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

Table of figures

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            <s xml:id="echoid-s6412" xml:space="preserve">Ex quibus quoque ſequitur, quando obſtaculo non omnino immobili inſi ſtit E-
              <lb/>
              <note position="left" xlink:label="note-0232-01" xlink:href="note-0232-01a" xml:space="preserve">593.</note>
            laſterium hoc ad partem oppoſitam exerere vim ſuam totam, demtâ illâ, quâ obſtacu-
              <lb/>
            lum poteſt movere.</s>
            <s xml:id="echoid-s6413" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6414" xml:space="preserve">Si hæc applicemus ad caſum memoratum, facile videmus corpori B com-
              <lb/>
              <note position="left" xlink:label="note-0232-02" xlink:href="note-0232-02a" xml:space="preserve">594.</note>
            municari duos gradus vis, quibus partes elaſticæ fuere flexæ, & </s>
            <s xml:id="echoid-s6415" xml:space="preserve">prætereaim-
              <lb/>
            preſſionem qua elaſterium fuit translatum, durante expanſione , quæ
              <note symbol="*" position="left" xlink:label="note-0232-03" xlink:href="note-0232-03a" xml:space="preserve">591.</note>
            ſio eſt actio corporis A in Elaſterium, & </s>
            <s xml:id="echoid-s6416" xml:space="preserve">valet vim a corpore A in hac a-
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            ctione amiſſam . </s>
            <s xml:id="echoid-s6417" xml:space="preserve">Amiſit autem A unum gradum vis, qui ergo ipſi B,
              <note symbol="*" position="left" xlink:label="note-0232-04" xlink:href="note-0232-04a" xml:space="preserve">478.</note>
            ter duos memoratos, fuit communicatus; </s>
            <s xml:id="echoid-s6418" xml:space="preserve">accepit ergo B tres gradus vis, qui
              <lb/>
            additi uni gradui, quem ante elaſterii actionem habebat, dant quatuor gra-
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            dus vis. </s>
            <s xml:id="echoid-s6419" xml:space="preserve">Quod explicandum erat.</s>
            <s xml:id="echoid-s6420" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6421" xml:space="preserve">Ratiocinium omnino ſimile eſt in aliis caſibus, in quibus poſt ſeparatio-
              <lb/>
              <note position="left" xlink:label="note-0232-05" xlink:href="note-0232-05a" xml:space="preserve">595.</note>
            nem ad eandem partem corpora tendunt, aut unum quieſcit; </s>
            <s xml:id="echoid-s6422" xml:space="preserve">ſi autem ad
              <lb/>
            partes propoſitas poſt ictum moveantur ex iiſdem principiis difficultas tolli-
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            tur, uthoc patebit exemplo.</s>
            <s xml:id="echoid-s6423" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6424" xml:space="preserve">Sit corpus A cujus maſſa eſt I. </s>
            <s xml:id="echoid-s6425" xml:space="preserve">quod velocitate 6.</s>
            <s xml:id="echoid-s6426" xml:space="preserve">, id eſt, cum vi 36. </s>
            <s xml:id="echoid-s6427" xml:space="preserve">,
              <note position="left" xlink:label="note-0232-06" xlink:href="note-0232-06a" xml:space="preserve">596.</note>
            currit in corpus duplum quieſcens B; </s>
            <s xml:id="echoid-s6428" xml:space="preserve">ponimus corpora perfecte elaſtica.
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            </s>
            <s xml:id="echoid-s6429" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0232-07" xlink:href="note-0232-07a" xml:space="preserve">470.</note>
            Poſt ictum B habebit velocitatem 4, id eſt, vim 32. </s>
            <s xml:id="echoid-s6430" xml:space="preserve">& </s>
            <s xml:id="echoid-s6431" xml:space="preserve">A redibit velocitate 2,
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              <note symbol="*" position="left" xlink:label="note-0232-08" xlink:href="note-0232-08a" xml:space="preserve">519. 567.
