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

< >
[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)
[571.] PROPOSITIO XCII.
Page: 625 (608)
[572.] PROPOSITIO XCIII.
Page: 626 (609)
[573.] CAPUT SEXTUM. De Cohærentia Corporum quibus fulcrum ſupponitur. PROPOSITIO XCIV.
Page: 627 (610)
[574.] EXPERIMENTUM CLXXXVI.
Page: 629 (612)
[575.] PROPOSITIO XCV.
Page: 629 (612)
[576.] PROPOSITIO CXVI.
Page: 630 (613)
[577.] CAPUT SEPTIMUM. De Cohærentia reſpectiva ſolidorum duobus fulcris impoſitorum.
Page: 631 (614)
[578.] EXPERIMENTUM CLXXXVII.
Page: 632 (615)
[579.] EXPERIMENTUM CLXXXVIII.
Page: 633 (616)
[580.] EXPERIMENTUM CLXXXIX.
Page: 633 (616)
< >
page |< < (566) of 795 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div514" type="section" level="1" n="514">
          <pb o="566" file="0582" n="583" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
        </div>
        <div xml:id="echoid-div515" type="section" level="1" n="515">
          <head xml:id="echoid-head627" xml:space="preserve">PROPOSITIO XXXVII.</head>
          <p style="it">
            <s xml:id="echoid-s13571" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s13572" xml:space="preserve">XIX. </s>
            <s xml:id="echoid-s13573" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s13574" xml:space="preserve">4. </s>
            <s xml:id="echoid-s13575" xml:space="preserve">Potentiæ frangentes applicatæ extremitati-
              <lb/>
            bus duorum Cylindrorum A B C D, E F P, ejusdem materiæ, ſed
              <lb/>
            longitudine & </s>
            <s xml:id="echoid-s13576" xml:space="preserve">craſſitie diverſorum, ſunt in ratione compoſita ex
              <lb/>
            triplicata diametrorum baſium A B, E F. </s>
            <s xml:id="echoid-s13577" xml:space="preserve">& </s>
            <s xml:id="echoid-s13578" xml:space="preserve">inverſa longitudi-
              <lb/>
            num A D, E P. </s>
            <s xml:id="echoid-s13579" xml:space="preserve">ſepoſita corporum gravitate.</s>
            <s xml:id="echoid-s13580" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13581" xml:space="preserve">Eſt Cohærentia baſeos A K B L, ad Cohærentiam baſeos E M F O,
              <lb/>
            in ratione triplicata diametri A B ad E F per Propoſ. </s>
            <s xml:id="echoid-s13582" xml:space="preserve">XXXVI. </s>
            <s xml:id="echoid-s13583" xml:space="preserve">ad-
              <lb/>
            eoque poſitis Cylindris B Q, F P æque longis, erunt potentiæ fran-
              <lb/>
            gentes in Q & </s>
            <s xml:id="echoid-s13584" xml:space="preserve">P, in ratione triplicata diametrorum A B, E F, ſed
              <lb/>
            potentia in Q eſt ad eam in D frangentem, uti A D ad A Q per
              <lb/>
            Prop. </s>
            <s xml:id="echoid-s13585" xml:space="preserve">X X. </s>
            <s xml:id="echoid-s13586" xml:space="preserve">Quare erit potentia frangens in D, ad eam in P Cy-
              <lb/>
            lindri F P, in ratione compoſita ex triplicata A B ad E F, & </s>
            <s xml:id="echoid-s13587" xml:space="preserve">A Q
              <lb/>
            = E P ad A D.</s>
            <s xml:id="echoid-s13588" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div516" type="section" level="1" n="516">
          <head xml:id="echoid-head628" xml:space="preserve">PROPOSITIO XXXVIII.</head>
          <p style="it">
            <s xml:id="echoid-s13589" xml:space="preserve">Tab XXIII. </s>
            <s xml:id="echoid-s13590" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s13591" xml:space="preserve">37. </s>
            <s xml:id="echoid-s13592" xml:space="preserve">Duo Cylindri ſimiles A B C D, E F G H
              <lb/>
            ejusdem materiæ, horizontaliter parieti infixi, ſuſtinere poſſunt
              <lb/>
            ab extremitatibus D & </s>
            <s xml:id="echoid-s13593" xml:space="preserve">H, pondera I & </s>
            <s xml:id="echoid-s13594" xml:space="preserve">K quæ ſunt baſibus propor-
              <lb/>
            tionalia ſepoſitâ Cylindrorum gravitate.</s>
            <s xml:id="echoid-s13595" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13596" xml:space="preserve">Eſt Cohærentia Cylindri A B C D, ad Cohærentiam Cylindri
              <lb/>
            E F G H, uti cubus diametri A B ad cubum diametri E F per Prop.
              <lb/>
            </s>
            <s xml:id="echoid-s13597" xml:space="preserve">XXXVI. </s>
            <s xml:id="echoid-s13598" xml:space="preserve">ſed quia Cylindri ſunt ſimiles, eſt A B, E F:</s>
            <s xml:id="echoid-s13599" xml:space="preserve">: A D. </s>
            <s xml:id="echoid-s13600" xml:space="preserve">E H. </s>
            <s xml:id="echoid-s13601" xml:space="preserve">
              <lb/>
            ergo
              <emph style="ol">AB</emph>
              <emph style="super">c</emph>
            ,
              <emph style="ol">EF</emph>
              <emph style="super">c</emph>
            :</s>
            <s xml:id="echoid-s13602" xml:space="preserve">:
              <emph style="ol">AD</emph>
              <emph style="super">c</emph>
            ,
              <emph style="ol">EH</emph>
              <emph style="super">c</emph>
            . </s>
            <s xml:id="echoid-s13603" xml:space="preserve">unde erunt Cohærentiæ cylindro-
              <lb/>
            rum uti
              <emph style="ol">AD</emph>
              <emph style="super">c</emph>
            , ad EH
              <emph style="super">c</emph>
            . </s>
            <s xml:id="echoid-s13604" xml:space="preserve">Eſt vero momentum ponderis I = I X
              <lb/>
            A D. </s>
            <s xml:id="echoid-s13605" xml:space="preserve">quod eſt æquale Cohærentiæ baſeos, ſive =
              <emph style="ol">AD</emph>
              <emph style="super">c</emph>
            . </s>
            <s xml:id="echoid-s13606" xml:space="preserve">adeoque
              <lb/>
            utrimque facta diviſione per A D, erit I =
              <emph style="ol">AD</emph>
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s13607" xml:space="preserve">eodem modo pon-
              <lb/>
            deris K momentum eſt = K X E H. </s>
            <s xml:id="echoid-s13608" xml:space="preserve">& </s>
            <s xml:id="echoid-s13609" xml:space="preserve">Cohærentia, cui æquale
              <lb/>
            eſſe debet, eſt =
              <emph style="ol">EH</emph>
              <emph style="super">c</emph>
            . </s>
            <s xml:id="echoid-s13610" xml:space="preserve">quareutrimque facta diviſioneper E H, erit
              <lb/>
            K =
              <emph style="ol">EH</emph>
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s13611" xml:space="preserve">erit igitur pondus I ad pondusK:</s>
            <s xml:id="echoid-s13612" xml:space="preserve">:
              <emph style="ol">AD</emph>
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s13613" xml:space="preserve">E H
              <emph style="super">q</emph>
            :</s>
            <s xml:id="echoid-s13614" xml:space="preserve">: A B
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s13615" xml:space="preserve">
              <emph style="ol">EF</emph>
              <emph style="super">q</emph>
            :</s>
            <s xml:id="echoid-s13616" xml:space="preserve">:
              <lb/>
            baſis A B S ad baſin E F R. </s>
            <s xml:id="echoid-s13617" xml:space="preserve">adeoque pondera ſunt baſibus proportio-
              <lb/>
            nalia.</s>
            <s xml:id="echoid-s13618" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum