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

Table of contents

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[201.] Experimentum 5.
Page: 218 (134)
[202.] Experimentum 6.
Page: 218 (134)
[203.] Experimentum 7.
Page: 220 (136)
[204.] Experimentum 8.
Page: 222 (138)
[205.] Experimentum 9.
Page: 222 (138)
[206.] Experimentum 10.
Page: 223 (139)
[207.] Experimentum 11.
Page: 223 (139)
[208.] Experimentum 12.
Page: 223 (139)
[209.] SCHOLIUM 1. Demonſtrationes n. 499. 510
Page: 228 (141)
[210.] Demonſtrationes Algebraicæ n. 513. 516.
Page: 228 (141)
[211.] SCHOLIUM 2. De percuſſione corporum lineis rigidis inter ſe cohæ-rentium, & circa centra agitatorum.
Page: 230 (143)
[212.] SCHOLIUM 3. Examen Experimenti circa corpora in lancem, aut brachium, libræ impingentia.
Page: 233 (146)
[213.] BILANX Qua altitudines conferuntur, a quibus corpus cadens, pondera paululum elevat.
Page: 234 (147)
[214.] Experimentum.
Page: 234 (147)
[215.] SCHOLIUM 4. De Centro oſcillationis, & percuſſionis.
Page: 237 (150)
[216.] CAPUT XXIV. De congreſſu corporum Elaſticorum.
Page: 238 (151)
[217.] Definitio.
Page: 239 (152)
[218.] Experimentum 1.
Page: 240 (153)
[219.] Regula I.
Page: 241 (146)
[220.] Regula II.
Page: 241 (146)
[221.] Experimentum 2.
Page: 242 (155)
[222.] Experimentum 3.
Page: 242 (155)
[223.] Experimentum 4.
Page: 242 (155)
[224.] Experimentum 5.
Page: 243 (156)
[225.] Experimentum 6.
Page: 243 (156)
[226.] Experimentum 7.
Page: 243 (156)
[227.] Experimentum 8.
Page: 244 (157)
[228.] Experimentum 9.
Page: 244 (157)
[229.] Experimentum 10.
Page: 244 (157)
[230.] Experimentum 11.
Page: 245 (158)
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          <pb o="150" file="0218" n="237" rhead="PHYSICES ELEMENTA"/>
          <p>
            <s xml:id="echoid-s5952" xml:space="preserve">Et præcedens æquatio mutatur in hanc
              <lb/>
            {a = {
              <emph style="ol">b + </emph>
            c x d x P/G
              <emph style="super">q</emph>
            } = {
              <emph style="ol">123 {1/2} + 1320 + P</emph>
            x 21P/67
              <emph style="super">q</emph>
            x 100} = {
              <emph style="ol">1443 {1/2} + P</emph>
            x 21P/448900}</s>
          </p>
          <p>
            <s xml:id="echoid-s5953" xml:space="preserve">Subſtituendo ſucceſſive pro P quatuor, octo, & </s>
            <s xml:id="echoid-s5954" xml:space="preserve">duodecim uncias, id eſt,
              <lb/>
            ſcrupula 96, 192, 288 detegimus a = 6, 91. </s>
            <s xml:id="echoid-s5955" xml:space="preserve">a = 14, 68; </s>
            <s xml:id="echoid-s5956" xml:space="preserve">& </s>
            <s xml:id="echoid-s5957" xml:space="preserve">a = 23, 32.</s>
            <s xml:id="echoid-s5958" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5959" xml:space="preserve">Quæ altitudines parum admodum differunt cum altitudinibus experimento de-
              <lb/>
            tectis; </s>
            <s xml:id="echoid-s5960" xml:space="preserve">differentia autem tribuenda eſt mutationi figuræ jugi in computatione
              <note symbol="*" position="left" xlink:label="note-0218-01" xlink:href="note-0218-01a" xml:space="preserve">548.</note>
            </s>
          </p>
        </div>
        <div xml:id="echoid-div843" type="section" level="1" n="215">
          <head xml:id="echoid-head305" xml:space="preserve">SCHOLIUM 4.</head>
          <head xml:id="echoid-head306" style="it" xml:space="preserve">De Centro oſcillationis, & percuſſionis.</head>
          <p>
            <s xml:id="echoid-s5961" xml:space="preserve">Superius , ex demonſtratis circa preſſionem, deduximus methodum
              <note position="left" xlink:label="note-0218-02" xlink:href="note-0218-02a" xml:space="preserve">551.</note>
            nandi centrum oſcillationis; </s>
            <s xml:id="echoid-s5962" xml:space="preserve">eandem ibi traditam regulam quàm facilli-
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0218-03" xlink:href="note-0218-03a" xml:space="preserve">311. 312.</note>
            me deducimus ex demonſtratis circa vires.</s>
            <s xml:id="echoid-s5963" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5964" xml:space="preserve">Corpus eandem acquirit velocitatem, ideoque vim, a certa altitudine caden-
