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

Table of Notes

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              <pb o="63" file="0111" n="120" rhead="MATHEMATICA. LIB. I. CAP XVIII."/>
            tur, ſi eodem tempore cadere incipiant, ſunt ſemper in ea-
              <lb/>
            dem ratione quam in principio caſus ; </s>
            <s xml:id="echoid-s2698" xml:space="preserve">ergo ſpatia
              <note symbol="*" position="right" xlink:label="note-0111-01" xlink:href="note-0111-01a" xml:space="preserve">251. 263.</note>
            tempore percurrunt, quæ ſunt in ratione longitudinis plani
              <lb/>
            ad illius altitudinem.
              <lb/>
            </s>
            <s xml:id="echoid-s2699" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0111-02" xlink:href="note-0111-02a" xml:space="preserve">237.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s2700" xml:space="preserve">In plano
              <emph style="sc">A</emph>
            B ſpatium a corpore percurſum, dum aliud li-
              <lb/>
              <note position="right" xlink:label="note-0111-03" xlink:href="note-0111-03a" xml:space="preserve">266.</note>
            bere cadit per altitudinem plani
              <emph style="sc">A</emph>
            C, determinatur, du-
              <lb/>
              <note position="right" xlink:label="note-0111-04" xlink:href="note-0111-04a" xml:space="preserve">TAB. X.
                <lb/>
              fig. 9.</note>
            cendo ad
              <emph style="sc">A</emph>
            B perpendicularem CG: </s>
            <s xml:id="echoid-s2701" xml:space="preserve">tunc enim longitudo
              <lb/>
            plani
              <emph style="sc">A</emph>
            B eſt ad illius altitudinem
              <emph style="sc">A</emph>
            C, ut
              <emph style="sc">A</emph>
            C ad
              <emph style="sc">A</emph>
            G. </s>
            <s xml:id="echoid-s2702" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0111-05" xlink:href="note-0111-05a" xml:space="preserve">8 El. VI.</note>
            circulus deſcribatur diametro
              <emph style="sc">A</emph>
            C, punctum G erit in pe-
              <lb/>
            ripheria circuli; </s>
            <s xml:id="echoid-s2703" xml:space="preserve">quia angulus in ſemicirculo, ut
              <emph style="sc">A</emph>
            GC,
              <lb/>
            ſemper eſt rectus ; </s>
            <s xml:id="echoid-s2704" xml:space="preserve">& </s>
            <s xml:id="echoid-s2705" xml:space="preserve">ideo punctum ut G, pro plano
              <note symbol="*" position="right" xlink:label="note-0111-06" xlink:href="note-0111-06a" xml:space="preserve">31 El. III.</note>
            cunque inclinato, ſemper eſt in eadem illa peripheria: </s>
            <s xml:id="echoid-s2706" xml:space="preserve">un-
              <lb/>
            de ſequitur, chordas omnes, ut
              <emph style="sc">A</emph>
            G eſſe inter ſe ut vires,
              <lb/>
            quibus corpora ſuper his deſcendere conantur; </s>
            <s xml:id="echoid-s2707" xml:space="preserve">& </s>
            <s xml:id="echoid-s2708" xml:space="preserve">has per-
              <lb/>
            curri a corporibus devolventibus, in tempore in quo cor-
              <lb/>
            pus, libere cadendo, poteſt percurrere diametrum
              <emph style="sc">A</emph>
            C;
              <lb/>
            </s>
            <s xml:id="echoid-s2709" xml:space="preserve">& </s>
            <s xml:id="echoid-s2710" xml:space="preserve">ita tempora devolutionum per illas chordasſunt æqualia.</s>
            <s xml:id="echoid-s2711" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2712" xml:space="preserve">Per punctum C nulla poteſt duci chorda ut HC, quin de-
              <lb/>
            tur per
              <emph style="sc">A</emph>
            chorda ut
              <emph style="sc">A</emph>
            G ei parallela, id eſt, æqualiter in-
              <lb/>
