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

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            <s xml:id="echoid-s4657" xml:space="preserve">
              <pb o="113" file="0173" n="188" rhead="MATHEMATICA. LIB. I. CAR. XXII."/>
            vim corpori communicant; </s>
            <s xml:id="echoid-s4658" xml:space="preserve">cûm autem elaſteria ſint æqua-
              <lb/>
            lia, vires ſunt ut numeri Elaſteriorum, quorum expanſione
              <lb/>
            communicantur. </s>
            <s xml:id="echoid-s4659" xml:space="preserve">Corpus verò expanſione Elaſteriorum non
              <lb/>
            poteſt celeritatem acquirere, miſi motu accelerato, ita ut
              <lb/>
            per ſingulos gradus minores velocitatis tranſeat. </s>
            <s xml:id="echoid-s4660" xml:space="preserve">Sit A F
              <lb/>
              <note position="right" xlink:label="note-0173-01" xlink:href="note-0173-01a" xml:space="preserve">
                <emph style="sc">TAB. XVL.</emph>
                <lb/>
              fig. 2.</note>
            celeritas corporis; </s>
            <s xml:id="echoid-s4661" xml:space="preserve">A b, bc, cd, & </s>
            <s xml:id="echoid-s4662" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4663" xml:space="preserve">gradus infinitè exi-
              <lb/>
            gui celeritatis, A b primus, bc ſecundus, & </s>
            <s xml:id="echoid-s4664" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4665" xml:space="preserve">per quos o-
              <lb/>
            mnes tranſit corpus antequam acquirat celeritatem AF.
              <lb/>
            </s>
            <s xml:id="echoid-s4666" xml:space="preserve">Parallelogramma A bhe, bcif, cdlg, & </s>
            <s xml:id="echoid-s4667" xml:space="preserve">c ſunt in-
              <lb/>
            ter ſe reſpectivè, ut numeri Elaſteriorum, quibus gradus
              <lb/>
            velocitatis primus, ſecundus, tertius, &</s>
            <s xml:id="echoid-s4668" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4669" xml:space="preserve">acquiruntur; </s>
            <s xml:id="echoid-s4670" xml:space="preserve">
              <lb/>
            ideoque areæ A dle, AFG e, ſunt inter ſe ut numerie-
              <lb/>
            laſteriorum, quibus velocitates A d, AF acquiruntur, id
              <lb/>
            eſt ſunt hæ areæ inter ſe ut Vires ejuſdem corporis, aut
              <lb/>
              <note position="right" xlink:label="note-0173-02" xlink:href="note-0173-02a" xml:space="preserve">447.</note>
            duorum corporum æqualium, hiſce velocitatibus motorum;
              <lb/>
            </s>
            <s xml:id="echoid-s4671" xml:space="preserve">eùm autem lineæ A e, eh, bf, fi, & </s>
            <s xml:id="echoid-s4672" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4673" xml:space="preserve">ſint infinitè exi-
              <lb/>
            guæ; </s>
            <s xml:id="echoid-s4674" xml:space="preserve">areæ A dle, AFG e à triangulis ſimilibus adl, afg,
              <lb/>
            non differunt, & </s>
            <s xml:id="echoid-s4675" xml:space="preserve">ſunt inter ſe ut quadrata laterum homolo-
              <lb/>
            gorum , aut velocitatum A d, AF, quod
              <note symbol="*" position="right" xlink:label="note-0173-03" xlink:href="note-0173-03a" xml:space="preserve">19. El.
                <lb/>
                <emph style="sc">VI</emph>
              .</note>
            experimentis; </s>
            <s xml:id="echoid-s4676" xml:space="preserve">ſed pauca antea præmittenda ſunt.</s>
            <s xml:id="echoid-s4677" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4678" xml:space="preserve">Vires eſſe inter ſe ut quadrata velocitatum, aliis demon-
              <lb/>
            ſtrationibus, quæ ex principiis quæ nil inter ſe, neque cum
              <lb/>
            his quæ hìc ponuntur commune habent, deductis, in ſequenti-
              <lb/>
            bus etiam demonſtrabo, ubi de viribus obliquis, & </s>
            <s xml:id="echoid-s4679" xml:space="preserve">de reſiſten-
              <lb/>
            tia fluidorum, agam.</s>
            <s xml:id="echoid-s4680" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4681" xml:space="preserve">Vires, quas corpus cadendo acquirit, ſunt ut altitudines,
              <lb/>
              <note position="right" xlink:label="note-0173-04" xlink:href="note-0173-04a" xml:space="preserve">448.</note>
            quas cadendo percurrit, ab initio caſits; </s>
            <s xml:id="echoid-s4682" xml:space="preserve">ſunt enim hæ ut
              <lb/>
            quadrata velocitatum in fine deſcenſus . </s>
            <s xml:id="echoid-s4683" xml:space="preserve">Cum
              <note symbol="*" position="right" xlink:label="note-0173-05" xlink:href="note-0173-05a" xml:space="preserve">255.</note>
            hæc ſequentibus Experimentis immediatè demonſtretur,
              <lb/>
            patet gravitatem, quæ æqualibus temporibus æquales corpo-
              <lb/>
              <note position="right" xlink:label="note-0173-06" xlink:href="note-0173-06a" xml:space="preserve">419.</note>
            ri communicat gradus celeritatis, non iidem æquales
              <note symbol="*" position="right" xlink:label="note-0173-07" xlink:href="note-0173-07a" xml:space="preserve">251.</note>
            vis communicare, ſed illud, quo corpus ad Tellurem
              <note symbol="*" position="right" xlink:label="note-0173-08" xlink:href="note-0173-08a" xml:space="preserve">442.</note>
            dit, cum ipſo corpore moveri , dum in corpus
              <note symbol="*" position="right" xlink:label="note-0173-09" xlink:href="note-0173-09a" xml:space="preserve">439.</note>
            agit, ut in quieſcens.</s>
            <s xml:id="echoid-s4684" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4685" xml:space="preserve">Si corpora fuerint inæqualia, æqualibus velocitatibus
              <lb/>
              <note position="right" xlink:label="note-0173-10" xlink:href="note-0173-10a" xml:space="preserve">450.</note>
            mota, vires inſitæ ſunt inter ſe ut quantitates materiæ </s>
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