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

Table of Notes

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        <div xml:id="echoid-div1461" type="section" level="1" n="356">
          <head xml:id="echoid-head489" xml:space="preserve">SCHOLIUM 4.</head>
          <head xml:id="echoid-head490" style="it" xml:space="preserve">De Retardatione ex ſecunda Cauſâ.</head>
          <p>
            <s xml:id="echoid-s10295" xml:space="preserve">SIAB, logarithmicæ aſymtotos, ſpatium a corpore in fluido percurſum repræſentat,
              <lb/>
              <note position="left" xlink:label="note-0386-01" xlink:href="note-0386-01a" xml:space="preserve">998.</note>
            poterunt velocitates in ſingulis punctis ordinatis repræſentari; </s>
            <s xml:id="echoid-s10296" xml:space="preserve">ſunt enim velo-
              <lb/>
              <note position="left" xlink:label="note-0386-02" xlink:href="note-0386-02a" xml:space="preserve">TAB. XXXVII.
                <lb/>
              fig. 1.</note>
            citatum decrementa, in ſpatiis infinite exiguis æqualibus, AD, DF,
              <lb/>
            FH, &</s>
            <s xml:id="echoid-s10297" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10298" xml:space="preserve">ut ipſæ velocitates , & </s>
            <s xml:id="echoid-s10299" xml:space="preserve">decrementa ordinatarum AC,
              <note symbol="*" position="left" xlink:label="note-0386-03" xlink:href="note-0386-03a" xml:space="preserve">993.</note>
            FG, &</s>
            <s xml:id="echoid-s10300" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10301" xml:space="preserve">ut ipſæ ordinatæ.</s>
            <s xml:id="echoid-s10302" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">983.</note>
          <p>
            <s xml:id="echoid-s10303" xml:space="preserve">Unde ſequitur ſi ſpatia fuerint æqualia, ut AL, LX, XB, velocitates
              <lb/>
              <note position="left" xlink:label="note-0386-05" xlink:href="note-0386-05a" xml:space="preserve">999.</note>
            in punctis A, L, X, B, quæ deſignantur ordinatis AC, LM, XZ, BK,
              <lb/>
            eſſe in progreſſione geometrica ; </s>
            <s xml:id="echoid-s10304" xml:space="preserve">ut notavimus in n. </s>
            <s xml:id="echoid-s10305" xml:space="preserve">961.</s>
            <s xml:id="echoid-s10306" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">980.</note>
          <p>
            <s xml:id="echoid-s10307" xml:space="preserve">Sit A T logarithmicæ aſymtos; </s>
            <s xml:id="echoid-s10308" xml:space="preserve">BY logarithmica; </s>
            <s xml:id="echoid-s10309" xml:space="preserve">BM ejuſdem conti-
              <lb/>
              <note position="left" xlink:label="note-0386-07" xlink:href="note-0386-07a" xml:space="preserve">1000.</note>
            nuatio in ſitu contrario poſita.</s>
            <s xml:id="echoid-s10310" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">TAB. XXXVII.
            <lb/>
          fig. 3.</note>
          <p>
            <s xml:id="echoid-s10311" xml:space="preserve">Si nunc ſumamus ordinatam quamcunque ut TYM; </s>
            <s xml:id="echoid-s10312" xml:space="preserve">Logarithmus ra-
              <lb/>
            tionis TM ad AB eſt AT, qui etiam eſt logarithmus rationis AB ad TY;</s>
            <s xml:id="echoid-s10313" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0386-09" xlink:href="note-0386-09a" xml:space="preserve">982.</note>
            ſunt ergo in continua proportione TM, AB, TY : </s>
            <s xml:id="echoid-s10314" xml:space="preserve">& </s>
            <s xml:id="echoid-s10315" xml:space="preserve">quadratum
              <note symbol="*" position="left" xlink:label="note-0386-10" xlink:href="note-0386-10a" xml:space="preserve">980.</note>
            valet TM x TY: </s>
            <s xml:id="echoid-s10316" xml:space="preserve">ſuntque æqualia eidem quadrato AB, ideoque inter ſe,
              <lb/>
            rectangula omnia ut TM x TY, SX x SL; </s>
            <s xml:id="echoid-s10317" xml:space="preserve">PE x PG, &</s>
            <s xml:id="echoid-s10318" xml:space="preserve">c.</s>
            <s xml:id="echoid-s10319" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10320" xml:space="preserve">Idcirco creſcunt ordinatæ, quæ curvâ BM terminantur, ut minuuntur
              <lb/>
              <note position="left" xlink:label="note-0386-11" xlink:href="note-0386-11a" xml:space="preserve">1001.</note>
            reſpondentes, quæ curva BY terminantur, ſuntque primæ inverſè ut ſe-
              <lb/>
            cundæ.</s>
            <s xml:id="echoid-s10321" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10322" xml:space="preserve">Spatiola infinite exigua velocitate æquabili ſingula percurruntur; </s>
            <s xml:id="echoid-s10323" xml:space="preserve">ſunt ergo
              <lb/>
              <note position="left" xlink:label="note-0386-12" xlink:href="note-0386-12a" xml:space="preserve">1002.</note>
            momenta quibus talia ſpatiola æqualia AC, CP, PQ, &</s>
            <s xml:id="echoid-s10324" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10325" xml:space="preserve">percurruntur
              <lb/>
            inverſè ut velocitates quibus percurruntur , id eſt inverſè ut AB,
              <note symbol="*" position="left" xlink:label="note-0386-13" xlink:href="note-0386-13a" xml:space="preserve">95.</note>
            PE, & </s>
            <s xml:id="echoid-s10326" xml:space="preserve">c ; </s>
            <s xml:id="echoid-s10327" xml:space="preserve">aut directe ut AB, CF, PG &</s>
            <s xml:id="echoid-s10328" xml:space="preserve">c ; </s>
            <s xml:id="echoid-s10329" xml:space="preserve">quæ ſunt ut
              <note symbol="*" position="left" xlink:label="note-0386-14" xlink:href="note-0386-14a" xml:space="preserve">998.</note>
            B b, F f. </s>
            <s xml:id="echoid-s10330" xml:space="preserve">G g &</s>
            <s xml:id="echoid-s10331" xml:space="preserve">c .</s>
            <s xml:id="echoid-s10332" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">1001.</note>
          <p>
            <s xml:id="echoid-s10333" xml:space="preserve">Totum igitur tempus quo linea ut AQ percurritur, omnibus hiſce diffe-
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0386-16" xlink:href="note-0386-16a" xml:space="preserve">983.</note>
            rentiis conjunctim repræſentatur, id eſt, lineâ NH; </s>
            <s xml:id="echoid-s10334" xml:space="preserve">eodem modo OM
              <lb/>
            repræſentat tempus quo QT percurritur: </s>
            <s xml:id="echoid-s10335" xml:space="preserve">ſi vero ſpatia AQ, QT, fue-
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0386-17" xlink:href="note-0386-17a" xml:space="preserve">983.</note>
            rint æqualia, erit NH ad OM, ut QH ad TM , id eſt inverſè ut
              <note symbol="*" position="left" xlink:label="note-0386-18" xlink:href="note-0386-18a" xml:space="preserve">1001.</note>
            ad TY , aut AB ad QK .</s>
            <s xml:id="echoid-s10336" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">980.</note>
          <p>
            <s xml:id="echoid-s10337" xml:space="preserve">Tempora ergo, quibus ſpatia æqualia ſucceſſivè percurruntur, ſunt inverſè
              <lb/>
              <note position="left" xlink:label="note-0386-20" xlink:href="note-0386-20a" xml:space="preserve">1003.</note>
            ut velocitates in fine, aut inverſè ut velocitates in initiis ſpatiorum; </s>
            <s xml:id="echoid-s10338" xml:space="preserve">ut mo-
              <lb/>
            nuimus in n. </s>
            <s xml:id="echoid-s10339" xml:space="preserve">961.</s>
            <s xml:id="echoid-s10340" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10341" xml:space="preserve">Ponamus iterum corpus quod in linea AB movetur, & </s>
            <s xml:id="echoid-s10342" xml:space="preserve">ex ſecunda cauſa
              <lb/>
              <note position="left" xlink:label="note-0386-21" xlink:href="note-0386-21a" xml:space="preserve">1004.</note>
            ſola retardatur, ſit AC velocitas in A, & </s>
            <s xml:id="echoid-s10343" xml:space="preserve">CM logarithmica, quæ in aliis pun-
              <lb/>
              <note position="left" xlink:label="note-0386-22" xlink:href="note-0386-22a" xml:space="preserve">TAB. XXXVII.
                <lb/>
              fig. 2.</note>
            ctis velocitates determinat ; </s>
            <s xml:id="echoid-s10344" xml:space="preserve">ut hac curvâ, & </s>
            <s xml:id="echoid-s10345" xml:space="preserve">tabulis utamur in computa- tionibus neceſſe eſt, ut determinemus magnitudinem ſubtangentis logarithmi-
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0386-23" xlink:href="note-0386-23a" xml:space="preserve">998.</note>
            cæ, quæ uſu venire poteſt in caſu quocunque propoſito, aut quod idem eſt,
              <lb/>
            debemus determinare, in figura data quacunque, quodnam ſpatium ſubtan-
              <lb/>
            gente repræſentatur.</s>
            <s xml:id="echoid-s10346" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10347" xml:space="preserve">Ponamus AC eſſe velocitatem, qua ſi corpus in fluido feratur, reſiſtentia
              <lb/>
            ex ſecunda cauſa ipſi ponderi corporis æqualis ſit.</s>
            <s xml:id="echoid-s10348" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10349" xml:space="preserve">Ergo Corporis pondus, id eſt, preſſio ex gravitate quæ corpus adſcendens retar-
              <lb/>
              <note position="left" xlink:label="note-0386-24" xlink:href="note-0386-24a" xml:space="preserve">1005.</note>
            dat, æqualis eſt preſſioni quam corpus de quo agimus ex reſiſtentia ex ſecunda
              <lb/>
            cauſa patitur. </s>
            <s xml:id="echoid-s10350" xml:space="preserve">Preſſiones hæ ambæ immediate corpus transferunt, quando </s>
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