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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[531.] EXPERIMENTUM CLXXXV.
Page: 593 (576)
[532.] PROPOSITIO LIII.
Page: 596 (579)
[533.] PROPOSITIO LIV.
Page: 598 (581)
[534.] PROPOSITIO LV.
Page: 599 (582)
[535.] PROPOSITIO LVI.
Page: 600 (583)
[536.] PROPOSITIO LVII.
Page: 601 (584)
[537.] De Conis & Pyramidibus. PROPOSITIO LVIII.
Page: 602 (585)
[538.] PROPOSITIO LIX.
Page: 602 (585)
[539.] PROPOSITIO LX.
Page: 603 (586)
[540.] PROPOSITIO LXI.
Page: 604 (587)
[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)
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              <pb o="600" file="0616" n="617" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
            {4 a c r r- 8 a c r x+4 a c x x-4 a c r r {x/r}-8 a c r {x/r}-4 a c x x {x/r}/15 r}.
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            <s xml:id="echoid-s14898" xml:space="preserve">quæ quantitas multiplicata per {5/16} a-{5/16}a {x/r}. </s>
            <s xml:id="echoid-s14899" xml:space="preserve">dat momentum
              <lb/>
            ſegmenti F K B F. </s>
            <s xml:id="echoid-s14900" xml:space="preserve">eſt autem Cohærentia baſeos F C K = 8 r
              <emph style="super">3</emph>
            -16 r r x
              <lb/>
            + 16 r x x-8 x 3. </s>
            <s xml:id="echoid-s14901" xml:space="preserve">quare determinata ſunt momenta ſolidi A B O,
              <lb/>
            F B K. </s>
            <s xml:id="echoid-s14902" xml:space="preserve">& </s>
            <s xml:id="echoid-s14903" xml:space="preserve">Cohærentiæ ipſorum.</s>
            <s xml:id="echoid-s14904" xml:space="preserve"/>
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        <div xml:id="echoid-div557" type="section" level="1" n="557">
          <head xml:id="echoid-head671" xml:space="preserve">PROPOSITIO LXXVIII.</head>
          <p style="it">
            <s xml:id="echoid-s14905" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14906" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s14907" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s14908" xml:space="preserve">6. </s>
            <s xml:id="echoid-s14909" xml:space="preserve">Solidi parabolici utrimque plani A M O F E,
              <lb/>
            cujus vertex eſt E, tum abſciſſæ portionis D G P E H, Cohæren-
              <lb/>
            tiæ baſium A M O F, D G P H, parieti ad horizontem perpendicu-
              <lb/>
            lari affix arum ſunt inter ſe ut longitudines axium E B. </s>
            <s xml:id="echoid-s14910" xml:space="preserve">E C. </s>
            <s xml:id="echoid-s14911" xml:space="preserve">poſi-
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            tis ſuperficiebus A E F, M E O ad horizontem perpendicularibus.</s>
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          <p>
            <s xml:id="echoid-s14913" xml:space="preserve">Nam eſt Cohærentia baſeos A F O M, ad D G P H in ratione du-
              <lb/>
            plicata altitudinis A F, ad D G. </s>
            <s xml:id="echoid-s14914" xml:space="preserve">& </s>
            <s xml:id="echoid-s14915" xml:space="preserve">ſimplici latitudinis F O, ad
              <lb/>
            G P. </s>
            <s xml:id="echoid-s14916" xml:space="preserve">ſed eſt G P = F O. </s>
            <s xml:id="echoid-s14917" xml:space="preserve">quare erunt ambarum baſium Cohærentiæ,
              <lb/>
            uti quadrata altitudinum A F, D G. </s>
            <s xml:id="echoid-s14918" xml:space="preserve">ſed ex natura Parabolæ eſt E B,
              <lb/>
            E C:</s>
            <s xml:id="echoid-s14919" xml:space="preserve">:
              <emph style="ol">A F
                <emph style="super">q</emph>
              </emph>
            . </s>
            <s xml:id="echoid-s14920" xml:space="preserve">
              <emph style="ol">D G
                <emph style="super">q</emph>
              </emph>
            . </s>
            <s xml:id="echoid-s14921" xml:space="preserve">quare ſunt Cohærentiæ baſium uti longitudines
              <lb/>
            axium E B, E C.</s>
            <s xml:id="echoid-s14922" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14923" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s14924" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14925" xml:space="preserve">Si ſolidi Parabolici dimidium E B F O E conſideretur,
              <lb/>
            & </s>
            <s xml:id="echoid-s14926" xml:space="preserve">abſciſſa portio E C G P E, vel alterum dimidium E B A M E, & </s>
            <s xml:id="echoid-s14927" xml:space="preserve">
              <lb/>
            abſciſſa portio E C D H E, eadem demonſtratio locum habebit,
              <lb/>
            eritque Cohærentia baſeos B F O, ad C G P, aut B A M ad D C H,
              <lb/>
            uti longitudo E B ad E C</s>
          </p>
          <p>
            <s xml:id="echoid-s14928" xml:space="preserve">Corol 2. </s>
            <s xml:id="echoid-s14929" xml:space="preserve">Si ex vertice integri vel dimidii ſolidi hujus Parabolici
              <lb/>
            pendeat pondus P, hujus momentum ad Cohærentiam baſium
              <lb/>
            A M O F, D G P H eandem habebit rationem, adeoque erunt
              <lb/>
            ejuſmodi ſolida æqualis ubivis Cohærentiæ, non conſiderata eorum
              <lb/>
            gravitate.</s>
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          </p>
          <p>
            <s xml:id="echoid-s14931" xml:space="preserve">Nam momentum ponderis P pendentis ex vecte E B, eſt ad mo-
              <lb/>
            mentum ejuſdem ponderis P, pendentis ex vecte E C, veluti eſt
              <lb/>
            E B ad E C: </s>
            <s xml:id="echoid-s14932" xml:space="preserve">ſed Cohærentiæ horum ſolidorum ſunt uti E B ad E </s>
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