            clinata, & </s>
            <s xml:id="echoid-s2713" xml:space="preserve">æqualis; </s>
            <s xml:id="echoid-s2714" xml:space="preserve">igitur in ſemicirculo, ut
              <emph style="sc">A</emph>
            HC, Vires
              <lb/>
              <note position="right" xlink:label="note-0111-07" xlink:href="note-0111-07a" xml:space="preserve">267.</note>
            quibus corpora juxta chordas, in puncto infimo terminatas
              <lb/>
            deſcendere conantur, ſunt inter ſe ut hæ chordæ & </s>
            <s xml:id="echoid-s2715" xml:space="preserve">quando
              <lb/>
              <note position="right" xlink:label="note-0111-08" xlink:href="note-0111-08a" xml:space="preserve">268.</note>
            corpus ſibi permittitur eodem tempore, ad punctum infimum
              <lb/>
            ſemicirculi perveniet, ſive libere cadat juxta diametrum,
              <lb/>
            ſive deſcendat ſuper chorda HC quacunque.</s>
            <s xml:id="echoid-s2716" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2717" xml:space="preserve">Tempus devolutionis per totum planum
              <emph style="sc">A</emph>
            B poteſt confer-
              <lb/>
              <note position="right" xlink:label="note-0111-09" xlink:href="note-0111-09a" xml:space="preserve">269.</note>
            ri cum tempore deſcenſus per plani altitudinem
              <emph style="sc">A</emph>
            C; </s>
            <s xml:id="echoid-s2718" xml:space="preserve">nam
              <lb/>
            hocce tempus eſt æquale tempori devolutionis per
              <emph style="sc">A</emph>
            G; </s>
            <s xml:id="echoid-s2719" xml:space="preserve">& </s>
            <s xml:id="echoid-s2720" xml:space="preserve">
              <lb/>
            quadrata temporum ſunt inter ſe ut
              <emph style="sc">A</emph>
            B ad
              <emph style="sc">A</emph>
            G ; </s>
            <s xml:id="echoid-s2721" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0111-10" xlink:href="note-0111-10a" xml:space="preserve">264 255.</note>
              <emph style="sc">A</emph>
            B eſt ad
              <emph style="sc">A</emph>
            C ut
              <emph style="sc">A</emph>
            C ad
              <emph style="sc">A</emph>
            G: </s>
            <s xml:id="echoid-s2722" xml:space="preserve">quadrata igitur linearum
              <emph style="sc">A</emph>
            B & </s>
            <s xml:id="echoid-s2723" xml:space="preserve">
              <lb/>
              <emph style="sc">A</emph>
            C ſunt inter ſe, ut
              <emph style="sc">A</emph>
            B ad
              <emph style="sc">A</emph>
            G; </s>
            <s xml:id="echoid-s2724" xml:space="preserve">& </s>
            <s xml:id="echoid-s2725" xml:space="preserve">ideo iſtæ lineæ
              <emph style="sc">A</emph>
            B
              <lb/>
            & </s>
            <s xml:id="echoid-s2726" xml:space="preserve">
              <emph style="sc">A</emph>
            C ſunt inter ſe, ut tempora deſcenſus per
              <emph style="sc">A</emph>
            B, & </s>
            <s xml:id="echoid-s2727" xml:space="preserve">
              <lb/>
              <emph style="sc">A</emph>
            G, aut
              <emph style="sc">A</emph>
            C, id eſt, tempora, in eo caſu, ſunt ut ſpa-
              <lb/>
            tia percurſa.</s>
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          </p>
          <p>
            <s xml:id="echoid-s2729" xml:space="preserve">In eodem caſu velocitates in fine deſcenſus ſunt æquales;
              <lb/>
            </s>
            <s xml:id="echoid-s2730" xml:space="preserve">
              <note position="right" xlink:label="note-0111-11" xlink:href="note-0111-11a" xml:space="preserve">270.</note>
            nam poſt tempora æqualia, quando corpora ſunt in G & </s>
            <s xml:id="echoid-s2731" xml:space="preserve"/>
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