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

Page concordance

< >
Scan Original
231 144
232 145
233 146
234 147
235 148
236 149
237 150
238 151
239 152
240 153
241 146
242 155
243 156
244 157
245 158
246 159
247 160
248
249
250
251 161
252 162
253
254
255
256 163
257 164
258 165
259 166
260 167
< >
page |< < (151) of 824 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div843" type="section" level="1" n="215">
          <p>
            <s xml:id="echoid-s5990" xml:space="preserve">
              <pb o="151" file="0219" n="238" rhead="MATHEMATICA. LIB. I. CAP. XXIII."/>
            tro ſuſpenſionis exerit nullum ibi generet motum . </s>
            <s xml:id="echoid-s5991" xml:space="preserve">Ita autem obex, in
              <note symbol="*" position="right" xlink:label="note-0219-01" xlink:href="note-0219-01a" xml:space="preserve">523.</note>
            incurrit pendulum, diſponi poteſt ut nullam pendulum in puncto ſuſpenſi-
              <lb/>
            onis exerat in retinaculum ſuum preſſionem. </s>
            <s xml:id="echoid-s5992" xml:space="preserve">Punctum penduli quod in hoc
              <lb/>
            caſu in obicem incurrit vocatur centrum percuſſionis.
              <lb/>
            </s>
            <s xml:id="echoid-s5993" xml:space="preserve">
              <note position="right" xlink:label="note-0219-02" xlink:href="note-0219-02a" xml:space="preserve">553.</note>
            </s>
          </p>
          <p style="it">
            <s xml:id="echoid-s5994" xml:space="preserve">Centri hujus hæc eſt proprietas, dari æquilibrium inter actiones quibus corpora
              <lb/>
            ab utraque parte hujus centri in pendulum agunt.</s>
            <s xml:id="echoid-s5995" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5996" xml:space="preserve">Poſſumus ergo conſiderare pendulum quaſivectem, cujus ſuſtentaculum eſt
              <lb/>
            obex, in quem incurrit, poſitus in ipſo centro percuſſionis, & </s>
            <s xml:id="echoid-s5997" xml:space="preserve">æquilibrium
              <lb/>
            dari dum in hunc vectem corpora incurrunt, velocitatibus quibus in pendulo
              <lb/>
            moventur.</s>
            <s xml:id="echoid-s5998" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5999" xml:space="preserve">Penduli A I formati corporibus A & </s>
            <s xml:id="echoid-s6000" xml:space="preserve">D, junctis lineâ inflexi, ſuſpenſâ in
              <lb/>
              <note position="right" xlink:label="note-0219-03" xlink:href="note-0219-03a" xml:space="preserve">554.</note>
            I, centrum percuſſionis erit H, ſi poſitis, vecte cujus ſuſtentaculum eſt H,
              <lb/>
              <note position="right" xlink:label="note-0219-04" xlink:href="note-0219-04a" xml:space="preserve">TAB. XXIII.
                <lb/>
              fig. 1.</note>
            & </s>
            <s xml:id="echoid-s6001" xml:space="preserve">in hunc incurrentibus corporibus A & </s>
            <s xml:id="echoid-s6002" xml:space="preserve">D, in ipſis punctis A & </s>
            <s xml:id="echoid-s6003" xml:space="preserve">D, velo-
              <lb/>
            citatibus quas in pendulo habent, detur inter haſce actiones æquilibrium; </s>
            <s xml:id="echoid-s6004" xml:space="preserve">tunc
              <lb/>
            enim punctum I penduli ullo motu affici non poteſt, aut ſiretineatur, ullam exe-
              <lb/>
            rere preſſionem.</s>
            <s xml:id="echoid-s6005" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6006" xml:space="preserve">Ut caſum æquilibrii determinemus poſitis variis corporibus, ſingulorum
              <lb/>
            actiones determinari debent, id eſt, ſunt hæ actiones conferendæ inter ſe.</s>
            <s xml:id="echoid-s6007" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6008" xml:space="preserve">Relictâ nunc penduli conſideratione, ad ſolum vectem attendendo; </s>
            <s xml:id="echoid-s6009" xml:space="preserve">ſit Cor-
              <lb/>
              <note position="right" xlink:label="note-0219-05" xlink:href="note-0219-05a" xml:space="preserve">555.</note>
            poris A velocitas m, & </s>
            <s xml:id="echoid-s6010" xml:space="preserve">a diſtantia AH; </s>
            <s xml:id="echoid-s6011" xml:space="preserve">Corporis D velocitas n, & </s>
            <s xml:id="echoid-s6012" xml:space="preserve">d diſtantia
              <lb/>
            HD. </s>
            <s xml:id="echoid-s6013" xml:space="preserve">Eodem modo in vectem agit corpus A, utrum in A ad partem M, aut in
              <lb/>
            L ad partem N, eadem velocitate in hunc incurrat poſitis HA & </s>
            <s xml:id="echoid-s6014" xml:space="preserve">HL æqualibus.
              <lb/>
            </s>
            <s xml:id="echoid-s6015" xml:space="preserve">Actio etiam erit eadem ſi, ſervatis corporum velocitatibus, concipiamus hæc ro-
              <lb/>
            tari circa centrum H & </s>
            <s xml:id="echoid-s6016" xml:space="preserve">ità agitata in vectem incurrere per e L & </s>
            <s xml:id="echoid-s6017" xml:space="preserve">f D. </s>
            <s xml:id="echoid-s6018" xml:space="preserve">Conti-
              <lb/>
            nuetur Hfin G, ut HG & </s>
            <s xml:id="echoid-s6019" xml:space="preserve">He, aut HA, ſint æquales, æquilibrium dabitur,
              <lb/>
            ſi velocitas puncti eſe habeat ad velocitatem puncti G, ut Ddd ad Aaa , id
              <note symbol="*" position="right" xlink:label="note-0219-06" xlink:href="note-0219-06a" xml:space="preserve">533.</note>
            Ddd, Aaa:</s>
            <s xml:id="echoid-s6020" xml:space="preserve">: m, {an/d}, hæc enim eſt velocitas-puncti G; </s>
            <s xml:id="echoid-s6021" xml:space="preserve">ergo Aam = Ddn;
              <lb/>
            </s>
            <s xml:id="echoid-s6022" xml:space="preserve">unde patet actionem ſequi rationem producti maſſæ corporis per velocitatem, & </s>
            <s xml:id="echoid-s6023" xml:space="preserve">di-
              <lb/>
            ſtantiam a fulcro.</s>
            <s xml:id="echoid-s6024" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6025" xml:space="preserve">In pendulo velocitas ſequitur rationem diſtantiæ à puncto ſuſpenſionis;
              <lb/>
            </s>
            <s xml:id="echoid-s6026" xml:space="preserve">& </s>
            <s xml:id="echoid-s6027" xml:space="preserve">diſtantia a fulcro, eſt diſtantia a centro percuſſionis; </s>
            <s xml:id="echoid-s6028" xml:space="preserve">ergo actio corporis
              <lb/>
            ſequitur rationem producti corporis per ſuas diſtantias a centris ſuſpenſionis
              <lb/>
            & </s>
            <s xml:id="echoid-s6029" xml:space="preserve">percuſſionis, daturque æquilibrium inter actiones ab utraque parte centri
              <lb/>
            percuſſionis, quando producta hæc ab utraque parte hujus centri ſunt æqualia,
              <lb/>
            quam eandem cùm centrum oſcillationis habeat proprietatem , ſequitur
              <note position="right" xlink:label="note-0219-07" xlink:href="note-0219-07a" xml:space="preserve">556.</note>
            cum centro percuſſionis coincidere.
              <lb/>
            </s>
            <s xml:id="echoid-s6030" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0219-08" xlink:href="note-0219-08a" xml:space="preserve">309.</note>
            </s>
          </p>
        </div>
        <div xml:id="echoid-div852" type="section" level="1" n="216">
          <head xml:id="echoid-head307" xml:space="preserve">CAPUT XXIV.</head>
          <head xml:id="echoid-head308" style="it" xml:space="preserve">De congreſſu corporum Elaſticorum.</head>
          <p>
            <s xml:id="echoid-s6031" xml:space="preserve">Corpora elaſtica, poſt ictum, ut jam notavimus, ſeparan-
              <lb/>
            tur, ſed vi diverſa in circumſtantiis ſimilibus; </s>
            <s xml:id="echoid-s6032" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0219-09" xlink:href="note-0219-09a" xml:space="preserve">483.</note>
            in variis corporibus elaſticitas differt.</s>
            <s xml:id="echoid-s6033" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum