlink:href="note-0384-15a" xml:space="preserve">990.</note>
            ut ipſa momenta; </s>
            <s xml:id="echoid-s10258" xml:space="preserve">id eſt ſunt hæ in momentis infinitè exiguis inæqualibus, in
              <lb/>
            ratione compoſita rationis retar dationum, & </s>
            <s xml:id="echoid-s10259" xml:space="preserve">accelerationum, poſitis momentis æ-
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0384-16" xlink:href="note-0384-16a" xml:space="preserve">988.</note>
            qualibus , & </s>
            <s xml:id="echoid-s10260" xml:space="preserve">rationis ipſorum momentorum inæqualium .</s>
            <s xml:id="echoid-s10261" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">989.</note>
          <p>
            <s xml:id="echoid-s10262" xml:space="preserve">Quando ſpatiola infinite exigua ſunt æqualia, momenta quibus ſingula
              <lb/>
              <note position="left" xlink:label="note-0384-18" xlink:href="note-0384-18a" xml:space="preserve">991.</note>
            ſpatiola percurruntur ſunt inverſè ut velocitates , ergo retardationes, & </s>
            <s xml:id="echoid-s10263" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0384-19" xlink:href="note-0384-19a" xml:space="preserve">95.</note>
            </s>
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