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              568.</note>
            habebitque vim. </s>
            <s xml:id="echoid-s6432" xml:space="preserve">4 . </s>
            <s xml:id="echoid-s6433" xml:space="preserve">Hoc, jam ante demonſtratum, nunc eſt illuſtrandum.</s>
            <s xml:id="echoid-s6434" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6435" xml:space="preserve">Ante inſtauratam figuram, corpora ambo cum duobus gradibus velocita-
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            tis moventur , & </s>
            <s xml:id="echoid-s6436" xml:space="preserve">Elaſtrum fuit flexum vi 24. </s>
            <s xml:id="echoid-s6437" xml:space="preserve">. </s>
            <s xml:id="echoid-s6438" xml:space="preserve">Si navem concipiamus
              <note symbol="*" position="left" xlink:label="note-0232-09" xlink:href="note-0232-09a" xml:space="preserve">519.</note>
            qua corpora poſt ictum, ante ſeparationem quieſcunt, id eſt cujus velocitas
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0232-10" xlink:href="note-0232-10a" xml:space="preserve">510.</note>
            etiam eſt duo; </s>
            <s xml:id="echoid-s6439" xml:space="preserve">corpora in hac ſeparantur viribus & </s>
            <s xml:id="echoid-s6440" xml:space="preserve">velocitatibus, quæ ſunt in-
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            verſe ut maſſæ ; </s>
            <s xml:id="echoid-s6441" xml:space="preserve">B velocitate 2.</s>
            <s xml:id="echoid-s6442" xml:space="preserve">, & </s>
            <s xml:id="echoid-s6443" xml:space="preserve">A celeritate 4.</s>
            <s xml:id="echoid-s6444" xml:space="preserve">, ſi Elaſtrum minus
              <note symbol="*" position="left" xlink:label="note-0232-11" xlink:href="note-0232-11a" xml:space="preserve">472 561.</note>
            ſet flexum, etiam vires fuiſſent inverſè ut maſſæ ; </s>
            <s xml:id="echoid-s6445" xml:space="preserve">ergo, pro parte
              <note symbol="*" position="left" xlink:label="note-0232-12" xlink:href="note-0232-12a" xml:space="preserve">564.</note>
            Elaſterio, in hac ratione ſunt vires, ideoque velocitates ; </s>
            <s xml:id="echoid-s6446" xml:space="preserve">idcirco ubi B
              <note symbol="*" position="left" xlink:label="note-0232-13" xlink:href="note-0232-13a" xml:space="preserve">472.</note>
            bet unum gradum velocitatis in nave, A duos habet, & </s>
            <s xml:id="echoid-s6447" xml:space="preserve">actio elaſtri valet 6.
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            </s>
            <s xml:id="echoid-s6448" xml:space="preserve">gradus vis.</s>
            <s xml:id="echoid-s6449" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6450" xml:space="preserve">Tum, motus abſolutos conſiderando, B habet velocitatem 3, & </s>
            <s xml:id="echoid-s6451" xml:space="preserve">A quieſcit;
              <lb/>
            </s>
            <s xml:id="echoid-s6452" xml:space="preserve">Elaſtrum verò vim 18. </s>
            <s xml:id="echoid-s6453" xml:space="preserve">ſuperſtitem exerit, dum corpori B ſecundum gradum
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            velocitatis in nave & </s>
            <s xml:id="echoid-s6454" xml:space="preserve">corpori A tertium & </s>
            <s xml:id="echoid-s6455" xml:space="preserve">quartum in ipſa communicat. </s>
            <s xml:id="echoid-s6456" xml:space="preserve">Ha-
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            bet nunc B, ſepoſita nave, velocitatem 4. </s>
            <s xml:id="echoid-s6457" xml:space="preserve">& </s>
            <s xml:id="echoid-s6458" xml:space="preserve">redit A velocìtate 2.</s>
            <s xml:id="echoid-s6459" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6460" xml:space="preserve">Corpus B ante elaſtrum relaxatum vim habet 8 , dum Elaſtrum
              <note symbol="*" position="left" xlink:label="note-0232-14" xlink:href="note-0232-14a" xml:space="preserve">470.</note>
            6. </s>
            <s xml:id="echoid-s6461" xml:space="preserve">gradus vis exerit nondum redit A, verſamurque in caſu n. </s>
            <s xml:id="echoid-s6462" xml:space="preserve">595. </s>
            <s xml:id="echoid-s6463" xml:space="preserve">ideo ſex
              <lb/>
            hi gradus corpori B communicantur, & </s>
            <s xml:id="echoid-s6464" xml:space="preserve">præterea quantum amittit A ut hoc
              <lb/>
            in n. </s>
            <s xml:id="echoid-s6465" xml:space="preserve">594. </s>
            <s xml:id="echoid-s6466" xml:space="preserve">explicavimus, id eſt 4; </s>
            <s xml:id="echoid-s6467" xml:space="preserve">habetque B vim 18. </s>
            <s xml:id="echoid-s6468" xml:space="preserve">quæ reſpondet velo-
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            citati 3 ; </s>
            <s xml:id="echoid-s6469" xml:space="preserve">maſſa enim eſt duo.</s>
            <s xml:id="echoid-s6470" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">470.</note>
          <p>
            <s xml:id="echoid-s6471" xml:space="preserve">Elaſtrum nunc ab una parte inſiſtit corpori quieſcenti, ad alteram corpo-
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            ri agitato, ipſumque huc uſque totum fuit translatum, nunc autem pro par-
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            te tantum transfertur & </s>
            <s xml:id="echoid-s6472" xml:space="preserve">poteſt repellere corpus A vi 4, ideoque reliquam tan-
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            tum vim 14 poterit ipſi B imprimere ; </s>
            <s xml:id="echoid-s6473" xml:space="preserve">hi additi ad 18, dant gradus 32. </s>
            <s xml:id="echoid-s6474" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0232-16" xlink:href="note-0232-16a" xml:space="preserve">593.</note>
            ut ex aute demonſtratis liquet revera habet.</s>
            <s xml:id="echoid-s6475" xml:space="preserve"/>
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