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

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          <p>
            <s xml:id="echoid-s4551" xml:space="preserve">
              <pb o="109" file="0167" n="181" rhead="MATHEMATICA. LIB. I. CAP XXI."/>
            {RMM - RNN + HNN - NNX/D
              <emph style="super">c</emph>
            } & </s>
            <s xml:id="echoid-s4552" xml:space="preserve">{H
              <emph style="super">n</emph>
            -nH
              <emph style="super">n-1</emph>
            X/D
              <emph style="super">c</emph>
            } id eſt propter
              <lb/>
            communem denominatorem, ſunt analogi numeratores.</s>
            <s xml:id="echoid-s4553" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4554" xml:space="preserve">In Ellipſi a circulo parum differenti, H cum ſemi parametro R vix dif-
              <lb/>
            fert, ut ex generatione Ellipſeos & </s>
            <s xml:id="echoid-s4555" xml:space="preserve">parametri definitione ſequitur ; </s>
            <s xml:id="echoid-s4556" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0167-01" xlink:href="note-0167-01a" xml:space="preserve">397.</note>
            go -RNN HNN ſeſe mutuo deſtruunt & </s>
            <s xml:id="echoid-s4557" xml:space="preserve">RMM fit HMM; </s>
            <s xml:id="echoid-s4558" xml:space="preserve">quanti-
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0167-02" xlink:href="note-0167-02a" xml:space="preserve">La Hire
                <lb/>
              ſect. con.
                <lb/>
              det. poſt.
                <lb/>
              pro. 3. lib
                <lb/>
              3.</note>
            tatesque analogæ ſunt HMM-NNX & </s>
            <s xml:id="echoid-s4559" xml:space="preserve">H
              <emph style="super">n</emph>
            -nH
              <emph style="super">n-1</emph>
            X, id eſt partes con-
              <lb/>
            ſtantes ſunt inter ſe ut indeterminatæ quæ per X multiplicantur; </s>
            <s xml:id="echoid-s4560" xml:space="preserve">ergo HMM,
              <lb/>
            NNX :</s>
            <s xml:id="echoid-s4561" xml:space="preserve">: H
              <emph style="super">n</emph>
            , nH
              <emph style="super">n-1</emph>
            X: </s>
            <s xml:id="echoid-s4562" xml:space="preserve">dividendo antecedentia per H, conſequentia per X, & </s>
            <s xml:id="echoid-s4563" xml:space="preserve">
              <lb/>
            dividendo terminos ſecundæ rationis per H
              <emph style="super">n-1</emph>
            habemus
              <lb/>
            MM, NN :</s>
            <s xml:id="echoid-s4564" xml:space="preserve">: I, n. </s>
            <s xml:id="echoid-s4565" xml:space="preserve">& </s>
            <s xml:id="echoid-s4566" xml:space="preserve">
              <lb/>
            M, N :</s>
            <s xml:id="echoid-s4567" xml:space="preserve">: I, I n</s>
          </p>
          <p style="it">
            <s xml:id="echoid-s4568" xml:space="preserve">Id eſt, motus angularis corporis in Ellipſi translatd ſe habet ad ipſius motum
              <lb/>
              <note position="right" xlink:label="note-0167-03" xlink:href="note-0167-03a" xml:space="preserve">431.</note>
            angularem in eadem Ellipſi quieſcente, ut unitas ad radicem quadratam numeri,
              <lb/>
            qui tribus excedit indicem poteſtatis, cujus rationem vis ſequitur</s>
          </p>
          <p>
            <s xml:id="echoid-s4569" xml:space="preserve">Ex dato igitur motu angulari curvæ, poteſtas quam ſequitur vis detegitur
              <lb/>
            & </s>
            <s xml:id="echoid-s4570" xml:space="preserve">vice verſa ex datâ poteſtate detegitur motus curvæ angularis.</s>
            <s xml:id="echoid-s4571" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4572" xml:space="preserve">Exemplum unicum dabo, quod uſum ſuum habet in Aſtronomicis Detur cor-
              <lb/>
              <note position="right" xlink:label="note-0167-04" xlink:href="note-0167-04a" xml:space="preserve">432.</note>
            pus quod movetur in Ellipſi quæ ſingulis revolutionibus tribus gradibus progre-
              <lb/>
            diatur, id eſt motus ipſius in curva translata eſt 363 grad dum m orbe qui-
              <lb/>
            eſcente foret 360. </s>
            <s xml:id="echoid-s4573" xml:space="preserve">grad.</s>
            <s xml:id="echoid-s4574" xml:space="preserve">; M ergo ad N, ut 363. </s>
            <s xml:id="echoid-s4575" xml:space="preserve">ad 360. </s>
            <s xml:id="echoid-s4576" xml:space="preserve">aut ut 121 ad 120;
              <lb/>
            </s>
            <s xml:id="echoid-s4577" xml:space="preserve">& </s>
            <s xml:id="echoid-s4578" xml:space="preserve">MM ad NN ut 14641, ad 14400: </s>
            <s xml:id="echoid-s4579" xml:space="preserve">ergo n = {14400/14641}, & </s>
            <s xml:id="echoid-s4580" xml:space="preserve">poteſtas diſtantiæ
              <lb/>
            cujus proportionem ſequitur vis eſt {14400/14641} - 3 = -{29523/14641} quare vis eſt reci-
              <lb/>
            procè ut D
              <emph style="super">2</emph>
            {9523/14641} = D
              <emph style="super">2</emph>
            {241/14641} = D
              <emph style="super">2</emph>
            {4/243} proximè.</s>
            <s xml:id="echoid-s4581" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div671" type="section" level="1" n="187">
          <head xml:id="echoid-head265" xml:space="preserve">LIBRI I. PARS IV.</head>
          <head xml:id="echoid-head266" xml:space="preserve">De Viribus inſitis, & Colliſione
            <lb/>
          corporum.</head>
          <head xml:id="echoid-head267" xml:space="preserve">CAPUT XXII.</head>
          <head xml:id="echoid-head268" xml:space="preserve">De Viribus corporibus motis inſitis.</head>
          <p>
            <s xml:id="echoid-s4582" xml:space="preserve">Vi inſitâ corpus de loco in locum transferri diximus
              <note symbol="*" position="right" xlink:label="note-0167-05" xlink:href="note-0167-05a" xml:space="preserve">12.</note>
            de virium comparatione nunc agendum; </s>
            <s xml:id="echoid-s4583" xml:space="preserve">quod ut or-
              <lb/>
            dine fiat, de harum geneſi quædam præmittenda erunt.</s>
            <s xml:id="echoid-s4584" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4585" xml:space="preserve">Vidimus antea corpus ex loco moveri, ſi preſſio, con-
              <lb/>
            traria preſſione non deſtructa, in illud agat ; </s>
            <s xml:id="echoid-s4586" xml:space="preserve">quod
              <note symbol="*" position="right" xlink:label="note-0167-06" xlink:href="note-0167-06a" xml:space="preserve">101.</note>
            obtinebit, ſi corpus nullo obſtaculo retineatur: </s>
            <s xml:id="echoid-s4587" xml:space="preserve">quacunque
              <lb/>
              <note position="right" xlink:label="note-0167-07" xlink:href="note-0167-07a" xml:space="preserve">433.</note>
            celeritate corpus cedit hanc in perpetuum ſervabit </s>
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