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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            <s xml:id="echoid-s15008" xml:space="preserve">
              <pb o="603" file="0619" n="620" rhead="CORPORUM FIRMORUM."/>
            ad horizontem perpendiculari, erit momentum gravitatis in ſolido
              <lb/>
            A T C K B, ad momentum gravitatis in ſegmento A O F M B, poſi-
              <lb/>
            tâ ſectione O F M parallela ad T C K, uti Cohærentia baſeos
              <lb/>
            T C K ad Cohærentiam baſeos O F M.</s>
            <s xml:id="echoid-s15009" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15010" xml:space="preserve">Vocetur C T, r. </s>
            <s xml:id="echoid-s15011" xml:space="preserve">A T, a. </s>
            <s xml:id="echoid-s15012" xml:space="preserve">O A, b. </s>
            <s xml:id="echoid-s15013" xml:space="preserve">O F, {b br.</s>
            <s xml:id="echoid-s15014" xml:space="preserve">/a a} C K, c. </s>
            <s xml:id="echoid-s15015" xml:space="preserve">Eſt ſpatium
              <lb/>
            O F A = {1/3} O F X O A = {1/3} {b
              <emph style="super">3</emph>
            r,/a a} & </s>
            <s xml:id="echoid-s15016" xml:space="preserve">ſpatium T C A = {1/3} a r: </s>
            <s xml:id="echoid-s15017" xml:space="preserve">adeo-
              <lb/>
            que ſoliditas O F M A B eſt = {b
              <emph style="super">3</emph>
            c r.</s>
            <s xml:id="echoid-s15018" xml:space="preserve">/3 a a} & </s>
            <s xml:id="echoid-s15019" xml:space="preserve">ſoliditas T C K A B = {1/3} a r c.
              <lb/>
            </s>
            <s xml:id="echoid-s15020" xml:space="preserve">diſtantia autem centri gravitatis ab O F in plano O F A eſt = {3/10} A O. </s>
            <s xml:id="echoid-s15021" xml:space="preserve">
              <lb/>
            adeoque erit in corpore O F A M. </s>
            <s xml:id="echoid-s15022" xml:space="preserve">a ſectione O F M remotum {3/10} A O. </s>
            <s xml:id="echoid-s15023" xml:space="preserve">
              <lb/>
            hinc momentum ſolidi O A B M F, erit = {b
              <emph style="super">4</emph>
            c r.</s>
            <s xml:id="echoid-s15024" xml:space="preserve">/10 a a} & </s>
            <s xml:id="echoid-s15025" xml:space="preserve">momentum ſo-
              <lb/>
            lidi T C K A B ex gravitate erit = {a a r c.</s>
            <s xml:id="echoid-s15026" xml:space="preserve">/10} Eſt autem Cohærentia
              <lb/>
            baſeos O F M = {b
              <emph style="super">4</emph>
            r r c.</s>
            <s xml:id="echoid-s15027" xml:space="preserve">/a
              <emph style="super">4</emph>
            } & </s>
            <s xml:id="echoid-s15028" xml:space="preserve">Cohærentia baſeos T C K = r r c: </s>
            <s xml:id="echoid-s15029" xml:space="preserve">ordi-
              <lb/>
            nentur momenta gravitatis & </s>
            <s xml:id="echoid-s15030" xml:space="preserve">Cohærentiæ in proportionem, erit
              <lb/>
            {b
              <emph style="super">4</emph>
            c r.</s>
            <s xml:id="echoid-s15031" xml:space="preserve">/10 a a} {b
              <emph style="super">4</emph>
            r r c/a
              <emph style="super">4</emph>
            }:</s>
            <s xml:id="echoid-s15032" xml:space="preserve">: {a a r c.</s>
            <s xml:id="echoid-s15033" xml:space="preserve">/10} r r c. </s>
            <s xml:id="echoid-s15034" xml:space="preserve">
              <lb/>
            multiplicando enim extrema & </s>
            <s xml:id="echoid-s15035" xml:space="preserve">media per ſe habentur producta
              <lb/>
            utrimque æqualia. </s>
            <s xml:id="echoid-s15036" xml:space="preserve">{b
              <emph style="super">4</emph>
            c c r
              <emph style="super">3</emph>
            /10 a a} = {a a b
              <emph style="super">4</emph>
            c c r
              <emph style="super">3</emph>
            .</s>
            <s xml:id="echoid-s15037" xml:space="preserve">/10 a
              <emph style="super">4</emph>
            } adeoque quantitates an-
              <lb/>
            tea fuerunt proportionales, unde momenta gravium ſunt inter
              <lb/>
            ſe veluti Cohærentiæ: </s>
            <s xml:id="echoid-s15038" xml:space="preserve">hoc etiam alio modo demonſtravit Cl. </s>
            <s xml:id="echoid-s15039" xml:space="preserve">
              <lb/>
            Leibnitſius.</s>
            <s xml:id="echoid-s15040" xml:space="preserve"/>
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          <head xml:id="echoid-head676" xml:space="preserve">PROPOSITIO LXXXIII.</head>
          <p>
            <s xml:id="echoid-s15041" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s15042" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s15043" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s15044" xml:space="preserve">8. </s>
            <s xml:id="echoid-s15045" xml:space="preserve">Sit ſolidum B R S A a D C parallelopipedum
              <lb/>
            rectangulum, cujus latus B D C E ad horizontem perpendiculare:
              <lb/>
            </s>
            <s xml:id="echoid-s15046" xml:space="preserve">ſit ſolidum parabolicum A a B E R S ex priori abſciſſum, atque ver-
              <lb/>
            tex parabolæ in a & </s>
            <s xml:id="echoid-s15047" xml:space="preserve">A, axes in a R, A S. </s>
            <s xml:id="echoid-s15048" xml:space="preserve">ordinatæ B R, E S: </s>
            <s xml:id="echoid-s15049" xml:space="preserve">tum
              <lb/>
            ſolidum reliquum B D C E a A baſi B D C E applicatum parieti </s>
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