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

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        <div xml:id="echoid-div493" type="section" level="1" n="157">
          <pb o="77" file="0129" n="140" rhead="MATHEMATICA. LIB. I. CAP. XIX."/>
          <p>
            <s xml:id="echoid-s3282" xml:space="preserve">Ponamus Cycloïdem ADB, inverſam, cujus axis ſit verticalis, & </s>
            <s xml:id="echoid-s3283" xml:space="preserve">corpus
              <lb/>
              <note position="right" xlink:label="note-0129-01" xlink:href="note-0129-01a" xml:space="preserve">324.</note>
            ex A deſcendere, demonſtrandum anguliut d DE, aut BEL , coſinum
              <note symbol="*" position="right" xlink:label="note-0129-02" xlink:href="note-0129-02a" xml:space="preserve">285. 316.</note>
            portionalem eſſe radici quadratæ altitudinis FL , id eſt proportionem
              <note symbol="*" position="right" xlink:label="note-0129-03" xlink:href="note-0129-03a" xml:space="preserve">323.</note>
            qui chordæ FE cujus quadratum ad inſtar altitudinis FL augetur & </s>
            <s xml:id="echoid-s3284" xml:space="preserve">minui-
              <lb/>
              <note position="right" xlink:label="note-0129-04" xlink:href="note-0129-04a" xml:space="preserve">TAB. XII.
                <lb/>
              fig. 5.</note>
            tur . </s>
            <s xml:id="echoid-s3285" xml:space="preserve">Angulus BE l æqualis eſt angulo BFE ; </s>
            <s xml:id="echoid-s3286" xml:space="preserve">cujus coſinus ſi
              <note symbol="*" position="right" xlink:label="note-0129-05" xlink:href="note-0129-05a" xml:space="preserve">293.</note>
            circuli ſit F, & </s>
            <s xml:id="echoid-s3287" xml:space="preserve">radius FB, eſt FE; </s>
            <s xml:id="echoid-s3288" xml:space="preserve">quod in omnibus punctis cycloïdis Io-
              <lb/>
              <note position="right" xlink:label="note-0129-06" xlink:href="note-0129-06a" xml:space="preserve">8. El. VI.</note>
            cum habet, manente eodem radio FB.</s>
            <s xml:id="echoid-s3289" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3290" xml:space="preserve">Linea ergo celerrimi deſcenſus, à puncto ad punctum, eſt Cycloïs inverſa, cu-
              <lb/>
              <note position="right" xlink:label="note-0129-07" xlink:href="note-0129-07a" xml:space="preserve">325.</note>
            jus punctum extremum, ut A, cum ſuperiori puncto coincidit & </s>
            <s xml:id="echoid-s3291" xml:space="preserve">quæ per punctum
              <lb/>
            alterum tranſit.</s>
            <s xml:id="echoid-s3292" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div503" type="section" level="1" n="158">
          <head xml:id="echoid-head228" xml:space="preserve">CAPUT XX.</head>
          <head xml:id="echoid-head229" style="it" xml:space="preserve">De Projectione Gravium.</head>
          <p>
            <s xml:id="echoid-s3293" xml:space="preserve">SI in corpus motum potentia agat, mutatur motus .</s>
            <s xml:id="echoid-s3294" xml:space="preserve">
              <note position="right" xlink:label="note-0129-08" xlink:href="note-0129-08a" xml:space="preserve">326.</note>
            Corpus projiciatur per AB, in tempore, in quo poteſt
              <lb/>
              <note position="right" xlink:label="note-0129-09" xlink:href="note-0129-09a" xml:space="preserve">TAB XIII.
                <lb/>
              fig. I.</note>
            percurrere AB, vi gravitatis, fertur terræ centrum verſus
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0129-10" xlink:href="note-0129-10a" xml:space="preserve">245</note>
            per BF, & </s>
            <s xml:id="echoid-s3295" xml:space="preserve">ita, motu compoſito ex iſtis duobus, movetur
              <lb/>
            per AF ; </s>
            <s xml:id="echoid-s3296" xml:space="preserve">& </s>
            <s xml:id="echoid-s3297" xml:space="preserve">hoc motu, ſecundo momento, percurreret
              <note symbol="*" position="right" xlink:label="note-0129-11" xlink:href="note-0129-11a" xml:space="preserve">246.</note>
            FC, ipſi AF æqualem, niſi ſecundo momento eadem vi
              <lb/>
            gravitatis translatum foret per CG, ita ut motus in ſecun-
              <lb/>
            do momento ſit per FG; </s>
            <s xml:id="echoid-s3298" xml:space="preserve">eodem modo, motus tertii mo-
              <lb/>
            menti eſt per GH, & </s>
            <s xml:id="echoid-s3299" xml:space="preserve">quarti momenti per HI; </s>
            <s xml:id="echoid-s3300" xml:space="preserve">cùm verò
              <lb/>
            vis gravitatis continuò agat, illa temporis momenta mini-
              <lb/>
            ma ſunt, & </s>
            <s xml:id="echoid-s3301" xml:space="preserve">ubique dabitur motus aliter compoſitus, id eſt,
              <lb/>
            directionis inflexio; </s>
            <s xml:id="echoid-s3302" xml:space="preserve">in eo caſu ergo corpus movetur in li-
              <lb/>
            nea curva.</s>
            <s xml:id="echoid-s3303" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3304" xml:space="preserve">Hic motus corporis ex projectione magis ſimpliciter con-
              <lb/>
              <note position="right" xlink:label="note-0129-12" xlink:href="note-0129-12a" xml:space="preserve">327.</note>
            ſiderari poteſt in omnibus projectionibus, quæ a nobis fie-
              <lb/>
            ri poſſunt; </s>
            <s xml:id="echoid-s3305" xml:space="preserve">quia omnes lineæ, quæ ad terræ centrum ten-
              <lb/>
            dunt, pro parallelis haberi poſſunt; </s>
            <s xml:id="echoid-s3306" xml:space="preserve">quare directio motus
              <lb/>
            ex gravitate ſemper eſt eadem; </s>
            <s xml:id="echoid-s3307" xml:space="preserve">unde motus ex projectione
              <lb/>
            ex duobus tantum motibus conſtat, primo æquabili per li-
              <lb/>
            neam projectionis, ſecundo terram verſus accelerato .</s>
            <s xml:id="echoid-s3308" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">251.</note>
          <p>
            <s xml:id="echoid-s3309" xml:space="preserve">Projiciatur corpus per lineam AE, horizonti parallelam;
              <lb/>
            </s>
            <s xml:id="echoid-s3310" xml:space="preserve">
              <note position="right" xlink:label="note-0129-14" xlink:href="note-0129-14a" xml:space="preserve">TAB XIII.
                <lb/>
              fig. 25</note>
            temporibus æqualibus, hoc motu, percurret partes æquales
              <lb/>
            AB, BC, CD, DE: </s>
            <s xml:id="echoid-s3311" xml:space="preserve">Ex gravitate fertur motu ad horizontem
              <lb/>
            perpendiculari, directione BF, CG, DH, aut EI, quæ hìc
              <lb/>
            parallelæ ponuntur; </s>
            <s xml:id="echoid-s3312" xml:space="preserve">motus hic eſt acceleratus, & </s>
            <s xml:id="echoid-s3313" xml:space="preserve">ideò, </s>
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