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

Table of contents

< >
[261.] SCHOLIUM.
Page: 304 (199)
[262.] FINIS LIBRI PRIMI.
Page: 304 (199)
[263.] PHYSICES ELEMENTA MATHEMATICA EXPERIMENTIS CONFIRMATA. LIBER II. Pars I. de Gravitate, & Preſſione Fluidorum. CAPUT I. De Gravitate partium Fluidorum, & illius Effectu in ipſis Fluidis.
Page: 305 (200)
[264.] Bilanx Hydrostatica.
Page: 309 (201)
[265.] Experimentum 1.
Page: 309 (201)
[266.] Experimentum 2.
Page: 310 (202)
[267.] Experimentum 3.
Page: 311 (203)
[268.] Experimentum 4.
Page: 311 (203)
[269.] Experimentum. 5.
Page: 312 (204)
[270.] Experimentum 6.
Page: 312 (204)
[271.] CAPUT II. De Actione Fluidorum in Fundos, Latera, & Opercula, vaſorum quibus continentur.
Page: 312 (204)
[272.] Machina
Page: 313 (205)
[273.] Experimentum 1.
Page: 314 (206)
[274.] Experimentum 2.
Page: 318 (207)
[275.] Experimentum 3.
Page: 318 (207)
[276.] Machina Qua demonſtratur Preſſio Fluidorum lateralis.
Page: 319 (208)
[277.] Experimentum 4.
Page: 319 (208)
[278.] Experimentum 5.
Page: 320 (209)
[279.] Follis hydrostaticus.
Page: 320 (209)
[280.] Experimentum 6.
Page: 320 (209)
[281.] CAPUT III. De Solidis fluidis immerſis.
Page: 322 (211)
[282.] Definitio 1.
Page: 322 (211)
[283.] Definitio. 2.
Page: 322 (211)
[284.] Definitio. 3.
Page: 322 (211)
[285.] Definitio. 4.
Page: 322 (211)
[286.] Experimentum 1.
Page: 323 (212)
[287.] Experimentum 2.
Page: 323 (212)
[288.] Experimentum 3.
Page: 325 (214)
[289.] Definitio 5.
Page: 325 (214)
[290.] Experimentum 4.
Page: 329 (215)
< >
page |< < (145) of 824 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div810" type="section" level="1" n="211">
          <p>
            <s xml:id="echoid-s5725" xml:space="preserve">
              <pb o="145" file="0213" n="232" rhead="MATHEMATICA. LIB. I. CAP XXIII."/>
              <emph style="ol">Bbb + Ddd</emph>
            x aa; </s>
            <s xml:id="echoid-s5726" xml:space="preserve">habemus {
              <emph style="ol">Aaa + Ccc</emph>
            x
              <emph style="ol">Bbb + Ddd</emph>
            x rr/
              <emph style="ol">Aaa + Ccc</emph>
            x bb +
              <emph style="ol">Bbb + D dd</emph>
            x aa} vim
              <lb/>
              <note position="right" xlink:label="note-0213-01" xlink:href="note-0213-01a" xml:space="preserve">537.</note>
            amiſſam data velocitate reſpectivar.</s>
            <s xml:id="echoid-s5727" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5728" xml:space="preserve">Si Corpora memorata A & </s>
            <s xml:id="echoid-s5729" xml:space="preserve">B, cum reliquis circa centra I & </s>
            <s xml:id="echoid-s5730" xml:space="preserve">H agitata, ve-
              <lb/>
              <note position="right" xlink:label="note-0213-02" xlink:href="note-0213-02a" xml:space="preserve">538.</note>
            locitatibus quibuſcunque in ſe mutuo incurrant directè, poſt ictum ambo eâ-
              <lb/>
            dem velocitate feruntur , & </s>
            <s xml:id="echoid-s5731" xml:space="preserve">ſeparantur non ex actione corporum, ſed
              <note symbol="*" position="right" xlink:label="note-0213-03" xlink:href="note-0213-03a" xml:space="preserve">484.</note>
            circa centra diverſa H & </s>
            <s xml:id="echoid-s5732" xml:space="preserve">I moventur.</s>
            <s xml:id="echoid-s5733" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5734" xml:space="preserve">Concipiamus dari punctum quod eadem velocitate fertur, qua corpora poſt
              <lb/>
            ictum ante ſeparationem ſeruntur, & </s>
            <s xml:id="echoid-s5735" xml:space="preserve">juxta eandem directionem.</s>
            <s xml:id="echoid-s5736" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5737" xml:space="preserve">Reſpectu hujus puncti corpora poſt impactionem quieſcunt; </s>
            <s xml:id="echoid-s5738" xml:space="preserve">ideo reſpectu
              <lb/>
            ipſius anteictum contrariis velocitatibus movebantur in ratione
              <emph style="ol">Bbb + Ddd</emph>
              <lb/>
            x aa ad
              <emph style="ol">Aaa + Ccc</emph>
            x bb , haſque velocitates amittunt, cum reſpectu
              <note symbol="*" position="right" xlink:label="note-0213-04" xlink:href="note-0213-04a" xml:space="preserve">533.</note>
            poſt ictum quieſcant, quare hæ ipſæ velocitates ſunt mutationes, quæ ex ictu
              <lb/>
            in velocitatibus contingunt, quæ ergo mutationes ſunt in memoratà ratione;
              <lb/>
            </s>
            <s xml:id="echoid-s5739" xml:space="preserve">& </s>
            <s xml:id="echoid-s5740" xml:space="preserve">componendo
              <emph style="ol">Aaa + Ccc</emph>
            x bb +
              <emph style="ol">Bbb + Ddd</emph>
            x aa ad
              <emph style="ol">Aaa + Ccc</emph>
            x bb
              <lb/>
            ut ſumma mutationum, id eſt velocitas reſpectiva, ad mutationem in veloci-
              <lb/>
            tate corporis B.</s>
            <s xml:id="echoid-s5741" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5742" xml:space="preserve">Si nunc velocitas corporis A dicatur p; </s>
            <s xml:id="echoid-s5743" xml:space="preserve">& </s>
            <s xml:id="echoid-s5744" xml:space="preserve">q velocitas corporis B, poſita
              <lb/>
            hac minori; </s>
            <s xml:id="echoid-s5745" xml:space="preserve">velocitas reſpectiva erit p-q ſi motus eandem partem verſus
              <lb/>
            dirigantur, & </s>
            <s xml:id="echoid-s5746" xml:space="preserve">mutatio velocitatis corporis B, detegitur
              <lb/>
            {
              <emph style="ol">Aaa + Ccc</emph>
            x bbp -
              <emph style="ol">Aaa + Ccc</emph>
            x bbq/
              <emph style="ol">Aaa + Ccc</emph>
            x bb +
              <emph style="ol">Bbb + Ddd</emph>
            x aa} quæ mutatio eſt velocitas
              <lb/>
            acquiſita; </s>
            <s xml:id="echoid-s5747" xml:space="preserve">quia minor velocitas in motibus conſpirantibus augetur: </s>
            <s xml:id="echoid-s5748" xml:space="preserve">quare ſi
              <lb/>
            addatur ipſi velocitati q habemus velocitatem amborum corporum
              <lb/>
            poſt ictum; </s>
            <s xml:id="echoid-s5749" xml:space="preserve">quæ ergo eſt {
              <emph style="ol">Aaa + Ccc</emph>
            x bbp +
              <emph style="ol">Bbb + Ddd</emph>
            x aaq/
              <emph style="ol">Aaa + Ccc</emph>
            x bb +
              <emph style="ol">Bbb + Ddd</emph>
            x aa}.
              <lb/>
            </s>
            <s xml:id="echoid-s5750" xml:space="preserve">
              <note position="right" xlink:label="note-0213-05" xlink:href="note-0213-05a" xml:space="preserve">539.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s5751" xml:space="preserve">Si motus in contrariam partem dirigantur velocitas reſpectiva eſt p + q & </s>
            <s xml:id="echoid-s5752" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0213-06" xlink:href="note-0213-06a" xml:space="preserve">540.</note>
            velocitas poſt ictum ſimili ratiocinio detegitur
              <lb/>
            {
              <emph style="ol">Aaa + Ccc</emph>
            x bbp -
              <emph style="ol">Bbb + Ddd</emph>
            x aaq/
              <emph style="ol">Aaa + Ccc</emph>
            x bb +
              <emph style="ol">Bbb + Ddd</emph>
            x aa} ſubtracto nempe in nu-
              <lb/>
            meratore producto minore ex majore.</s>
            <s xml:id="echoid-s5753" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5754" xml:space="preserve">Clarè patet non intereſſe utrum in hac colliſione corpora, quæ eidem lineæ
              <lb/>
              <note position="right" xlink:label="note-0213-07" xlink:href="note-0213-07a" xml:space="preserve">541.</note>
            juguntur, ad eandem partem dentur centri circa quod linea movetur, an ad
              <lb/>
            partes diverſas, nam eodem niodo corpus movetur, à quacunque parte centri
              <lb/>
            detur, ſimodo diſtantia ab hoc ſit eadem, vim etiam centrifugam, qua corpora
              <lb/>
            a centro recedere conantur, & </s>
            <s xml:id="echoid-s5755" xml:space="preserve">actiones quas, dum concurrunt, in retinacu-
              <lb/>
            la exerunt, non hîc conſiderari debere, ſatis manifeſtum eſt .</s>
            <s xml:id="echoid-s5756" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">523.</note>
          <p>
            <s xml:id="echoid-s5757" xml:space="preserve">Demonſtrata hæc ad numerum quemcunque corporum poſſunt applicari, & </s>
            <s xml:id="echoid-s5758" xml:space="preserve">u-
              <lb/>
              <note position="right" xlink:label="note-0213-09" xlink:href="note-0213-09a" xml:space="preserve">542.</note>
            niverſales regulæ ex demonſtratis quam facillime illiciuntur.</s>
            <s xml:id="echoid-s5759" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5760" xml:space="preserve">Videmus etiam quid obtineat, Si corpus in lineâ rectâ motum directè in aliudin-
              <lb/>
              <note position="right" xlink:label="note-0213-10" xlink:href="note-0213-10a" xml:space="preserve">543.</note>
            currat quod cum aliis lineæ rectæ, circa centrum mobili, cohæret; </s>
            <s xml:id="echoid-s5761" xml:space="preserve">Corpus enim il-
              <lb/>
            lud in linea recta motum agit quaſi lineæ rectæ, circa punctum quodcunque
              <lb/>
            mobili, adhæreret.</s>
            <s xml:id="echoid-s5762" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum