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

Page concordance

< >
Scan Original
421 286
422
423
424
425 287
426 288
427 289
428 290
429 291
430 292
431 293
432 294
433 295
434 296
435
436
437
438 297
439 298
440 299
441 300
442 301
443 302
444 303
445 304
446 305
447 306
448 307
449 308
450
< >
page |< < (286) of 824 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1455" type="section" level="1" n="355">
          <pb o="286" file="0386" n="421" rhead="PHYSICES ELEMENTA"/>
        </div>
        <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>
          </p>
        </div>
      </text>
    </echo>
Impressum