Musschenbroek, Petrus van, Physicae experimentales, et geometricae de magnete, tuborum capillarium vitreorumque speculorum attractione, magnitudine terrae, cohaerentia corporum firmorum dissertationes: ut et ephemerides meteorologicae ultraiectinae

Table of contents

< >
[471.] EXPERIMENTUM CLX.
Page: 555 (538)
[472.] EXPERIMENTUM CLXI.
Page: 556 (539)
[473.] EXPERIMENTUM CLXII.
Page: 558 (541)
[474.] EXPERIMENTUM CLXIII.
Page: 559 (542)
[475.] EXPERIMENTUM CLXIV.
Page: 559 (542)
[476.] EXPERIMENTUM CLXV.
Page: 559 (542)
[477.] EXPERIMENTUM CLXVI.
Page: 559 (542)
[478.] EXPERIMENTUM CLXVII.
Page: 559 (542)
[479.] EXPERIMENTUM CLXVIII.
Page: 560 (543)
[480.] EXPERIMENTUM CLXIX.
Page: 560 (543)
[481.] EXPERIMENTUM CLXX.
Page: 560 (543)
[482.] EXPERIMENTUM CLXXI.
Page: 561 (544)
[483.] EXPERIMENTUM CLXXII.
Page: 561 (544)
[484.] EXPERIMENTUM CLXXIII.
Page: 561 (544)
[485.] EXPERIMENTUM CLXXIV.
Page: 562 (545)
[486.] EXPERIMENTUM CLXXV.
Page: 562 (545)
[487.] EXPERIMENTUM CLXXVI.
Page: 562 (545)
[488.] EXPERIMENTUM CLXXVII.
Page: 562 (545)
[489.] EXPERIMENTUM CLXXVIII.
Page: 564 (547)
[490.] EXPERIMENTUM CLXXIX.
Page: 564 (547)
[491.] EXPERIMENTUM CLXXX.
Page: 564 (547)
[492.] EXPERIMENTUM CLXXXI.
Page: 564 (547)
[493.] EXPERIMENTUM CLXXXII.
Page: 564 (547)
[494.] EXPERIMENTUM CLXXXIII.
Page: 564 (547)
[495.] PROPOSITIO XIX.
Page: 565 (548)
[496.] PROPOSITIO XX.
Page: 566 (549)
[497.] PROPOSITIO XXI.
Page: 567 (550)
[498.] EXPERIMENTUM CLXXXIV.
Page: 568 (551)
[499.] PROPOSITIO XXII.
Page: 568 (551)
[500.] Pro Corporibus Flexibilibus.
Page: 569 (552)
< >
page |< < (569) of 795 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div521" type="section" level="1" n="521">
          <pb o="569" file="0585" n="586" rhead="CORPORUM FIRMORUM."/>
          <p>
            <s xml:id="echoid-s13701" xml:space="preserve">Vocetur A B, a. </s>
            <s xml:id="echoid-s13702" xml:space="preserve">A D, b. </s>
            <s xml:id="echoid-s13703" xml:space="preserve">E F c. </s>
            <s xml:id="echoid-s13704" xml:space="preserve">E H, d. </s>
            <s xml:id="echoid-s13705" xml:space="preserve">Erit ſoliditas B D ad
              <lb/>
            ſoliditatem F H:</s>
            <s xml:id="echoid-s13706" xml:space="preserve">: a a b. </s>
            <s xml:id="echoid-s13707" xml:space="preserve">c c d. </s>
            <s xml:id="echoid-s13708" xml:space="preserve">& </s>
            <s xml:id="echoid-s13709" xml:space="preserve">momentum e pondere A B C D,
              <lb/>
            ad momentum e pondere E F G H:</s>
            <s xml:id="echoid-s13710" xml:space="preserve">: a a b X {1/2} b. </s>
            <s xml:id="echoid-s13711" xml:space="preserve">c c d X {1/2} d.
