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

< >
[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)
[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)
< >
page |< < (562) of 795 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div510" type="section" level="1" n="510">
          <pb o="562" file="0578" n="579" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
        </div>
        <div xml:id="echoid-div511" type="section" level="1" n="511">
          <head xml:id="echoid-head623" xml:space="preserve">PROPOSITIO XXXIII.</head>
          <p style="it">
            <s xml:id="echoid-s13430" xml:space="preserve">Tab XXV. </s>
            <s xml:id="echoid-s13431" xml:space="preserve">fig 1. </s>
            <s xml:id="echoid-s13432" xml:space="preserve">Datis duobus parallelopipedis A B C D,
              <lb/>
            E G H K, datæ longitudini I L aliud parallelopipedum ejusdem ma-
              <lb/>
            teriæ applicare I M N L, quod ad E G H K habeat rationem datam,
              <lb/>
            & </s>
            <s xml:id="echoid-s13433" xml:space="preserve">in quo gravitatis momentum ad ſuam Cohærentiam ſit in eadem
              <lb/>
            proportione, in quâ momentum gravitatis A B C D eſt ad ſuam Co-
              <lb/>
            hærentiam.</s>
            <s xml:id="echoid-s13434" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13435" xml:space="preserve">Ponatur A B = a. </s>
            <s xml:id="echoid-s13436" xml:space="preserve">B C = b. </s>
            <s xml:id="echoid-s13437" xml:space="preserve">A D = d. </s>
            <s xml:id="echoid-s13438" xml:space="preserve">& </s>
            <s xml:id="echoid-s13439" xml:space="preserve">in altero ſolido ſit E G = e,
              <lb/>
            G H = f. </s>
            <s xml:id="echoid-s13440" xml:space="preserve">E K = g data ratio ſit uti k ad l. </s>
            <s xml:id="echoid-s13441" xml:space="preserve">tum præterea I L = p.
              <lb/>
            </s>
            <s xml:id="echoid-s13442" xml:space="preserve">I M = x. </s>
            <s xml:id="echoid-s13443" xml:space="preserve">M N = z.</s>
            <s xml:id="echoid-s13444" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13445" xml:space="preserve">Erit momentum parallelopipedi A B C D = {1/2} a b d d.
              <lb/>
            </s>
            <s xml:id="echoid-s13446" xml:space="preserve">Cohærentia = a a b.</s>
            <s xml:id="echoid-s13447" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13448" xml:space="preserve">Parallelopipedi momentum I M N L = {1/2} p p x z.
              <lb/>
            </s>
            <s xml:id="echoid-s13449" xml:space="preserve">Cohærentia = x x z.</s>
            <s xml:id="echoid-s13450" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13451" xml:space="preserve">Ponitur momentum A B C D ad ſuam Cohærentiam, uti I M N L
              <lb/>
            momentum ad ſuam; </s>
            <s xml:id="echoid-s13452" xml:space="preserve">hoc eſt {1/2} a b d d. </s>
            <s xml:id="echoid-s13453" xml:space="preserve">a a b:</s>
            <s xml:id="echoid-s13454" xml:space="preserve">: {1/2} p p x z. </s>
            <s xml:id="echoid-s13455" xml:space="preserve">x x z. </s>
            <s xml:id="echoid-s13456" xml:space="preserve">unde
              <lb/>
            fit x = {a p p.</s>
            <s xml:id="echoid-s13457" xml:space="preserve">/d d} præterea ponitur parallelopipedum E G H K ad I M N L
              <lb/>
            in ratione k ad l. </s>
            <s xml:id="echoid-s13458" xml:space="preserve">hoc eſt e f g, p x z:</s>
            <s xml:id="echoid-s13459" xml:space="preserve">: k. </s>
            <s xml:id="echoid-s13460" xml:space="preserve">l. </s>
            <s xml:id="echoid-s13461" xml:space="preserve">adeoque e f g l
              <lb/>
            = k p z x & </s>
            <s xml:id="echoid-s13462" xml:space="preserve">loco x ponendo æquale {a p p.</s>
            <s xml:id="echoid-s13463" xml:space="preserve">/d d} erit {e f g l = a k p
              <emph style="super">3</emph>
            z.</s>
            <s xml:id="echoid-s13464" xml:space="preserve">/d d} hinc
              <lb/>
            z = {d d e f g l.</s>
            <s xml:id="echoid-s13465" xml:space="preserve">/a k p
              <emph style="super">3</emph>
            }</s>
          </p>
        </div>
        <div xml:id="echoid-div512" type="section" level="1" n="512">
          <head xml:id="echoid-head624" xml:space="preserve">PROPOSITIO XXXIV.</head>
          <p style="it">
            <s xml:id="echoid-s13466" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s13467" xml:space="preserve">XIX. </s>
            <s xml:id="echoid-s13468" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s13469" xml:space="preserve">3. </s>
            <s xml:id="echoid-s13470" xml:space="preserve">Dato parallelopipedo A E F D, una cum pon-
              <lb/>
            dere quodam O annexo D. </s>
            <s xml:id="echoid-s13471" xml:space="preserve">datæ longitudini a k & </s>
            <s xml:id="echoid-s13472" xml:space="preserve">latitudini e o
              <lb/>
            applicare aliud parallelopipedum, cujus momentum ex gravitate,
              <lb/>
            ſimul cum pondere P pendente ex k, habeat ad ſuam Cohærentiam
              <lb/>
            rationem eandem, quam A E F D cum pondere O ad ſuam Cohæ-
              <lb/>
            rentiam.</s>
            <s xml:id="echoid-s13473" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13474" xml:space="preserve">Vocetur A E a. </s>
            <s xml:id="echoid-s13475" xml:space="preserve">E F b. </s>
            <s xml:id="echoid-s13476" xml:space="preserve">A D d. </s>
            <s xml:id="echoid-s13477" xml:space="preserve">pondus O ſit = o tum </s>
          </p>
        </div>
      </text>
    </echo>
Impressum