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

List of thumbnails

< >
231
231 (144) 		232
232 (145)
233
233 (146) 		234
234 (147)
235
235 (148) 		236
236 (149)
237
237 (150) 		238
238 (151)
239
239 (152) 		240
240 (153)
< >
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