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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          <p>
            <s xml:id="echoid-s14546" xml:space="preserve">
              <pb o="591" file="0607" n="608" rhead="CORPORUM FIRMORUM"/>
            ſit = x. </s>
            <s xml:id="echoid-s14547" xml:space="preserve">deinde G D = d. </s>
            <s xml:id="echoid-s14548" xml:space="preserve">F G = b. </s>
            <s xml:id="echoid-s14549" xml:space="preserve">peripheria baſeos {cd/r}. </s>
            <s xml:id="echoid-s14550" xml:space="preserve">pondus Q = q.</s>
            <s xml:id="echoid-s14551" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14552" xml:space="preserve">Erit ſoliditas Parabolicæ Conoidis A B C = {bcr/4} & </s>
            <s xml:id="echoid-s14553" xml:space="preserve">momentum
              <lb/>
            ex gravitate = {bbcr/12}. </s>
            <s xml:id="echoid-s14554" xml:space="preserve">& </s>
            <s xml:id="echoid-s14555" xml:space="preserve">momentum ponderis P appenſi = b x. </s>
            <s xml:id="echoid-s14556" xml:space="preserve">ita
              <lb/>
            quoque erit ſoliditas Conoidis D E F = {bcdd/4r}. </s>
            <s xml:id="echoid-s14557" xml:space="preserve">& </s>
            <s xml:id="echoid-s14558" xml:space="preserve">momentum ex
              <lb/>
            Gravitate = {bbcdd/12r}. </s>
            <s xml:id="echoid-s14559" xml:space="preserve">atque momentum ponderis Q appenſi = bq.
              <lb/>
            </s>
            <s xml:id="echoid-s14560" xml:space="preserve">Cohærentia vero baſeos A B eſt = 8r
              <emph style="super">3</emph>
            , & </s>
            <s xml:id="echoid-s14561" xml:space="preserve">baſeos D E = 8d
              <emph style="super">3</emph>
            : </s>
            <s xml:id="echoid-s14562" xml:space="preserve">ſuppo-
              <lb/>
            nitur in Propoſitione {bbcdd/12r} + bq. </s>
            <s xml:id="echoid-s14563" xml:space="preserve">8d
              <emph style="super">3</emph>
            :</s>
            <s xml:id="echoid-s14564" xml:space="preserve">: {bbcr/12} + bx. </s>
            <s xml:id="echoid-s14565" xml:space="preserve">8r
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s14566" xml:space="preserve">
              <lb/>
            multiplicatis extremis & </s>
            <s xml:id="echoid-s14567" xml:space="preserve">mediis per ſe, fit {8bbcddr
              <emph style="super">3</emph>
            /12r} + 8bqr
              <emph style="super">3</emph>
              <lb/>
            = {8bbcd
              <emph style="super">3</emph>
            r/12} + 8bd
              <emph style="super">3</emph>
            x. </s>
            <s xml:id="echoid-s14568" xml:space="preserve">& </s>
            <s xml:id="echoid-s14569" xml:space="preserve">tranſponendo ac dividendo fit
              <lb/>
            {8bbcddr
              <emph style="super">3</emph>
            /12r} + 8bqr
              <emph style="super">3</emph>
            - {8bbcd
              <emph style="super">3</emph>
            r/12}/8bd
              <emph style="super">3</emph>
            } = x. </s>
            <s xml:id="echoid-s14570" xml:space="preserve">
              <lb/>
            ſive {bcrr/12d} + {qr
              <emph style="super">3</emph>
            /d
              <emph style="super">3</emph>
            } - {bcr/12}. </s>
            <s xml:id="echoid-s14571" xml:space="preserve">= x.</s>
            <s xml:id="echoid-s14572" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div545" type="section" level="1" n="545">
          <head xml:id="echoid-head659" xml:space="preserve">PROPOSITIO LXVI.</head>
          <p style="it">
            <s xml:id="echoid-s14573" xml:space="preserve">Tab XXVI fig. </s>
            <s xml:id="echoid-s14574" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14575" xml:space="preserve">Data Conoide Parabolica A B C, datoque
              <lb/>
            pondere P, cujus momentum ſimul cum momento ponderis dati ſolidi
              <lb/>
            ad Cobærentiam ejuſdem ſolidi, quamlibet babeat proportionem,
              <lb/>
            ſuper data baſi aliam Conoidem Parabolicam conſtruere, cujus
              <lb/>
            ponderis momentum ad ſuam Cobærentiam ſit in eadem propor-
              <lb/>
            tione.</s>
            <s xml:id="echoid-s14576" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14577" xml:space="preserve">Ponatur F B = r. </s>
            <s xml:id="echoid-s14578" xml:space="preserve">peripheria = c. </s>
            <s xml:id="echoid-s14579" xml:space="preserve">F C = a. </s>
            <s xml:id="echoid-s14580" xml:space="preserve">pondus appenſum = p.
              <lb/>
            </s>
            <s xml:id="echoid-s14581" xml:space="preserve">baſeos datæ radius = b. </s>
            <s xml:id="echoid-s14582" xml:space="preserve">peripheria baſeos datæ = {bc/r}. </s>
            <s xml:id="echoid-s14583" xml:space="preserve">longitudo
              <lb/>
            quæſita = x.</s>
            <s xml:id="echoid-s14584" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14585" xml:space="preserve">Erit ſolidum A B C = {acr/4}. </s>
            <s xml:id="echoid-s14586" xml:space="preserve">ejuſque momentum oriundum ex </s>
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