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

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[551.] PROPOSITIO LXXII.
Page: 612 (595)
[552.] PROPOSITIO LXXIII.
Page: 613 (596)
[553.] PROPOSITIO LXXIV.
Page: 614 (597)
[554.] PROPOSITIO LXXV.
Page: 614 (597)
[555.] PROPOSITIO LXXVI.
Page: 616 (599)
[556.] PROPOSITIO LXXVII.
Page: 616 (599)
[557.] PROPOSITIO LXXVIII.
Page: 617 (600)
[558.] PROPOSITIO LXXIX.
Page: 618 (601)
[559.] PROPOSITIO LXXX.
Page: 619 (602)
[560.] PROPOSITIO LXXXI.
Page: 619 (602)
[561.] PROPOSITIO LXXXII.
Page: 619 (602)
[562.] PROPOSITIO LXXXIII.
Page: 620 (603)
[563.] PROPOSITIO LXXXIV.
Page: 621 (604)
[564.] De Corporibus Hyperbolicis. PROPOSITIO LXXXV.
Page: 622 (605)
[565.] PROPOSITIO LXXXVI.
Page: 622 (605)
[566.] PROPOSITIO LXXXVII.
Page: 623 (606)
[567.] PROPOSITIO LXXXVIII.
Page: 623 (606)
[568.] PROPOSITIO LXXXIX.
Page: 624 (607)
[569.] De Hemisphæriis. PROPOSITIO XC.
Page: 624 (607)
[570.] PROPOSITIO XCI.
Page: 625 (608)
[571.] PROPOSITIO XCII.
Page: 625 (608)
[572.] PROPOSITIO XCIII.
Page: 626 (609)
[573.] CAPUT SEXTUM. De Cohærentia Corporum quibus fulcrum ſupponitur. PROPOSITIO XCIV.
Page: 627 (610)
[574.] EXPERIMENTUM CLXXXVI.
Page: 629 (612)
[575.] PROPOSITIO XCV.
Page: 629 (612)
[576.] PROPOSITIO CXVI.
Page: 630 (613)
[577.] CAPUT SEPTIMUM. De Cohærentia reſpectiva ſolidorum duobus fulcris impoſitorum.
Page: 631 (614)
[578.] EXPERIMENTUM CLXXXVII.
Page: 632 (615)
[579.] EXPERIMENTUM CLXXXVIII.
Page: 633 (616)
[580.] EXPERIMENTUM CLXXXIX.
Page: 633 (616)
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          <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>
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