              <lb/>
            do, quamcunque viam in deſcenſu ſequatur & </s>
            <s xml:id="echoid-s5965" xml:space="preserve">vis acquiſita huic
              <note symbol="*" position="left" xlink:label="note-0218-04" xlink:href="note-0218-04a" xml:space="preserve">271.</note>
            proportionalis eſt . </s>
            <s xml:id="echoid-s5966" xml:space="preserve">Dum corpora pendulo compoſito juncta
              <note symbol="*" position="left" xlink:label="note-0218-05" xlink:href="note-0218-05a" xml:space="preserve">448.</note>
            nulla actione vis deſcendendo acquiſita deſtruitur; </s>
            <s xml:id="echoid-s5967" xml:space="preserve">nihil etiam datur quoau-
              <lb/>
            geri poſſet, ergo ſumma virium æqualis eſt ſummæ virium quas corpora,
              <lb/>
            ſeparatim a ſuis altitudinibus cadendo, pot uiſſent acquirere.</s>
            <s xml:id="echoid-s5968" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5969" xml:space="preserve">Sint corpora A, B, C, D, diſtantiæ a puncto ſuſpenſionis a, b, c, & </s>
            <s xml:id="echoid-s5970" xml:space="preserve">d. </s>
            <s xml:id="echoid-s5971" xml:space="preserve">Alti-
              <lb/>
            tudines, a quibus corporahæc deſcendunt, ſunt ut a, b, c, & </s>
            <s xml:id="echoid-s5972" xml:space="preserve">d & </s>
            <s xml:id="echoid-s5973" xml:space="preserve">in eadem ra-
              <lb/>
            tione velocitates. </s>
            <s xml:id="echoid-s5974" xml:space="preserve">Dicatur diſtantia centri oſcillationis à puncto ſuſpenſio-
              <lb/>
            nis x, & </s>
            <s xml:id="echoid-s5975" xml:space="preserve">velocitas acquiſ@ta deſcendendo ab altitudine a qua centrum hoc deſcen-
              <lb/>
            dit √ x; </s>
            <s xml:id="echoid-s5976" xml:space="preserve">ideò velocitas corporis A, ſi libere cecidiſſet, fuiſſet √ a & </s>
            <s xml:id="echoid-s5977" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0218-06" xlink:href="note-0218-06a" xml:space="preserve">255.</note>
            vis A a ; </s>
            <s xml:id="echoid-s5978" xml:space="preserve">ſummaque virium ſi ſingula corpora libere cecidiſſent Aa + Bb
              <note symbol="*" position="left" xlink:label="note-0218-07" xlink:href="note-0218-07a" xml:space="preserve">470.</note>
            Cc + Dd. </s>
            <s xml:id="echoid-s5979" xml:space="preserve">Si quædam corpora dentur ad partem oppoſitam puncti ſuſpenſio-
              <lb/>
            nis adſcendunt & </s>
            <s xml:id="echoid-s5980" xml:space="preserve">horum vires negativæ ſunt.</s>
            <s xml:id="echoid-s5981" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5982" xml:space="preserve">In corporibus pendulo junctis velocitas corporis A detegitur hac regulâ
              <lb/>
            x, a:</s>
            <s xml:id="echoid-s5983" xml:space="preserve">: vx, {a/vx}. </s>
            <s xml:id="echoid-s5984" xml:space="preserve">Cæterorumque corporum velocitates ſunt {b/vx}, {c/vx} & </s>
            <s xml:id="echoid-s5985" xml:space="preserve">
              <lb/>
            {d/vx}; </s>
            <s xml:id="echoid-s5986" xml:space="preserve">ſummaque virium {Aaa/x} + {Bbb/x} + {Ccc/x} + {Ddd/x} , quæ cum
              <note symbol="*" position="left" xlink:label="note-0218-08" xlink:href="note-0218-08a" xml:space="preserve">470.</note>
            ratæ ſummæ æqualis ſit; </s>
            <s xml:id="echoid-s5987" xml:space="preserve">detegimus x = {Aaa + Bbb + Ccc + Ddd/Aa + Bb + Cc + Dd} juxtare-
              <lb/>
            gulam n. </s>
            <s xml:id="echoid-s5988" xml:space="preserve">311.</s>
            <s xml:id="echoid-s5989" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5990" xml:space="preserve">Quando pendulum compoſitum in obicem fixum, ad quamcunque a cen-
              <lb/>
              <note position="left" xlink:label="note-0218-09" xlink:href="note-0218-09a" xml:space="preserve">552.</note>
            tro ſuſpenſionis diſtantiam poſitum, impingit, ſæpe in illud quod pendulum
              <lb/>
            ſuſtinet premit, integram tamen in obicem vim exerit, ſi preſſio quam in </s>
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