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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[541.] PROPOSITIO LXII.
Page: 605 (588)
[542.] PROPOSITIO LXIII.
Page: 605 (588)
[543.] De Conidibus Parabolicis. PROPOSITIO LXIV.
Page: 606 (589)
[544.] PROPOSITIO LXV.
Page: 607 (590)
[545.] PROPOSITIO LXVI.
Page: 608 (591)
[546.] PROPOSITIO LXVII.
Page: 609 (592)
[547.] PROPOSITIO LXVIII.
Page: 610 (593)
[548.] PROPOSITIO LXIX.
Page: 611 (594)
[549.] PROPOSITIO LXX.
Page: 611 (594)
[550.] PROPOSITIO LXXI.
Page: 612 (595)
[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)
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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>
        </div>
        <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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