              <lb/>
            </s>
            <s xml:id="echoid-s13712" xml:space="preserve">ſed eſt {1/2} b. </s>
            <s xml:id="echoid-s13713" xml:space="preserve">ad {1/2} d:</s>
            <s xml:id="echoid-s13714" xml:space="preserve">: b. </s>
            <s xml:id="echoid-s13715" xml:space="preserve">d. </s>
            <s xml:id="echoid-s13716" xml:space="preserve">quare momenta oriunda ex ponderibus
              <lb/>
            erunt uti a a b b. </s>
            <s xml:id="echoid-s13717" xml:space="preserve">ad c c d d.</s>
            <s xml:id="echoid-s13718" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13719" xml:space="preserve">Verum ſupponitur
              <emph style="ol">AD</emph>
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s13720" xml:space="preserve">
              <emph style="ol">EH</emph>
              <emph style="super">q</emph>
            :</s>
            <s xml:id="echoid-s13721" xml:space="preserve">: A B, E F. </s>
            <s xml:id="echoid-s13722" xml:space="preserve">hoc eſt Analytice
              <lb/>
            b b. </s>
            <s xml:id="echoid-s13723" xml:space="preserve">d d:</s>
            <s xml:id="echoid-s13724" xml:space="preserve">: a. </s>
            <s xml:id="echoid-s13725" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13726" xml:space="preserve">adeoque in momentis loco b b, d d. </s>
            <s xml:id="echoid-s13727" xml:space="preserve">ponendo quan-
              <lb/>
            titates proportionales, erunt momenta oriunda ex ponderibus in-
              <lb/>
            ter ſe uti a
              <emph style="super">3</emph>
            , ad c
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s13728" xml:space="preserve">Verum Cohærentiæ corporum ſunt inter ſe ut
              <lb/>
            Cubi diametrorum per Propoſ. </s>
            <s xml:id="echoid-s13729" xml:space="preserve">XXXVI. </s>
            <s xml:id="echoid-s13730" xml:space="preserve">quare Cohærentiæ ho-
              <lb/>
            rum cylindrorum erunt inter ſe, uti momenta è ponderibus ſolido-
              <lb/>
            rum oriunda.</s>
            <s xml:id="echoid-s13731" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div522" type="section" level="1" n="522">
          <head xml:id="echoid-head634" xml:space="preserve">PROPOSITIO XLIV.</head>
          <p style="it">
            <s xml:id="echoid-s13732" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s13733" xml:space="preserve">XXIII. </s>
            <s xml:id="echoid-s13734" xml:space="preserve">fig 37. </s>
            <s xml:id="echoid-s13735" xml:space="preserve">Dato corpore E F G H, datoque pondere K,
              <lb/>
            cujus momentum ſimul cum momento ponderis dati Cylindri ad Co-
              <lb/>
            hærentiam ejusdem, habeat quamlibet rationem datam, invenire
              <lb/>
            aliud corpus A B C D ſimile priori, cujus momentum gravitatis ad
              <lb/>
            Cohærentiam habeat eandem proportionem.</s>
            <s xml:id="echoid-s13736" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13737" xml:space="preserve">Ponatur {1/2} E F = a. </s>
            <s xml:id="echoid-s13738" xml:space="preserve">circumferentia baſeos = c. </s>
            <s xml:id="echoid-s13739" xml:space="preserve">E H = b. </s>
            <s xml:id="echoid-s13740" xml:space="preserve">pondus
              <lb/>
            K = p. </s>
            <s xml:id="echoid-s13741" xml:space="preserve">{1/2} A B = x. </s>
            <s xml:id="echoid-s13742" xml:space="preserve">A D = z. </s>
            <s xml:id="echoid-s13743" xml:space="preserve">ratio detur f ad d.</s>
            <s xml:id="echoid-s13744" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13745" xml:space="preserve">Eritſoliditas Cylindri = {1/2} a c b. </s>
            <s xml:id="echoid-s13746" xml:space="preserve">& </s>
            <s xml:id="echoid-s13747" xml:space="preserve">momentnm ex gravitate oriun-
              <lb/>
            dum = {1/4} a c b b. </s>
            <s xml:id="echoid-s13748" xml:space="preserve">eſt momentum ponderis = p b. </s>
            <s xml:id="echoid-s13749" xml:space="preserve">Cohærentia baſeos
              <lb/>
            = 8a
              <emph style="super">3</emph>
            : </s>
            <s xml:id="echoid-s13750" xml:space="preserve">ſtabunt igitur quantitates ſecundum hanc proportionem
              <lb/>
            {1/4} a c b b + p b. </s>
            <s xml:id="echoid-s13751" xml:space="preserve">a
              <emph style="super">3</emph>
            :</s>
            <s xml:id="echoid-s13752" xml:space="preserve">: f. </s>
            <s xml:id="echoid-s13753" xml:space="preserve">d.</s>
            <s xml:id="echoid-s13754" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13755" xml:space="preserve">Quia corpora E F G H, A B C D requiruntur ſimilia, erit a. </s>
            <s xml:id="echoid-s13756" xml:space="preserve">x:</s>
            <s xml:id="echoid-s13757" xml:space="preserve">: c. </s>
            <s xml:id="echoid-s13758" xml:space="preserve">{c x.</s>
            <s xml:id="echoid-s13759" xml:space="preserve">/a}
              <lb/>
            circumferentia baſeos A B. </s>
            <s xml:id="echoid-s13760" xml:space="preserve">totaque baſis {1/2} {c x x.</s>
            <s xml:id="echoid-s13761" xml:space="preserve">/a} & </s>
            <s xml:id="echoid-s13762" xml:space="preserve">ut habeatur
              <lb/>
            longitudo A D. </s>
            <s xml:id="echoid-s13763" xml:space="preserve">fiat {1/2} a c. </s>
            <s xml:id="echoid-s13764" xml:space="preserve">{1/2} {c x
              <emph style="super">2</emph>
            /a}:</s>
            <s xml:id="echoid-s13765" xml:space="preserve">: b. </s>
            <s xml:id="echoid-s13766" xml:space="preserve">{b x x/a a} = z. </s>
            <s xml:id="echoid-s13767" xml:space="preserve">adeoque erit ſo-
              <lb/>
            liditas Cylindri A B C D = {1/2} {b c x
              <emph style="super">4</emph>
            /a
              <emph style="super">3</emph>
            } quæ ducta in dimidiam </s>
          </p>
        </div>
      </text>
    </echo>
Impressum