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

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            <s xml:id="echoid-s7689" xml:space="preserve">
              <pb o="197" file="0277" n="302" rhead="MATHEMATICA. LIB. I. CAP. XXIX."/>
            libus ponderibus tenſis; </s>
            <s xml:id="echoid-s7690" xml:space="preserve">hæ æqualibus ponderibus æqualiter
              <lb/>
            inflectuntur , & </s>
            <s xml:id="echoid-s7691" xml:space="preserve">ideò agitantur ut pendula æqualia, in
              <note symbol="*" position="right" xlink:label="note-0277-01" xlink:href="note-0277-01a" xml:space="preserve">684</note>
            agunt gravitates, quæ ſunt inversè ut quantitates materiæ
              <lb/>
            in chordis , id eſt, ut quadrata diametrorum; </s>
            <s xml:id="echoid-s7692" xml:space="preserve">quæ
              <note symbol="*" position="right" xlink:label="note-0277-02" xlink:href="note-0277-02a" xml:space="preserve">112.</note>
            iterum invertenda eſt ad habendam proportionem quadra-
              <lb/>
            torum durationum vibrationum ; </s>
            <s xml:id="echoid-s7693" xml:space="preserve">Ideo diametri ipſæ
              <note symbol="*" position="right" xlink:label="note-0277-03" xlink:href="note-0277-03a" xml:space="preserve">301.</note>
            ut durationes.</s>
            <s xml:id="echoid-s7694" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7695" xml:space="preserve">Datis chordis ejuſdem generis quibuſcunque, vibratio
              <lb/>
              <note position="right" xlink:label="note-0277-04" xlink:href="note-0277-04a" xml:space="preserve">691.</note>
            num durationes ſunt in ratione compoſita, ex ratione inver-
              <lb/>
            ſa radicum quadratarum ponderum, quibus chordæ tendun-
              <lb/>
            tur , ratione longitudinum chordarum , & </s>
            <s xml:id="echoid-s7696" xml:space="preserve">ratione
              <note symbol="*" position="right" xlink:label="note-0277-05" xlink:href="note-0277-05a" xml:space="preserve">868.</note>
            metrorum . </s>
            <s xml:id="echoid-s7697" xml:space="preserve">Multiplicando diametrum per
              <note symbol="*" position="right" xlink:label="note-0277-06" xlink:href="note-0277-06a" xml:space="preserve">689.</note>
            dividendo productum per radicem quadratam ponderis,
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0277-07" xlink:href="note-0277-07a" xml:space="preserve">690.</note>
            quo chorda tenditur, ſi pro variis chordis eadem operatio
              <lb/>
            inſtituatur, quotientes diviſionum erunt inter ſe ut vibra-
              <lb/>
            tionum tempora.</s>
            <s xml:id="echoid-s7698" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7699" xml:space="preserve">Lamina elaſtica pro congerie chordarum haberi poteſt:
              <lb/>
            </s>
            <s xml:id="echoid-s7700" xml:space="preserve">
              <note position="right" xlink:label="note-0277-08" xlink:href="note-0277-08a" xml:space="preserve">692.</note>
            quando lamina inflectitur, fibræ quædam producuntur, & </s>
            <s xml:id="echoid-s7701" xml:space="preserve">
              <lb/>
            productiones inæquales ſunt in diverſis laminæ punctis, & </s>
            <s xml:id="echoid-s7702" xml:space="preserve">
              <lb/>
            ex iis, quæ de chordis dicta ſunt, curva, quæ a lamina in-
              <lb/>
            flexa formatur, detegitur.</s>
            <s xml:id="echoid-s7703" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7704" xml:space="preserve">Comparando inter ſe varias ejuſdem laminæ inflexiones,
              <lb/>
              <note position="right" xlink:label="note-0277-09" xlink:href="note-0277-09a" xml:space="preserve">693.</note>
            hæ proportionales ſunt viribus quibus lamina flectitur. </s>
            <s xml:id="echoid-s7705" xml:space="preserve">Sit
              <lb/>
              <note position="right" xlink:label="note-0277-10" xlink:href="note-0277-10a" xml:space="preserve">
                <emph style="sc">TA. XXVI.</emph>
                <lb/>
              fig. 5.</note>
            lamina AB, cujus extremitas A fixa eſt, duabus inflecta-
              <lb/>
            tur viribus, quibus perveniat ad ab & </s>
            <s xml:id="echoid-s7706" xml:space="preserve">ab; </s>
            <s xml:id="echoid-s7707" xml:space="preserve">ſi una fuerit
              <lb/>
            alterius dupla, bb & </s>
            <s xml:id="echoid-s7708" xml:space="preserve">bB erunt æquales; </s>
            <s xml:id="echoid-s7709" xml:space="preserve">& </s>
            <s xml:id="echoid-s7710" xml:space="preserve">ideo in vi-
              <lb/>
            brationibus motus laminæ eodem modo acceleratur ac
              <lb/>
              <note position="right" xlink:label="note-0277-11" xlink:href="note-0277-11a" xml:space="preserve">694.</note>
            motus chordæ , & </s>
            <s xml:id="echoid-s7711" xml:space="preserve">hæ vibrationes ſunt æque
              <note symbol="*" position="right" xlink:label="note-0277-12" xlink:href="note-0277-12a" xml:space="preserve">678.</note>
            næ .</s>
            <s xml:id="echoid-s7712" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0277-13" xlink:href="note-0277-13a" xml:space="preserve">686.</note>
            </s>
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        </div>
        <div xml:id="echoid-div1069" type="section" level="1" n="259">
          <head xml:id="echoid-head367" xml:space="preserve">
            <emph style="sc">Experimentum</emph>
          5.</head>
          <p>
            <s xml:id="echoid-s7713" xml:space="preserve">Lamina A ex variis laminis elaſticis junctis conſtat, The-
              <lb/>
              <note position="right" xlink:label="note-0277-14" xlink:href="note-0277-14a" xml:space="preserve">695.</note>
            cæ B inſeritur, ibique ad latus utrumque movetur inter re-
              <lb/>
              <note position="right" xlink:label="note-0277-15" xlink:href="note-0277-15a" xml:space="preserve">
                <emph style="sc">TA. XXVI.</emph>
                <lb/>
              fig. 6.</note>
            gulas cd, cd; </s>
            <s xml:id="echoid-s7714" xml:space="preserve">fila duo ſupremæ parti laminæ annectuntur,
              <lb/>
            & </s>
            <s xml:id="echoid-s7715" xml:space="preserve">per foramina e, e, in fundo Thecæ, immittuntur. </s>
            <s xml:id="echoid-s7716" xml:space="preserve">Pon-
              <lb/>
            dus ſemi-libræ filis appenditur, & </s>
            <s xml:id="echoid-s7717" xml:space="preserve">deſcendit hoc per ſpatium
              <lb/>
            ſemi-pollicis; </s>
            <s xml:id="echoid-s7718" xml:space="preserve">ſuperaddito æquali pondere, deſcenſus </s>
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