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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[521.] PROPOSITIO XLIII.
Page: 585 (568)
[522.] PROPOSITIO XLIV.
Page: 586 (569)
[523.] PROPOSITIO XLV.
Page: 587 (570)
[524.] PROPOSITIO XLVI.
Page: 588 (571)
[525.] PROPOSITIO XLVII.
Page: 589 (572)
[526.] PROPOSITIO XLVIII.
Page: 589 (572)
[527.] PROPOSITIO XLIX.
Page: 590 (573)
[528.] PROPOSITIO L.
Page: 590 (573)
[529.] PROPOSITIO LI.
Page: 591 (574)
[530.] PROPOSITIO LII.
Page: 592 (575)
[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)
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              <pb o="581" file="0597" n="598" rhead="CORPORUM FIRMORUM."/>
            circa Ellipſin, ad Cohærentiam Ellipſeos, in eadem ratione, ac
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            Cohærentia quadrati circa circulum, ad Cohærentiam circuli.</s>
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          <head xml:id="echoid-head645" xml:space="preserve">PROPOSITIO LIV.</head>
          <p style="it">
            <s xml:id="echoid-s14210" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14211" xml:space="preserve">XXV. </s>
            <s xml:id="echoid-s14212" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s14213" xml:space="preserve">9. </s>
            <s xml:id="echoid-s14214" xml:space="preserve">Sit dimidiati Cylindri ſegmentum A B C D E,
              <lb/>
            cujus baſis rectangula A B C applicata parieti perpendiculari ad
              <lb/>
            horizontem: </s>
            <s xml:id="echoid-s14215" xml:space="preserve">ſit parallelopipedum A B C E L M N, cujus baſis pla-
              <lb/>
            na A B C rectangula æqualis baſi Cylindrici ſegmenti, latus A B,
              <lb/>
            æquale A B, B C æquale B C, A E æquale radio D E in Cylindro,
              <lb/>
            erit momentum gravitatis in ſegmento Cylindrico ad momentum gra-
              <lb/>
            vitatis in parallelopipedo, uti duo ad tria.</s>
            <s xml:id="echoid-s14216" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s14217" xml:space="preserve">Ponatur radius A D = r. </s>
            <s xml:id="echoid-s14218" xml:space="preserve">peripheria circuli baſeos = p. </s>
            <s xml:id="echoid-s14219" xml:space="preserve">Iatitudo
              <lb/>
            B C = a.</s>
            <s xml:id="echoid-s14220" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14221" xml:space="preserve">Erit area dimidii circuli A D B E A = {1/4} r p, quæ ducta in latitu-
              <lb/>
            dinem B C = a, dat ſoliditatem ſegmenti Cylindrici A B C A = {1/4} a p r.
              <lb/>
            </s>
            <s xml:id="echoid-s14222" xml:space="preserve">centrum vero gravitatis in ſemicirculo diſtat a centro D circuli quanti-
              <lb/>
            tate {8rr/3p}. </s>
            <s xml:id="echoid-s14223" xml:space="preserve">in quam diſtantiam ducta ſoliditas, dat momentum
              <lb/>
            = {2/3} ar
              <emph style="super">3.</emph>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s14224" xml:space="preserve">Soliditas parallelopipedi A B C E L M N eſt = 2 arr, hujus cen-
              <lb/>
            trum gravitatis eſt in medio, cujus directio tranſit per {1/2} A E = {1/2} r.
              <lb/>
            </s>
            <s xml:id="echoid-s14225" xml:space="preserve">adeoque erit momentum parallelopipedi = {1/2} r X 2 arr = ar
              <emph style="super">3</emph>
            .</s>
            <s xml:id="echoid-s14226" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14227" xml:space="preserve">Eſt igitur momentum gravitatis in ſegmento cylindrico ad illud
              <lb/>
            in parallelopipedo:</s>
            <s xml:id="echoid-s14228" xml:space="preserve">, {2/3} ar
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s14229" xml:space="preserve">ar
              <emph style="super">3</emph>
            :</s>
            <s xml:id="echoid-s14230" xml:space="preserve">: 2,3.</s>
            <s xml:id="echoid-s14231" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14232" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s14233" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14234" xml:space="preserve">Si ergo ex latere B C parallelopipedi abſcindatur {1/3}pars,
              <lb/>
            per quam tranſeat ſegmentum parallelum ad ſuperficiem anteriorem
              <lb/>
            A B N M, erit momentum ex gravitate in parte reſidua parallelo-
              <lb/>
            pipedi æquale momento ſegmenti cylindrici = {2/3} ar
              <emph style="super">3</emph>
            .</s>
            <s xml:id="echoid-s14235" xml:space="preserve"/>
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            <s xml:id="echoid-s14236" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s14237" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14238" xml:space="preserve">Ut vero a parallelopipedo A B C L M N abſcindatur
              <lb/>
            pars, reliquumque habeat idem momentum gravitatis ac dimidia-
              <lb/>
            tus cylindrus, quæratur inter A M = r, ipſiuſque {2/3} partem media
              <lb/>
            proportionalis, quæ ſit = A O. </s>
            <s xml:id="echoid-s14239" xml:space="preserve">tum per O K tranſeat ſegmentum
              <lb/>
            parallelum baſi A B C, habebit parallelopipedum A B C O K idem
              <lb/>
            gravitatis momentum, quod dimidiatus cylindrus; </s>
            <s xml:id="echoid-s14240" xml:space="preserve">vocetur enim
              <lb/>
            A O, x, erit ſoliditas parallelopipedi A B C K O = 2 arx. </s>
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