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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[601.] PROPOSITIO XCIX.
Page: 643 (626)
[602.] PROPOSITIO C.
Page: 644 (627)
[603.] PROPOSITIO CI.
Page: 644 (627)
[604.] PROPOSITIO CII.
Page: 645 (628)
[605.] EXPERIMENTUM CCVIII.
Page: 645 (628)
[606.] PROPOSITIO CIII.
Page: 646 (629)
[607.] PROPOSITIO CIV.
Page: 647 (630)
[608.] PROPOSITIO CV.
Page: 648 (631)
[609.] PROPOSITIO CVI.
Page: 648 (631)
[610.] PROPOSITIO CVII.
Page: 649 (632)
[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)
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              <pb o="626" file="0642" n="643" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
            circulo R A S B inſcribantur lineæ R S, S V, ſumantur duæ lineæ
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            ad libitum, quarum X Z ſit 5, Z Y 7 partium, quæ jungantur ad
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            angulum rectum X Z Y: </s>
            <s xml:id="echoid-s15740" xml:space="preserve">per tria puncta X, Z, Y. </s>
            <s xml:id="echoid-s15741" xml:space="preserve">deſcribatur cir-
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            culus, fiat hic, vel alius ipſi æqualis, concentricus dato R A S B,
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            atque ex punctis X, Z, Y, ducantur ad centrum C rectæ, ſecabi-
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            tur peripheria in punctis R, S, V. </s>
            <s xml:id="echoid-s15742" xml:space="preserve">quæ ſi jungantur rectis R S, S V.
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            <s xml:id="echoid-s15743" xml:space="preserve">ſatisfactum erit quæſito.</s>
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          <head xml:id="echoid-head720" xml:space="preserve">PROPOSITIO XCIX.</head>
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            <s xml:id="echoid-s15745" xml:space="preserve">Tab XXIV fig. </s>
            <s xml:id="echoid-s15746" xml:space="preserve">9. </s>
            <s xml:id="echoid-s15747" xml:space="preserve">Si parallelopipedum vel cylindrus A O, in
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            medio B ſuffultus, propria gravitate utriuſque extremi B A, B O
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            fuerit fractur æ proximus, hic utroque extremo A & </s>
            <s xml:id="echoid-s15748" xml:space="preserve">O fulcro im-
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            poſitus, propriâ gravitate in medio B fractur æ quoque proximus
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            erit.</s>
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            <s xml:id="echoid-s15750" xml:space="preserve">Concipiatur primo fulcrum in medio B, & </s>
            <s xml:id="echoid-s15751" xml:space="preserve">loco gravitatis utri-
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            uſque extremi A B, B O, pondera R & </s>
            <s xml:id="echoid-s15752" xml:space="preserve">Q extremis appenſa eun-
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            dem præſtare effectum, quibus ſcilicet ſolidum in B redditur fra-
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            cturæ proximum, tum Fulcrum B tantopere premit ſurſum hoc ſo-
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            lidum, quantum ambo pondera R + Q agunt deorſum: </s>
            <s xml:id="echoid-s15753" xml:space="preserve">Quam
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            obrem concipiatur ſolidum A B O converti, atque extrema A & </s>
            <s xml:id="echoid-s15754" xml:space="preserve">O
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            imponi fulcris, quæ reſiſtant tantopere ac pondera R + Q egerunt,
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            atque ex medio B appendi pondus, quod deorſum agat, quantum
              <lb/>
            fulcrum B antea egit ſurſum, manifeſtum eſt Cylindrum in codem
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            ſtatu ac ante poni, hoc eſt fieri rupturæ proximum: </s>
            <s xml:id="echoid-s15755" xml:space="preserve">ſed pondera
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            R + Q agere ſuppoſita ſunt, quantum gravitas totius ſolidi A B O,
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            adeoque fulcrum B egit ſurſum, quantum gravitabat ſolidum, hinc
              <lb/>
            pondus in medio B, æquale actioni fulcri, erit etiam æquale gra-
              <lb/>
            vitati ſolidi, quare gravitas ſolidi A B O ponit id ipſum duobus
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            fulcris impoſitum, etiam fracturæ proximum.</s>
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            <s xml:id="echoid-s15757" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s15758" xml:space="preserve">Ergo parallelopipedum vel Cylindrus, qui propriâ gra-
              <lb/>
            vitate frangeretur duobus impoſitus fulcris, poteſt eſſe duplo lon-
              <lb/>
            gior. </s>
            <s xml:id="echoid-s15759" xml:space="preserve">quam parallelopipedum vel Cylindrus uno ſui extremo pa-
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            rieti infixus.</s>
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