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

< >
[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)
< >
page |< < (584) of 795 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div535" type="section" level="1" n="535">
          <pb o="584" file="0600" n="601" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
        </div>
        <div xml:id="echoid-div536" type="section" level="1" n="536">
          <head xml:id="echoid-head648" xml:space="preserve">PROPOSITIO LVII.</head>
          <p style="it">
            <s xml:id="echoid-s14308" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14309" xml:space="preserve">XXV. </s>
            <s xml:id="echoid-s14310" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s14311" xml:space="preserve">11. </s>
            <s xml:id="echoid-s14312" xml:space="preserve">Si idem Priſma Triangulare A B C M N po-
              <lb/>
            natur horizonti parallelum ita, ut ſuperficies ſuperior ſit Trian-
              <lb/>
            gulum, & </s>
            <s xml:id="echoid-s14313" xml:space="preserve">ſummum, quod geſtari poſſit ab extremo M T; </s>
            <s xml:id="echoid-s14314" xml:space="preserve">ſit pondus P,
              <lb/>
            erit hoc pondus ſemper ſummum, quodgeripoterit ab extremo, quam-
              <lb/>
            cunque habuerit hoc prisma longitudinem, ſepoſita ejus gravitate
              <lb/>
            propriâ.</s>
            <s xml:id="echoid-s14315" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14316" xml:space="preserve">Vocetur A B, a. </s>
            <s xml:id="echoid-s14317" xml:space="preserve">B B, b. </s>
            <s xml:id="echoid-s14318" xml:space="preserve">D T, c. </s>
            <s xml:id="echoid-s14319" xml:space="preserve">pondus P. </s>
            <s xml:id="echoid-s14320" xml:space="preserve">p. </s>
            <s xml:id="echoid-s14321" xml:space="preserve">ſed d T ſit = d. </s>
            <s xml:id="echoid-s14322" xml:space="preserve">erit b b
              <lb/>
            latus = {b d.</s>
            <s xml:id="echoid-s14323" xml:space="preserve">/c} Cohærentia baſeos A B B erit = a b b. </s>
            <s xml:id="echoid-s14324" xml:space="preserve">& </s>
            <s xml:id="echoid-s14325" xml:space="preserve">Cohærentia
              <lb/>
            baſeos a b b erit = {a a b d.</s>
            <s xml:id="echoid-s14326" xml:space="preserve">/c} Momentum vero ponderis P ſuſpenſi ex
              <lb/>
            D T eſt = p c. </s>
            <s xml:id="echoid-s14327" xml:space="preserve">& </s>
            <s xml:id="echoid-s14328" xml:space="preserve">momentum ejuſdem ponderis P ſuſpenſi ex dT
              <lb/>
            eſt = p d.</s>
            <s xml:id="echoid-s14329" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14330" xml:space="preserve">Si igitur momentum ponderis P ſuſpenſi ex D T longitudine ha-
              <lb/>
            beat ad Cohærentiam baſeos A B B eandem proportionem, quam
              <lb/>
            momentum ejuſdem ponderis P ſuſpenſi ex longitudine dT habet
              <lb/>
            ad ſuæ baſeos a b b Cohærentiam, tum erit eadem ratio Cohærentiæ
              <lb/>
            priſmatis ad momentum ponderis, ſive priſma fuerit longum vel bre-
              <lb/>
            ve. </s>
            <s xml:id="echoid-s14331" xml:space="preserve">ſed p c. </s>
            <s xml:id="echoid-s14332" xml:space="preserve">eſt ad a a b:</s>
            <s xml:id="echoid-s14333" xml:space="preserve">: p d. </s>
            <s xml:id="echoid-s14334" xml:space="preserve">{a a b d.</s>
            <s xml:id="echoid-s14335" xml:space="preserve">/c} ſupra vero oſtendimus Cohæ-
              <lb/>
            rentiam baſeos a b b eſſe = {a a b d.</s>
            <s xml:id="echoid-s14336" xml:space="preserve">/c} quare datur eadem ratio momen-
              <lb/>
            ti ponderis ad Cohærentiam in priſmate integro A B B T M & </s>
            <s xml:id="echoid-s14337" xml:space="preserve">in
              <lb/>
            parte abſciſſa a b b T M.</s>
            <s xml:id="echoid-s14338" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14339" xml:space="preserve">Scholion. </s>
            <s xml:id="echoid-s14340" xml:space="preserve">Si vero priſmata A B B M T, a b b M T concipiantur
              <lb/>
            gravia, ponduſque P ut ante appenſum, non erit eadem ratio mo-
              <lb/>
            mentorum ex gravitate propria & </s>
            <s xml:id="echoid-s14341" xml:space="preserve">pondere P ad Cohærentiam ba-
              <lb/>
            ſium in prismatibus longis & </s>
            <s xml:id="echoid-s14342" xml:space="preserve">brevibus: </s>
            <s xml:id="echoid-s14343" xml:space="preserve">Nam poſitis omnibus ut ſu-
              <lb/>
            pra, erit momentum ex gravitate priſmatis A B B M T oriundum
              <lb/>
            = {1/6} abcc. </s>
            <s xml:id="echoid-s14344" xml:space="preserve">& </s>
            <s xml:id="echoid-s14345" xml:space="preserve">momentum ex gravitate Priſmatis a b b M T = {1/6} {abdd.</s>
            <s xml:id="echoid-s14346" xml:space="preserve">/c}
              <lb/>
            hiſce addantur momenta ponderis P, quæ ſunt = p c in longiori
              <lb/>
            priſmate, & </s>
            <s xml:id="echoid-s14347" xml:space="preserve">= p d in breviori: </s>
            <s xml:id="echoid-s14348" xml:space="preserve">adeoque ſtabit hæc proportio {1/6} </s>
          </p>
        </div>
      </text>
    </echo>
Impressum