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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[611.] PROPOSITIO CVIII.
Page: 650 (633)
[612.] PROPOSITIO CIX.
Page: 650 (633)
[613.] PROPOSITIO CX.
Page: 651 (634)
[614.] PROPOSITIO CXI.
Page: 652 (635)
[615.] PROPOSITIO CXII.
Page: 653 (636)
[616.] PROPOSITIO CXIII.
Page: 653 (636)
[617.] PROPOSITIO CXIV.
Page: 654 (637)
[618.] PROPOSITIO CXV.
Page: 654 (637)
[619.] PROPOSITIO CXVI.
Page: 655 (638)
[620.] PROPOSITIO CXVII.
Page: 655 (638)
[621.] CAPUT OCTAVUM. De Cohærentia ſolidorum utrimque a foramine arcto exceptorum.
Page: 656 (639)
[622.] EXPERIMENTUM CCIX.
Page: 657 (640)
[623.] EXPERIMENTUM CCX.
Page: 657 (640)
[624.] EXPERIMENTUM CCXI.
Page: 658 (641)
[625.] EXPERIMENTUM CCXII.
Page: 658 (641)
[626.] EXPERIMENTUM CCXIII.
Page: 659 (642)
[627.] EXPERIMENTUM CCXIV.
Page: 659 (642)
[628.] EXPERIMENTUM CCXV.
Page: 659 (642)
[629.] EXPERIMENTUM CCXVI.
Page: 660 (643)
[630.] EXPERIMENTUM CCXVII.
Page: 660 (643)
[631.] EXPERIMENTUM CCXVIII.
Page: 660 (643)
[632.] EXPERIMENTUM CCXIX.
Page: 660 (643)
[633.] EXPERIMENTUM CCXX.
Page: 661 (644)
[634.] TABULA
Page: 664 (647)
[635.] EXPERIMENTUM CCXXI.
Page: 668 (651)
[636.] CAPUT NONUM. De Cohærentia corporum compreſſorum.
Page: 669 (652)
[637.] EXPERIMENTUM CCXXII.
Page: 672 (655)
[638.] EXPERIMENTUM CCXXIII.
Page: 672 (655)
[639.] EXPERIMENTUM CCXXIV.
Page: 672 (655)
[640.] EXPERIMENTUM CCXXV.
Page: 672 (655)
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          <pb o="602" file="0618" n="619" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
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        <div xml:id="echoid-div559" type="section" level="1" n="559">
          <head xml:id="echoid-head673" xml:space="preserve">PROPOSITIO LXXX.</head>
          <p>
            <s xml:id="echoid-s14970" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14971" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s14972" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s14973" xml:space="preserve">6. </s>
            <s xml:id="echoid-s14974" xml:space="preserve">Dato momento ſolidi parabolici A F O E M,
              <lb/>
            & </s>
            <s xml:id="echoid-s14975" xml:space="preserve">ponderis P ex vertice pendentis, datoque momento ſolidi abſciſſi
              <lb/>
            D G P E H, invenire pondus ex vertice E ſuſpendendum, ita ut
              <lb/>
            momentum ſolidi A F O E M cum ſuo pondere, ſit ad momentum ſo-
              <lb/>
            lidi D G P E cum ſuo in eadem proportione ad Cohærentias.</s>
            <s xml:id="echoid-s14976" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14977" xml:space="preserve">Quantitatibus deſignatis ut in præcedenti Propoſitione, & </s>
            <s xml:id="echoid-s14978" xml:space="preserve">pon-
              <lb/>
            dere appenſo ex E B = p. </s>
            <s xml:id="echoid-s14979" xml:space="preserve">pondere ex E C poſito = x, ordi-
              <lb/>
            nabitur hæc proportio.</s>
            <s xml:id="echoid-s14980" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14981" xml:space="preserve">{4/15}a b b d + b p. </s>
            <s xml:id="echoid-s14982" xml:space="preserve">a a d:</s>
            <s xml:id="echoid-s14983" xml:space="preserve">: {4/15} {b b c
              <emph style="super">5</emph>
            d/a
              <emph style="super">4</emph>
            } + {b c c x.</s>
            <s xml:id="echoid-s14984" xml:space="preserve">/a a} c c d.
              <lb/>
            </s>
            <s xml:id="echoid-s14985" xml:space="preserve">unde eruitur x = {4/15} a b d + p --
              <unsure/>
            {4/15} {b c
              <emph style="super">3</emph>
            d.</s>
            <s xml:id="echoid-s14986" xml:space="preserve">/a a}</s>
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        <div xml:id="echoid-div560" type="section" level="1" n="560">
          <head xml:id="echoid-head674" xml:space="preserve">PROPOSITIO LXXXI.</head>
          <p>
            <s xml:id="echoid-s14987" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14988" xml:space="preserve">26. </s>
            <s xml:id="echoid-s14989" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s14990" xml:space="preserve">6. </s>
            <s xml:id="echoid-s14991" xml:space="preserve">Si momentum Gravitatis in ſolido parabolico
              <lb/>
            A F O E M, & </s>
            <s xml:id="echoid-s14992" xml:space="preserve">momentum ponderis P ex vertice E pendentis, ha-
              <lb/>
            beat ad Cohærentiam baſeos A F O M eandem rationem, erit
              <lb/>
            magnitudo ſolidi Parabolici ſexies ſumta æqualis ponderi P decies
              <lb/>
            quinquies aucto.</s>
            <s xml:id="echoid-s14993" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14994" xml:space="preserve">Nam quantitatibus deſignatis ut ante, erit momentum gravitatis in
              <lb/>
            ſolido parabolico = {4/15} a b b d. </s>
            <s xml:id="echoid-s14995" xml:space="preserve">momentum ponderis P = b p. </s>
            <s xml:id="echoid-s14996" xml:space="preserve">Cohæ-
              <lb/>
            rentia baſeos = a a d; </s>
            <s xml:id="echoid-s14997" xml:space="preserve">ad quam cum utrumque momentum habet
              <lb/>
            eandem rationem, erit {4/15} a b b d = b p. </s>
            <s xml:id="echoid-s14998" xml:space="preserve">ſive {4/15} a b d = p. </s>
            <s xml:id="echoid-s14999" xml:space="preserve">unde 4 a b d
              <lb/>
            = 15 p. </s>
            <s xml:id="echoid-s15000" xml:space="preserve">Sed {2/3} a b d. </s>
            <s xml:id="echoid-s15001" xml:space="preserve">conſtituunt magnitudinem ſolidi parabolici, ea
              <lb/>
            vero ſexies ſumta eſt = 4 a b d. </s>
            <s xml:id="echoid-s15002" xml:space="preserve">quare ſexies magnitudo ſolidi eſt
              <lb/>
            = ponderi P decies quinquies aucto.</s>
            <s xml:id="echoid-s15003" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div561" type="section" level="1" n="561">
          <head xml:id="echoid-head675" xml:space="preserve">PROPOSITIO LXXXII.</head>
          <p>
            <s xml:id="echoid-s15004" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s15005" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s15006" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s15007" xml:space="preserve">7. </s>
            <s xml:id="echoid-s15008" xml:space="preserve">Sit ſolidum Paraboliforme A T C K B, ita
              <lb/>
            ut C ſit vertex Parabolæ, C T Tangens, in quam perpendicula-
              <lb/>
            ris ſit T A ſecans parabolam in A, ſit baſis T C K affixa </s>
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