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

Page concordance

< >
Scan Original
401
402
403
404 269
405 270
406 271
407 272
408 273
409 274
410 275
411 276
412 277
413 278
414 279
415 280
416 281
417 282
418 283
419 284
420 285
421 286
422
423
424
425 287
426 288
427 289
428 290
429 291
430 292
< >
page |< < (283) of 824 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1431" type="section" level="1" n="347">
          <p>
            <s xml:id="echoid-s10161" xml:space="preserve">
              <pb o="283" file="0383" n="418" rhead="MATHEMATICA. LIB. II. CAP XII."/>
            ce notantur, deteguntur altitudines ad quas pendulum ad-
              <lb/>
            ſcendit, ſi variis vicibus ab eadem altitudine dimittatur,
              <lb/>
            & </s>
            <s xml:id="echoid-s10162" xml:space="preserve">index alter mutetur, donec ad hunc pendulum in adſcen-
              <lb/>
            ſu appellat, ſed remoto indice ad ipſum non pertingat.</s>
            <s xml:id="echoid-s10163" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10164" xml:space="preserve">Differentiæ arcuum adſcenſu & </s>
            <s xml:id="echoid-s10165" xml:space="preserve">deſcenſu deſcriptorum
              <lb/>
            erunt proxime inter ſe ut quadrata arcuum deſcenſu de-
              <lb/>
            ſcriptorum, ſi ad hoc attendamus æqualiter vibrationes ſin-
              <lb/>
            gulas eſſe minuendas, propter reſiſtentiam ex partium
              <lb/>
            cohæſione.</s>
            <s xml:id="echoid-s10166" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10167" xml:space="preserve">Notandum autem pendulum non eſſe dimittendum niſi
              <lb/>
            quieſcente aquæ ſuperficie.</s>
            <s xml:id="echoid-s10168" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1433" type="section" level="1" n="348">
          <head xml:id="echoid-head479" xml:space="preserve">SCHOLIUM 1.
            <lb/>
          De Logarithmica.</head>
          <p>
            <s xml:id="echoid-s10169" xml:space="preserve">QUæ in ſcholiis ſequentibus de retardationibus corporum, in fluidis mo-
              <lb/>
            torum, demonſtrantur, lineæ logarithmicæ proprietates profundamen-
              <lb/>
            to habent. </s>
            <s xml:id="echoid-s10170" xml:space="preserve">Formationem ideò hujus curvæ, proprietatesque quibus in ſe-
              <lb/>
            quentibus indigemus, in hocſcholio exponam.</s>
            <s xml:id="echoid-s10171" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10172" xml:space="preserve">Sit AB recta, & </s>
            <s xml:id="echoid-s10173" xml:space="preserve">in hac partes infinite exiguæ AD, DF, FH, &</s>
            <s xml:id="echoid-s10174" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10175" xml:space="preserve">æ-
              <lb/>
              <note position="right" xlink:label="note-0383-01" xlink:href="note-0383-01a" xml:space="preserve">979.</note>
            quales inter ſe. </s>
            <s xml:id="echoid-s10176" xml:space="preserve">Sint præterea ad AB, perpendiculares AC, DE, FG,
              <lb/>
              <note position="right" xlink:label="note-0383-02" xlink:href="note-0383-02a" xml:space="preserve">TAB, XXXVII.
                <lb/>
              fig. 1.</note>
            HI, &</s>
            <s xml:id="echoid-s10177" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10178" xml:space="preserve">infinite parum differentes, & </s>
            <s xml:id="echoid-s10179" xml:space="preserve">quæ ſint progreſſione continua ge-
              <lb/>
            ometrica. </s>
            <s xml:id="echoid-s10180" xml:space="preserve">Si nunc curva tranſeat per extremitates C, E, G, I, &</s>
            <s xml:id="echoid-s10181" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10182" xml:space="preserve">erit hæc
              <lb/>
            logarithmica, cujus Aſymtotos erit AB, ad quam continuo curva acce-
              <lb/>
            dit, & </s>
            <s xml:id="echoid-s10183" xml:space="preserve">ad quam nunquam pertingere poteſt.</s>
            <s xml:id="echoid-s10184" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10185" xml:space="preserve">Eadem datur ratio inter ordinatas duas quaſcunque, ſi inter ipſas eadem detur
              <lb/>
              <note position="right" xlink:label="note-0383-03" xlink:href="note-0383-03a" xml:space="preserve">983.</note>
            diſtantia. </s>
            <s xml:id="echoid-s10186" xml:space="preserve">AB ſe habet HI, ut LM ad RS, ſi diſtantia AH diſtantiæ LR
              <lb/>
            fuerit æqualis. </s>
            <s xml:id="echoid-s10187" xml:space="preserve">Ratio enim quæ datur inter AC & </s>
            <s xml:id="echoid-s10188" xml:space="preserve">HI componitur ex ra-
              <lb/>
            tionibus AC ad DE, DE ad FG, & </s>
            <s xml:id="echoid-s10189" xml:space="preserve">FG ad HI; </s>
            <s xml:id="echoid-s10190" xml:space="preserve">ratio LM ad RS,
              <lb/>
            componitur ex rationibus LM ad NO, NO ad PQ, & </s>
            <s xml:id="echoid-s10191" xml:space="preserve">PQ ad RS: </s>
            <s xml:id="echoid-s10192" xml:space="preserve">ra-
              <lb/>
            tiones componentes ſingulæ ſunt æquales inter ſe ,
              <note symbol="*" position="right" xlink:label="note-0383-04" xlink:href="note-0383-04a" xml:space="preserve">979.</note>
            componentium in utroque caſu idem eſt, propter æquales diſtantias AH,
              <lb/>
            LR; </s>
            <s xml:id="echoid-s10193" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s10194" xml:space="preserve">æquales ſunt rationes compoſitæ. </s>
            <s xml:id="echoid-s10195" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s10196" xml:space="preserve">D. </s>
            <s xml:id="echoid-s10197" xml:space="preserve">E.</s>
            <s xml:id="echoid-s10198" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1436" type="section" level="1" n="349">
          <head xml:id="echoid-head480" xml:space="preserve">
            <emph style="sc">Definitio</emph>
          1.</head>
          <p style="it">
            <s xml:id="echoid-s10199" xml:space="preserve">Logarithmus ordinatæ cujuſcunque dicitur abſciſſa ipſi reſpondens, ubicunque ini-
              <lb/>
              <note position="right" xlink:label="note-0383-05" xlink:href="note-0383-05a" xml:space="preserve">981.</note>
            tium abſciſſarum ponatur.</s>
            <s xml:id="echoid-s10200" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1438" type="section" level="1" n="350">
          <head xml:id="echoid-head481" xml:space="preserve">
            <emph style="sc">Definitio</emph>
          2.</head>
          <p style="it">
            <s xml:id="echoid-s10201" xml:space="preserve">Diſtantia inter duas ordinatas vocatur logarithmus rationis quæ inter ipſas da-
              <lb/>
              <note position="right" xlink:label="note-0383-06" xlink:href="note-0383-06a" xml:space="preserve">982.</note>
            tur. </s>
            <s xml:id="echoid-s10202" xml:space="preserve">Eſtque differentia logarithmorum ipſarum ordinatarum.</s>
            <s xml:id="echoid-s10203" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10204" xml:space="preserve">Poſitis iterum AH & </s>
            <s xml:id="echoid-s10205" xml:space="preserve">LR æqualibus habemus</s>
          </p>
        </div>
        <div xml:id="echoid-div1440" type="section" level="1" n="351">
          <head xml:id="echoid-head482" xml:space="preserve">AC, HI :: LM, RS ; & dividendo</head>
          <note symbol="*" position="right" xml:space="preserve">982.</note>
          <p>
            <s xml:id="echoid-s10206" xml:space="preserve">AC - HI = TC, AC :</s>
            <s xml:id="echoid-s10207" xml:space="preserve">: LM - RS = VM, LM. </s>
            <s xml:id="echoid-s10208" xml:space="preserve">Quare eſt</s>
          </p>
        </div>
      </text>
    </echo>
Impressum