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

List of thumbnails

< >
281
281 		282
282
283
283 (181) 		284
284 (182)
285
285 (183) 		286
286 (184)
287
287 (185) 		288
288 (186)
289
289 (187) 		290
290 (188)
< >
page |< < (185) of 824 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1007" type="section" level="1" n="248">
          <pb o="185" file="0263" n="287" rhead="MATHEMATICA. LIB. I. CAP. XXVIII."/>
          <p>
            <s xml:id="echoid-s7288" xml:space="preserve">Circa motum hunc abſolutum plurimorum corporum nota-
              <lb/>
              <note position="right" xlink:label="note-0263-01" xlink:href="note-0263-01a" xml:space="preserve">650.</note>
            mus, ipſum, actione reſpectivâ, qualis eſt omnis colliſio, non
              <lb/>
            mutari; </s>
            <s xml:id="echoid-s7289" xml:space="preserve">ideoque Centrum gravitatis commune variorum
              <lb/>
              <note position="right" xlink:label="note-0263-02" xlink:href="note-0263-02a" xml:space="preserve">651.</note>
            corporum in eâdem lineâ, eâdem velocitate, ante & </s>
            <s xml:id="echoid-s7290" xml:space="preserve">poſt i-
              <lb/>
            ctum moveri. </s>
            <s xml:id="echoid-s7291" xml:space="preserve">Quod in omnibus colliſionibus ante explica-
              <lb/>
            tis obtineri demonſtrabimus.</s>
            <s xml:id="echoid-s7292" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7293" xml:space="preserve">Sint A & </s>
            <s xml:id="echoid-s7294" xml:space="preserve">B centra gravitatis duorum corporum, ſi ad C,
              <lb/>
              <note position="right" xlink:label="note-0263-03" xlink:href="note-0263-03a" xml:space="preserve">
                <emph style="sc">TA. XXV.</emph>
                <lb/>
              fig. 8.</note>
            centrum gravit atis commune, accedant ambo corpora, veloci-
              <lb/>
              <note position="right" xlink:label="note-0263-04" xlink:href="note-0263-04a" xml:space="preserve">652.</note>
            tatibus quæ ſunt inter ſe ut diſtantiæ ſuæ à centro, nempeut
              <lb/>
            AC ad BC, id eſt, inverſe ut maſſæ ipſorum corporum
              <note symbol="*" position="right" xlink:label="note-0263-05" xlink:href="note-0263-05a" xml:space="preserve">134. 143.</note>
            quieſcit in hoc motu centrum gravitatis; </s>
            <s xml:id="echoid-s7295" xml:space="preserve">nam dum eodem
              <lb/>
            tempore percurrunt A a, B b, quæ ſunt ut AC, BC,
              <lb/>
            reſtant a C, b C in eâdem ratione inverſa maſſarum, qua-
              <lb/>
            re & </s>
            <s xml:id="echoid-s7296" xml:space="preserve">in hoc ſitu C eſt commune gravitatis centrum ,
              <note symbol="*" position="right" xlink:label="note-0263-06" xlink:href="note-0263-06a" xml:space="preserve">134.</note>
            in motu hoc non fuit tranſlatum.</s>
            <s xml:id="echoid-s7297" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7298" xml:space="preserve">Eadem demonſtratio poteſt applicari ad motum corpo-
              <lb/>
              <note position="right" xlink:label="note-0263-07" xlink:href="note-0263-07a" xml:space="preserve">653.</note>
            rum à commune gravitatis centro recedentium, velocitati-
              <lb/>
            bus quæ ſunt inverſe ut maſſæ, in quo caſu ergo etiam cen-
              <lb/>
            trum hoc quieſcit.</s>
            <s xml:id="echoid-s7299" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7300" xml:space="preserve">Si varia dentur corpora, ut A, B, D, & </s>
            <s xml:id="echoid-s7301" xml:space="preserve">hæc in eâdem
              <lb/>
              <note position="right" xlink:label="note-0263-08" xlink:href="note-0263-08a" xml:space="preserve">654.</note>
            lineâ mota, accedant omnia ad C commune gravitatis centrum,
              <lb/>
              <note position="right" xlink:label="note-0263-09" xlink:href="note-0263-09a" xml:space="preserve">
                <emph style="sc">TA. XXV.</emph>
                <lb/>
              fig. 9.</note>
            aut recedant ab hoc, velocitatibus quæ in ſingulis corpori-
              <lb/>
            bus ſunt ut diſtantiæ ab hoc centro quieſcit etiam hoc ipſum.
              <lb/>
            </s>
            <s xml:id="echoid-s7302" xml:space="preserve">Nam cum in ſitu A, B, D ſumma productorum maſſarum
              <lb/>
            per diſtantias a C ab una parte hujus puncti æqualis ſit ſimi-
              <lb/>
            li ſummæ ad aliam partem , & </s>
            <s xml:id="echoid-s7303" xml:space="preserve">hoc locum habebit
              <note symbol="*" position="right" xlink:label="note-0263-10" xlink:href="note-0263-10a" xml:space="preserve">141. 143.</note>
            tis omnibus diſtantiis, ut hîc fit, in eadem ratione, quare
              <lb/>
            C manet centrum commune gravitatis ; </s>
            <s xml:id="echoid-s7304" xml:space="preserve">quod ergo
              <note symbol="*" position="right" xlink:label="note-0263-11" xlink:href="note-0263-11a" xml:space="preserve">141.</note>
            ſcit.</s>
            <s xml:id="echoid-s7305" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7306" xml:space="preserve">In hoc caſu, multiplicatis ſingulis maſſis per ſuas veloci-
              <lb/>
            tates, ſumma productorum ab una parte centri gravitatis,
              <lb/>
            æqualis eſt ſimili ſummæ ad aliam partem; </s>
            <s xml:id="echoid-s7307" xml:space="preserve">ponimus enim
              <lb/>
            velocitates ut diſtantias à centro hoc.</s>
            <s xml:id="echoid-s7308" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7309" xml:space="preserve">Ex hiſce ſequentes deducimus concluſiones.</s>
            <s xml:id="echoid-s7310" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7311" xml:space="preserve">Corporum duorum, aut trium, in ſe mutuo directè incur-
              <lb/>
              <note position="right" xlink:label="note-0263-12" xlink:href="note-0263-12a" xml:space="preserve">655.</note>
            rentium ita, ut poſt ictum, ſi non ſint elaſtica, quieſcant, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum