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

List of thumbnails

< >
581
581 (564) 		582
582 (565)
583
583 (566) 		584
584 (567)
585
585 (568) 		586
586 (569)
587
587 (570) 		588
588 (571)
589
589 (572) 		590
590 (573)
< >
page |< < (570) of 795 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div522" type="section" level="1" n="522">
          <p>
            <s xml:id="echoid-s13767" xml:space="preserve">
              <pb o="570" file="0586" n="587" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
            dinem A D, dabit momentum oriundum ex gravitate = {b b c x
              <emph style="super">6</emph>
            .</s>
            <s xml:id="echoid-s13768" xml:space="preserve">/4 a}
              <lb/>
            ſupponatur hic cylindrus ad Cohærentiam ſuam in eadem ratione
              <lb/>
            f ad d. </s>
            <s xml:id="echoid-s13769" xml:space="preserve">erit Cohærentia hujus 8x
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s13770" xml:space="preserve">unde {b b c x
              <emph style="super">6</emph>
            /4 a
              <emph style="super">5</emph>
            } 8x
              <emph style="super">3</emph>
            :</s>
            <s xml:id="echoid-s13771" xml:space="preserve">: f. </s>
            <s xml:id="echoid-s13772" xml:space="preserve">d
              <lb/>
            :</s>
            <s xml:id="echoid-s13773" xml:space="preserve">: {1/4} a c b b + p b a
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s13774" xml:space="preserve">multiplicatis extremis & </s>
            <s xml:id="echoid-s13775" xml:space="preserve">mediisperſe, fit {a
              <emph style="super">3</emph>
            b b c x
              <emph style="super">6</emph>
            /4a
              <emph style="super">5</emph>
            }
              <lb/>
            = {1/2} a c b b x
              <emph style="super">3</emph>
            + 8 p b x
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s13776" xml:space="preserve">factaque diviſione per {b b c x
              <emph style="super">3</emph>
            ,/4a a} manet x
              <emph style="super">3</emph>
              <lb/>
            =2a
              <emph style="super">3</emph>
            + 3 {2 a a p.</s>
            <s xml:id="echoid-s13777" xml:space="preserve">/b c} unde x =
              <emph style="super">3</emph>
            2 a
              <emph style="super">3</emph>
            + 32{a a p.</s>
            <s xml:id="echoid-s13778" xml:space="preserve">/b c} quo cognito valore
              <lb/>
            radii baſeos A B. </s>
            <s xml:id="echoid-s13779" xml:space="preserve">datur totum corpus A B C D, ejusque longitudo.</s>
            <s xml:id="echoid-s13780" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div523" type="section" level="1" n="523">
          <head xml:id="echoid-head635" xml:space="preserve">PROPOSITIO XLV.</head>
          <p style="it">
            <s xml:id="echoid-s13781" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s13782" xml:space="preserve">XXIII. </s>
            <s xml:id="echoid-s13783" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s13784" xml:space="preserve">37. </s>
            <s xml:id="echoid-s13785" xml:space="preserve">Dato Cylindro A B C D, cujus momentum
              <lb/>
            gravitatis ad Cohærentiam habeat rationem datam f ad, d: </s>
            <s xml:id="echoid-s13786" xml:space="preserve">ſecto-
              <lb/>
            que ab ipſo quolibet fruſto Q D, reperire pondus extremo Q ap-
              <lb/>
            pendendum, cujus momentum, unà cum momento ex gravitate re-
              <lb/>
            liquæ partis A B Q, ad Cohærentiam ſit in eâdem ratione f ad, d.</s>
            <s xml:id="echoid-s13787" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13788" xml:space="preserve">Ponatur {1/2} A B = r. </s>
            <s xml:id="echoid-s13789" xml:space="preserve">circumferentia baſeos = c. </s>
            <s xml:id="echoid-s13790" xml:space="preserve">longitudo A D = b.
              <lb/>
            </s>
            <s xml:id="echoid-s13791" xml:space="preserve">erit baſis = {1/2} c r. </s>
            <s xml:id="echoid-s13792" xml:space="preserve">& </s>
            <s xml:id="echoid-s13793" xml:space="preserve">ſoliditas cylindri A B C D = {1/2} b c r. </s>
            <s xml:id="echoid-s13794" xml:space="preserve">momentum
              <lb/>
            oriundum ex gravitate = {1/4} b b c r. </s>
            <s xml:id="echoid-s13795" xml:space="preserve">Cohærentia vero per Prop. </s>
            <s xml:id="echoid-s13796" xml:space="preserve">XXXVI. </s>
            <s xml:id="echoid-s13797" xml:space="preserve">
              <lb/>
            eſt uti cubus A B = 8 r
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s13798" xml:space="preserve">quare datur {1/4} b b c r. </s>
            <s xml:id="echoid-s13799" xml:space="preserve">8 r
              <emph style="super">3</emph>
            :</s>
            <s xml:id="echoid-s13800" xml:space="preserve">: f. </s>
            <s xml:id="echoid-s13801" xml:space="preserve">d.</s>
            <s xml:id="echoid-s13802" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13803" xml:space="preserve">Abſcindatur a cylindro ſegmentum Q D, ita ut maneat A Q
              <lb/>
            = l. </s>
            <s xml:id="echoid-s13804" xml:space="preserve">erit ſoliditas cylindri A B Q = {1/2} c r l, & </s>
            <s xml:id="echoid-s13805" xml:space="preserve">momentum ex gra-
              <lb/>
            vitate = {1/4} c r l l. </s>
            <s xml:id="echoid-s13806" xml:space="preserve">pondus inveniendum vocetur = x. </s>
            <s xml:id="echoid-s13807" xml:space="preserve">quod cum ſu-
              <lb/>
            ſpendendum ab extremo Q habebit momentum = l x. </s>
            <s xml:id="echoid-s13808" xml:space="preserve">quare ſum-
              <lb/>
            ma momenti ponderis & </s>
            <s xml:id="echoid-s13809" xml:space="preserve">Cylindri B Q erit = {1/4} c r l l. </s>
            <s xml:id="echoid-s13810" xml:space="preserve">+ l x quæ eſt
              <lb/>
            ad Cohærentiam baſeos 8r
              <emph style="super">3</emph>
            :</s>
            <s xml:id="echoid-s13811" xml:space="preserve">: f. </s>
            <s xml:id="echoid-s13812" xml:space="preserve">d. </s>
            <s xml:id="echoid-s13813" xml:space="preserve">unde {1/4} c r l l + l x = {1/4} b b c r.
              <lb/>
            </s>
            <s xml:id="echoid-s13814" xml:space="preserve">hinc erit x = {b b c r - c r l l.</s>
            <s xml:id="echoid-s13815" xml:space="preserve">/4l}</s>
          </p>
          <p>
            <s xml:id="echoid-s13816" xml:space="preserve">Sed poteſt dari generalior demonſtratio, quæ non modo Cylin-
              <lb/>
            dris, ſed Parallelopipedis, Conis, aliisque corporibus regularibus
              <lb/>
            applicari poteſt: </s>
            <s xml:id="echoid-s13817" xml:space="preserve">Sit enim Tab. </s>
            <s xml:id="echoid-s13818" xml:space="preserve">XXIII, fig. </s>
            <s xml:id="echoid-s13819" xml:space="preserve">39. </s>
            <s xml:id="echoid-s13820" xml:space="preserve">Corpus A B C, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum