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

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            <s xml:id="echoid-s2631" xml:space="preserve">
              <pb o="61" file="0109" n="118" rhead="MATHEMATICA. LIB. I. CAP. XVII."/>
            go hæc ſpatium tempore
              <emph style="sc">A</emph>
            B percurſum deſignat. </s>
            <s xml:id="echoid-s2632" xml:space="preserve">Eodem
              <lb/>
            modo area trianguli A1 f repræſentat ſpatium tempore A1.
              <lb/>
            </s>
            <s xml:id="echoid-s2633" xml:space="preserve">percurſum; </s>
            <s xml:id="echoid-s2634" xml:space="preserve">triangula hæc ſunt ſimilia, & </s>
            <s xml:id="echoid-s2635" xml:space="preserve">areæ illorum ſunt
              <lb/>
            inter ſe ut quadrata laterum
              <emph style="sc">A</emph>
            B, A1.</s>
            <s xml:id="echoid-s2636" xml:space="preserve">, id eſt, ſpatia ab i-
              <lb/>
              <note position="right" xlink:label="note-0109-01" xlink:href="note-0109-01a" xml:space="preserve">255.</note>
            nitio caſus percurſa ſunt inter ſe, ut quadrata temporum
              <lb/>
            per quæ corpus cecidit; </s>
            <s xml:id="echoid-s2637" xml:space="preserve">aut ut quadrata velocitatum inter
              <lb/>
            cadendum acquiſitarum.</s>
            <s xml:id="echoid-s2638" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2639" xml:space="preserve">Diviſo tempore
              <emph style="sc">A</emph>
            B in partes æquales, A1, 12, 23,
              <lb/>
              <note position="right" xlink:label="note-0109-02" xlink:href="note-0109-02a" xml:space="preserve">256.</note>
            3B; </s>
            <s xml:id="echoid-s2640" xml:space="preserve">ducantur per diviſiones lineæ ad baſin parallelæ ſpa-
              <lb/>
            tia percurſa in illis partibus, id eſt, in primo, ſecundo,
              <lb/>
            tertio, & </s>
            <s xml:id="echoid-s2641" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2642" xml:space="preserve">momento, poſitis momentis æqualibus, ſunt in-
              <lb/>
            ter ſe ut areæ A1f, 1fg2, 2gh3, 3hEB; </s>
            <s xml:id="echoid-s2643" xml:space="preserve">quæ areæ ut
              <lb/>
            ex inſpectione figuræ patet, ſunt inter ſe ut numeri impares
              <lb/>
            1. </s>
            <s xml:id="echoid-s2644" xml:space="preserve">3, 5. </s>
            <s xml:id="echoid-s2645" xml:space="preserve">7. </s>
            <s xml:id="echoid-s2646" xml:space="preserve">9.</s>
            <s xml:id="echoid-s2647" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2648" xml:space="preserve">Si corpus, poſtquam cecidit per tempus
              <emph style="sc">A</emph>
            B, non ulte-
              <lb/>
            rius acceleretur, ſed celeritate BE, eo caſu acquiſita, u-
              <lb/>
            niformiter motum continuet, per tempus BC, æquale tem-
              <lb/>
            pori caſus ſpatium eo motu percurſum deſignatur per aream
              <lb/>
            BEDC, duplam areæ trianguli ABE; </s>
            <s xml:id="echoid-s2649" xml:space="preserve">& </s>
            <s xml:id="echoid-s2650" xml:space="preserve">ideò</s>
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          <p style="it">
            <s xml:id="echoid-s2651" xml:space="preserve">Corpus ab altitudine quacunque libere cadens, eacum celeri-
              <lb/>
              <note position="right" xlink:label="note-0109-03" xlink:href="note-0109-03a" xml:space="preserve">257.</note>
            tate, quam cadendo acquiſivit in tempore æqualitempori caſus,
              <lb/>
            motu æquabili, ſpatium duplum prædictæ altitudinis percurret.</s>
            <s xml:id="echoid-s2652" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2653" xml:space="preserve">Quæ propoſitio in ſequentibus etiam Experimento con-
              <lb/>
            firmatur.</s>
            <s xml:id="echoid-s2654" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2655" xml:space="preserve">Motus corporis in altum projecti eodem modo retardatur,
              <lb/>
            quo corporis cadentis motus acceleratur, ut ſequitur ex lege
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0109-04" xlink:href="note-0109-04a" xml:space="preserve">245.</note>
            2 ; </s>
            <s xml:id="echoid-s2656" xml:space="preserve">in hoc caſu vis gravitatis cum motu acquiſito conſpi- rat, in illo contrarie agit; </s>
            <s xml:id="echoid-s2657" xml:space="preserve">cum vero vis gravitatis omnibus
              <lb/>
            momentis æqualibus, æquales corpori celeritates commu-
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0109-05" xlink:href="note-0109-05a" xml:space="preserve">251.</note>
            nicet , celeritas corporis projecti in altum, æqualibus
              <note position="right" xlink:label="note-0109-06" xlink:href="note-0109-06a" xml:space="preserve">258.</note>
            ribus, æqualiter minuitur, aut retardatur.</s>
            <s xml:id="echoid-s2658" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2659" xml:space="preserve">Vis eadem gravitatis generat motum in corpore cadente,
              <lb/>
            & </s>
            <s xml:id="echoid-s2660" xml:space="preserve">deſtruit in corpore adſcendente, agitque ſemper in corpus
              <lb/>
            motum ut in corpus quieſcens; </s>
            <s xml:id="echoid-s2661" xml:space="preserve">æqualibus ergo
              <note symbol="*" position="right" xlink:label="note-0109-07" xlink:href="note-0109-07a" xml:space="preserve">252.</note>
            celeritates eædem generantur, & </s>
            <s xml:id="echoid-s2662" xml:space="preserve">deſtr uuntur. </s>
            <s xml:id="echoid-s2663" xml:space="preserve">Corpus in
              <lb/>
              <note position="right" xlink:label="note-0109-08" xlink:href="note-0109-08a" xml:space="preserve">259.</note>
            altum projectum adſcendit, donec totum motum amiſerit;</s>
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