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

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        <div xml:id="echoid-div598" type="section" level="1" n="181">
          <head xml:id="echoid-head253" xml:space="preserve">SCHOLIUM 1.</head>
          <head xml:id="echoid-head254" style="it" xml:space="preserve">Generalia de viribus centralibus.</head>
          <p>
            <s xml:id="echoid-s4001" xml:space="preserve">Concipiamus dari vim, qua corpus, ubicunque detur, pellatur centrum
              <lb/>
              <note position="left" xlink:label="note-0156-01" xlink:href="note-0156-01a" xml:space="preserve">394.</note>
            C verſus, non intereſt quomodocunque in punctis diverſis varietur vis
              <lb/>
              <note position="left" xlink:label="note-0156-02" xlink:href="note-0156-02a" xml:space="preserve">TAB. XV.
                <lb/>
              fig. 2.</note>
            hæc; </s>
            <s xml:id="echoid-s4002" xml:space="preserve">concipiamus vim hanc non eſſe continuam, ſed illam ictibus in cor-
              <lb/>
            pus agere, & </s>
            <s xml:id="echoid-s4003" xml:space="preserve">momenta temporis inter ictus eſſe æqualia. </s>
            <s xml:id="echoid-s4004" xml:space="preserve">Ponamus etiam cor
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            pus projectum per AB hanc percurrere lineam in momento tali; </s>
            <s xml:id="echoid-s4005" xml:space="preserve">motum
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            per BL, æqualem AB, in momento ſequenti continuaret, niſi in B ictu
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            in corpus pelleretur hoc ad C; </s>
            <s xml:id="echoid-s4006" xml:space="preserve">ponamus celeritatem, ex hoc ictu oriundam
              <lb/>
            in corpore jam agitato, talem eſſe, ut hac corpus poſſit, in intervallo tem-
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            poris inter duos ictus, percurrere lineam LD; </s>
            <s xml:id="echoid-s4007" xml:space="preserve">ſi LD ſit parallela BC,
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            corpus duobus motibus agitatum pecurrit BD , daturque in D, in momento
              <note symbol="*" position="left" xlink:label="note-0156-03" xlink:href="note-0156-03a" xml:space="preserve">146.</note>
            quo ictu ſequenti iterum ad centrum pellitur. </s>
            <s xml:id="echoid-s4008" xml:space="preserve">Si ictus hic non daretur, in mo-
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            mento ſequenti percurreret DE, poſitis DE & </s>
            <s xml:id="echoid-s4009" xml:space="preserve">BD æqualibus, ſed eodem
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            tempore centrum verſus fertur, id eſt per DC pellitur, ſi juxta hanc dire-
              <lb/>
            ctionem percurrat lineam æqualem lineæ EF in tempore in quo percurre-
              <lb/>
            ret DE, motu compoſito corpus movetur per DF, poſitis EF & </s>
            <s xml:id="echoid-s4010" xml:space="preserve">DC pa-
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            rallelis. </s>
            <s xml:id="echoid-s4011" xml:space="preserve">Eodem modo demonſtramus in momento ſequenti corpus percur-
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            rere FH, ſi GH ſit æqualis ſpatio in hoc momento, ex ictu C verſus per-
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            currendo, poſitiſque FG & </s>
            <s xml:id="echoid-s4012" xml:space="preserve">DF æqualibus, ut & </s>
            <s xml:id="echoid-s4013" xml:space="preserve">GH & </s>
            <s xml:id="echoid-s4014" xml:space="preserve">FC parallelis.</s>
            <s xml:id="echoid-s4015" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4016" xml:space="preserve">Triangula ABC, BLC, habent baſes æquales AB, BL in eadem li-
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            nea, & </s>
            <s xml:id="echoid-s4017" xml:space="preserve">verticem communem C; </s>
            <s xml:id="echoid-s4018" xml:space="preserve">ſunt ergo æqualia . </s>
            <s xml:id="echoid-s4019" xml:space="preserve">Triangula
              <note symbol="*" position="left" xlink:label="note-0156-04" xlink:href="note-0156-04a" xml:space="preserve">38. El. 1.</note>
            BDC baſinhabent communem BC& </s>
            <s xml:id="echoid-s4020" xml:space="preserve">conſtituuntur inter parallelas BC, LD,
              <lb/>
            ſunt ergo æqualia . </s>
            <s xml:id="echoid-s4021" xml:space="preserve">Idcirco etiam æqualia ſunt triangula ABC, BDC.</s>
            <s xml:id="echoid-s4022" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0156-05" xlink:href="note-0156-05a" xml:space="preserve">37. El. 1.</note>
            Eodem modo demonſtramus æqualia triangula BDC, DFC & </s>
            <s xml:id="echoid-s4023" xml:space="preserve">in gene-
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            re æqualia eſſe inter ſe triangula quæcunque ut ABC, BDC, DFC;
              <lb/>
            </s>
            <s xml:id="echoid-s4024" xml:space="preserve">FHC, quorum baſes momentis æqualibus a corpore projecto percurrun-
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            tur. </s>
            <s xml:id="echoid-s4025" xml:space="preserve">Ex qua demonſtratione deducitur propoſitio n. </s>
            <s xml:id="echoid-s4026" xml:space="preserve">351.</s>
            <s xml:id="echoid-s4027" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4028" xml:space="preserve">Etiam patet corpus projectum & </s>
            <s xml:id="echoid-s4029" xml:space="preserve">vi centrum verſus tendenti agitatum, move-
              <lb/>
              <note position="left" xlink:label="note-0156-06" xlink:href="note-0156-06a" xml:space="preserve">395.</note>
            ri in plano, quod tranſit per lineam juxta quam corpus projicitur & </s>
            <s xml:id="echoid-s4030" xml:space="preserve">per centrum
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            virium, ut monuimus in n. </s>
            <s xml:id="echoid-s4031" xml:space="preserve">353.</s>
            <s xml:id="echoid-s4032" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4033" xml:space="preserve">Concipiamus nunc momenta inter duos ictus minui, ut & </s>
            <s xml:id="echoid-s4034" xml:space="preserve">ipſos ictus, ma-
              <lb/>
              <note position="left" xlink:label="note-0156-07" xlink:href="note-0156-07a" xml:space="preserve">396.</note>
            nentibus nihilominus illis æqualibus inter ſe, poſitis hiſce utcunque inæ-
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            qualibus, demonſtratio eadem locum habebit. </s>
            <s xml:id="echoid-s4035" xml:space="preserve">Si diminutio ſit in infinitum
              <lb/>
            mutantur ictus in preſſionem continuam, & </s>
            <s xml:id="echoid-s4036" xml:space="preserve">corpus in ſingulis punctis a via
              <lb/>
            recta deflectitur; </s>
            <s xml:id="echoid-s4037" xml:space="preserve">ſubjicitur tamen legi in demonſtratione præcedenti deter-
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            minata. </s>
            <s xml:id="echoid-s4038" xml:space="preserve">Si ergo corpus moveatur in curva ABDE, & </s>
            <s xml:id="echoid-s4039" xml:space="preserve">tempus concipia-
              <lb/>
              <note position="left" xlink:label="note-0156-08" xlink:href="note-0156-08a" xml:space="preserve">TAB. XIV-
                <lb/>
              fig. 11.</note>
            tur diviſum in momenta infinite exigua, & </s>
            <s xml:id="echoid-s4040" xml:space="preserve">æqualiainter ſe, area trianguli mixti
              <lb/>
            ACB continebit tot triangula exigua æqualia inter ſe, quot dantur momen-
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            ta in tempore, in quo percurritur AB, & </s>
            <s xml:id="echoid-s4041" xml:space="preserve">area trianguli mixti DCE eo-
              <lb/>
            dem modo continebit tot triangula æqualia inter ſe & </s>
            <s xml:id="echoid-s4042" xml:space="preserve">prioribus, quot dan-
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            tur momenta in tempore in quo percurritur DE; </s>
            <s xml:id="echoid-s4043" xml:space="preserve">ideoque @empora in quibus
              <lb/>
            corpus AB & </s>
            <s xml:id="echoid-s4044" xml:space="preserve">DE, percurrit, ſunt inter ſe ut numeri triangulorum æqua-
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            lium areis ACB, DCE, contentorum, id eſt ut ipſæ areæ. </s>
            <s xml:id="echoid-s4045" xml:space="preserve">Unde genera-
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            lem deducimus propoſitionem in n. </s>
            <s xml:id="echoid-s4046" xml:space="preserve">354. </s>
            <s xml:id="echoid-s4047" xml:space="preserve">memoratam</s>
          </p>
          <p>
            <s xml:id="echoid-s4048" xml:space="preserve">Cujus propoſitionis inverſa, quæ continentur in n. </s>
            <s xml:id="echoid-s4049" xml:space="preserve">355. </s>
            <s xml:id="echoid-s4050" xml:space="preserve">etiam demonſtratur.
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            </s>
            <s xml:id="echoid-s4051" xml:space="preserve">
              <note position="left" xlink:label="note-0156-09" xlink:href="note-0156-09a" xml:space="preserve">397.</note>
            Si corpus motum per AB in momento ſequenti, & </s>
            <s xml:id="echoid-s4052" xml:space="preserve">æquali, percurrat BD, quia
              <lb/>
              <note position="left" xlink:label="note-0156-10" xlink:href="note-0156-10a" xml:space="preserve">TAB. XV.
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              fig 2.</note>
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