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

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          <pb o="196" file="0276" n="301" rhead="PHYSICES ELEMENTA"/>
          <p>
            <s xml:id="echoid-s7664" xml:space="preserve">Nam cum cauſa movens ſit chordæ Elaſticitas transfertur
              <lb/>
              <note position="left" xlink:label="note-0276-01" xlink:href="note-0276-01a" xml:space="preserve">687.</note>
            cauſa hæc cum ipſa fibra, quæ reſpectu ipſius quieſcit, quare in
              <lb/>
            hanc, licet agitatam, premit quaſi quieſceret hæc, ita ut
              <lb/>
            hìc vis movens ſit ejuſdem generis cum gravitate .</s>
            <s xml:id="echoid-s7665" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">252.</note>
          <p>
            <s xml:id="echoid-s7666" xml:space="preserve">Poſitis duabus chordis ſimilibus & </s>
            <s xml:id="echoid-s7667" xml:space="preserve">æqualibus, ſed inæ-
              <lb/>
              <note position="left" xlink:label="note-0276-03" xlink:href="note-0276-03a" xml:space="preserve">688.</note>
            qualiter tenſis, vires inæquales requiruntur ut æqualiter
              <lb/>
            inflectantur; </s>
            <s xml:id="echoid-s7668" xml:space="preserve">ergo vibrationes temporibus inæqualibus pera-
              <lb/>
            gunt.</s>
            <s xml:id="echoid-s7669" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7670" xml:space="preserve">Motus illarum conferri poſſunt cum motibus pendulo-
              <lb/>
            rum in cycloïdibus vibratorum , & </s>
            <s xml:id="echoid-s7671" xml:space="preserve">æquales cycloïdes,
              <note symbol="*" position="left" xlink:label="note-0276-04" xlink:href="note-0276-04a" xml:space="preserve">685.</note>
            bus diverſis, deſcribentium; </s>
            <s xml:id="echoid-s7672" xml:space="preserve">quæ vires ſunt inverſe ut qua-
              <lb/>
            drata temporum vibrationum : </s>
            <s xml:id="echoid-s7673" xml:space="preserve">in chordis ergo etiam
              <note symbol="*" position="left" xlink:label="note-0276-05" xlink:href="note-0276-05a" xml:space="preserve">301.</note>
            drata temporum vibrationum ſunt inter ſe inverſe, ut vires
              <lb/>
            quibus æqualiter inflectuntur; </s>
            <s xml:id="echoid-s7674" xml:space="preserve">quæ ſunt ut pondera quibus
              <lb/>
            chordæ tenduntur .</s>
            <s xml:id="echoid-s7675" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0276-06" xlink:href="note-0276-06a" xml:space="preserve">674.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s7676" xml:space="preserve">Quando chordæ ſunt ſimiles, æque tenſæ, ſed diverſæ
              <lb/>
              <note position="left" xlink:label="note-0276-07" xlink:href="note-0276-07a" xml:space="preserve">689.</note>
            longitudinis, motus harum cum motu pendulorum etiam
              <lb/>
              <note position="left" xlink:label="note-0276-08" xlink:href="note-0276-08a" xml:space="preserve">
                <emph style="sc">TA. XXVI.</emph>
                <lb/>
              fig. 4.</note>
            confertur. </s>
            <s xml:id="echoid-s7677" xml:space="preserve">Non intereſt quantum ad actionem gravitatis
              <lb/>
            in corpus, & </s>
            <s xml:id="echoid-s7678" xml:space="preserve">ideo quantum ad motum corporis ex gravi-
              <lb/>
            tate, utrum manente materiâ, ipſa vis gravitatis minuatur
              <lb/>
            in certa ratione, an vero manente hac vi materia in ea-
              <lb/>
            dem ratione augeatur , quod ergo ad motum chordæ
              <note symbol="*" position="left" xlink:label="note-0276-09" xlink:href="note-0276-09a" xml:space="preserve">111.</note>
            iam applicari poteſt . </s>
            <s xml:id="echoid-s7679" xml:space="preserve">Ergo chordæ, ACB, adb,
              <note symbol="*" position="left" xlink:label="note-0276-10" xlink:href="note-0276-10a" xml:space="preserve">687.</note>
            ponderibus æqualibus inflectuntur, agitantur ut corpora in
              <lb/>
            quibus gravitates agerent, quæ forent inter ſe ut ab, ad
              <lb/>
            AB; </s>
            <s xml:id="echoid-s7680" xml:space="preserve">in hac enim ratione inverſa ſunt quantitates materiæ
              <lb/>
            in chordis. </s>
            <s xml:id="echoid-s7681" xml:space="preserve">Chordæ etiam hæ moventur ut pendula, quo-
              <lb/>
            rum longitudines ſunt ut cB ad Db, aut AB ad ab; </s>
            <s xml:id="echoid-s7682" xml:space="preserve">ergo
              <lb/>
            quadrata durationum vibrationum, quæ ſunt inversè ut vi-
              <lb/>
            res, & </s>
            <s xml:id="echoid-s7683" xml:space="preserve">directè ut longitudines pendulorum , ſunt in
              <note symbol="*" position="left" xlink:label="note-0276-11" xlink:href="note-0276-11a" xml:space="preserve">3@2.</note>
            tione compoſita ex inverſa ratione ab ad AB, id eſt, AB
              <lb/>
            ad ab, & </s>
            <s xml:id="echoid-s7684" xml:space="preserve">directa ipſius AB ad ab; </s>
            <s xml:id="echoid-s7685" xml:space="preserve">quæ ratio compoſita
              <lb/>
            eſt ratio quadratorum longitudinum; </s>
            <s xml:id="echoid-s7686" xml:space="preserve">chordarum igitur lon-
              <lb/>
            gitudines ſunt ut vibrationum tempora.</s>
            <s xml:id="echoid-s7687" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7688" xml:space="preserve">Eodem modo comparantur tempora vibrationum chorda-
              <lb/>
              <note position="left" xlink:label="note-0276-12" xlink:href="note-0276-12a" xml:space="preserve">690.</note>
            rum diverſæ craſſitiei, poſitis chordis æqualibus, & </s>
            <s xml:id="echoid-s7689" xml:space="preserve"/>
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