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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[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)
[581.] EXPERIMENTUM CXC.
Page: 633 (616)
[582.] EXPERIMENTUM CXCI.
Page: 633 (616)
[583.] EXPERIMENTUM CXCII.
Page: 635 (618)
[584.] EXPERIMENTUM CXCIII.
Page: 635 (618)
[585.] EXPERIMENTUM CXCIV.
Page: 635 (618)
[586.] EXPERIMENTUM CXCV.
Page: 635 (618)
[587.] EXPERIMENTUM CXCVI.
Page: 636 (619)
[588.] EXPERIMENTUM CXCVII.
Page: 636 (619)
[589.] EXPERIMENTUM CXCVIII.
Page: 636 (619)
[590.] EXPERIMENTUM CXCIX.
Page: 636 (619)
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              <pb o="549" file="0565" n="566" rhead="CORPORUM FIRMORUM."/>
            atque Potentia frangens extremitati D applicata agat directione
              <lb/>
            ad horizontem perpendiculari, fiet ruptura in orâ foraminis A E F.</s>
            <s xml:id="echoid-s12957" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s12958" xml:space="preserve">Poteſt conſiderari longitudo corporis A D ut vectis, cujus ful-
              <lb/>
            crum eſt ad A, potentia in D, eligatur quæcunque ſectio intermedia
              <lb/>
            C parallelela baſi A E F, in hac C, erit Cohærentia eadem ac in baſi
              <lb/>
            A E F, quia corpus eſt ubique æque craſſum: </s>
            <s xml:id="echoid-s12959" xml:space="preserve">eſt vero momentum po-
              <lb/>
            tentiæ D majus, applicatum vecti A D, quam D C breviori; </s>
            <s xml:id="echoid-s12960" xml:space="preserve">adeoque
              <lb/>
            potius ſuperabitur Cohærentia in A E F quam in C, & </s>
            <s xml:id="echoid-s12961" xml:space="preserve">quia vectis
              <lb/>
            A D eſt longiſſimus omnium in latere A D, cujus ope potentia maxi-
              <lb/>
            mum momentum exercet, franget hæc corpus in ora foraminis A E F.</s>
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          </p>
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        <div xml:id="echoid-div496" type="section" level="1" n="496">
          <head xml:id="echoid-head608" xml:space="preserve">PROPOSITIO XX.</head>
          <p style="it">
            <s xml:id="echoid-s12963" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s12964" xml:space="preserve">XIX. </s>
            <s xml:id="echoid-s12965" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s12966" xml:space="preserve">3. </s>
            <s xml:id="echoid-s12967" xml:space="preserve">Si dentur duo parallelopipeda horizontalia F E
              <lb/>
            A C, F E A D, ejusdem materiæ & </s>
            <s xml:id="echoid-s12968" xml:space="preserve">craſſitiei, ſed diverſæ longitu-
              <lb/>
            dinis A C, A D, quorum extremitatibus C & </s>
            <s xml:id="echoid-s12969" xml:space="preserve">D applicentur Po-
              <lb/>
            tentiæ rumpentes, harumque directiones ſint perpendiculares in A C
              <lb/>
            & </s>
            <s xml:id="echoid-s12970" xml:space="preserve">A D, ſepoſitâ corporum gravitate requirentur potentiæ ad C
              <lb/>
            & </s>
            <s xml:id="echoid-s12971" xml:space="preserve">D in ratione reciprocâ longitudinum A C, A D.</s>
            <s xml:id="echoid-s12972" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12973" xml:space="preserve">Quando franguntur hæc parallelopipeda in EAF primo ſolvun-
              <lb/>
            tur partes ſuperiores E, tum quæ propiores ſunt ad A, fitque ro-
              <lb/>
            tatio circa infimum punctum A, adeoque E A C, E A D poſſunt
              <lb/>
            conſiderari ut duo vectes incurvi, quorum centrum motus eſt in A,
              <lb/>
            & </s>
            <s xml:id="echoid-s12974" xml:space="preserve">qui brachia habent EA, AC, tum EA, AD: </s>
            <s xml:id="echoid-s12975" xml:space="preserve">Eſt autem Cohæ-
              <lb/>
            rentia baſium EAF eadem, quia ſunt baſes eædem, adeoque earum
              <lb/>
            reſiſtentia eſt eadem; </s>
            <s xml:id="echoid-s12976" xml:space="preserve">ſed reſiſtentia totius lateris A E poteſt conſi-
              <lb/>
            derari inſtar ponderis vel potentiæ applicatæ puncto E vectis E A:
              <lb/>
            </s>
            <s xml:id="echoid-s12977" xml:space="preserve">Eſt igitur potentia requiſita in C ad pondus vel potentiam in E, uti
              <lb/>
            E A ad A C: </s>
            <s xml:id="echoid-s12978" xml:space="preserve">& </s>
            <s xml:id="echoid-s12979" xml:space="preserve">potentia in D, ad idem pondus vel potentiam E,
              <lb/>
            uti EA ad AD. </s>
            <s xml:id="echoid-s12980" xml:space="preserve">quia EA eſt eadem quantitas poteſt poni = 1. </s>
            <s xml:id="echoid-s12981" xml:space="preserve">hinc
              <lb/>
            ſtabit C. </s>
            <s xml:id="echoid-s12982" xml:space="preserve">E:</s>
            <s xml:id="echoid-s12983" xml:space="preserve">: 1. </s>
            <s xml:id="echoid-s12984" xml:space="preserve">AC. </s>
            <s xml:id="echoid-s12985" xml:space="preserve">ſive {C/E}:</s>
            <s xml:id="echoid-s12986" xml:space="preserve">: {1.</s>
            <s xml:id="echoid-s12987" xml:space="preserve">/AC} tum D.</s>
            <s xml:id="echoid-s12988" xml:space="preserve">E:</s>
            <s xml:id="echoid-s12989" xml:space="preserve">: 1. </s>
            <s xml:id="echoid-s12990" xml:space="preserve">AD. </s>
            <s xml:id="echoid-s12991" xml:space="preserve">ſive {D/E}:</s>
            <s xml:id="echoid-s12992" xml:space="preserve">:
              <lb/>
            {1.</s>
            <s xml:id="echoid-s12993" xml:space="preserve">/AD} ſed eſt {C/E} ad {D/E}:</s>
            <s xml:id="echoid-s12994" xml:space="preserve">: C.</s>
            <s xml:id="echoid-s12995" xml:space="preserve">D. </s>
            <s xml:id="echoid-s12996" xml:space="preserve">quare C.</s>
            <s xml:id="echoid-s12997" xml:space="preserve">D:</s>
            <s xml:id="echoid-s12998" xml:space="preserve">: {1.</s>
            <s xml:id="echoid-s12999" xml:space="preserve">/AC} {1.</s>
            <s xml:id="echoid-s13000" xml:space="preserve">/AD}:</s>
            <s xml:id="echoid-s13001" xml:space="preserve">: AD. </s>
            <s xml:id="echoid-s13002" xml:space="preserve">AC
              <lb/>
            hoc eſt, erit C ad D in ratione reciproca longitudinum AC ad AD.</s>
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          <p>
            <s xml:id="echoid-s13004" xml:space="preserve">Hac propoſitione uſus fui in Experimentis præcedentibus, </s>
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