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

< >
[601.] PROPOSITIO XCIX.
Page: 643 (626)
[602.] PROPOSITIO C.
Page: 644 (627)
[603.] PROPOSITIO CI.
Page: 644 (627)
[604.] PROPOSITIO CII.
Page: 645 (628)
[605.] EXPERIMENTUM CCVIII.
Page: 645 (628)
[606.] PROPOSITIO CIII.
Page: 646 (629)
[607.] PROPOSITIO CIV.
Page: 647 (630)
[608.] PROPOSITIO CV.
Page: 648 (631)
[609.] PROPOSITIO CVI.
Page: 648 (631)
[610.] PROPOSITIO CVII.
Page: 649 (632)
[611.] PROPOSITIO CVIII.
Page: 650 (633)
[612.] PROPOSITIO CIX.
Page: 650 (633)
[613.] PROPOSITIO CX.
Page: 651 (634)
[614.] PROPOSITIO CXI.
Page: 652 (635)
[615.] PROPOSITIO CXII.
Page: 653 (636)
[616.] PROPOSITIO CXIII.
Page: 653 (636)
[617.] PROPOSITIO CXIV.
Page: 654 (637)
[618.] PROPOSITIO CXV.
Page: 654 (637)
[619.] PROPOSITIO CXVI.
Page: 655 (638)
[620.] PROPOSITIO CXVII.
Page: 655 (638)
[621.] CAPUT OCTAVUM. De Cohærentia ſolidorum utrimque a foramine arcto exceptorum.
Page: 656 (639)
[622.] EXPERIMENTUM CCIX.
Page: 657 (640)
[623.] EXPERIMENTUM CCX.
Page: 657 (640)
[624.] EXPERIMENTUM CCXI.
Page: 658 (641)
[625.] EXPERIMENTUM CCXII.
Page: 658 (641)
[626.] EXPERIMENTUM CCXIII.
Page: 659 (642)
[627.] EXPERIMENTUM CCXIV.
Page: 659 (642)
[628.] EXPERIMENTUM CCXV.
Page: 659 (642)
[629.] EXPERIMENTUM CCXVI.
Page: 660 (643)
[630.] EXPERIMENTUM CCXVII.
Page: 660 (643)
< >
page |< < (633) of 795 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div610" type="section" level="1" n="610">
          <pb o="633" file="0649" n="650" rhead="CORPORUM FIRMORUM."/>
        </div>
        <div xml:id="echoid-div611" type="section" level="1" n="611">
          <head xml:id="echoid-head730" xml:space="preserve">PROPOSITIO CVIII.</head>
          <p style="it">
            <s xml:id="echoid-s16002" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s16003" xml:space="preserve">XXVII. </s>
            <s xml:id="echoid-s16004" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s16005" xml:space="preserve">11. </s>
            <s xml:id="echoid-s16006" xml:space="preserve">Infinita ſolida priſmatica datæ latitudinis
              <lb/>
            invenire, quæ utrimque fulta, æqualis ſint Cohærentiæ reſpectu
              <lb/>
            propriæ gravitatis.</s>
            <s xml:id="echoid-s16007" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16008" xml:space="preserve">Sit parabola A I H I. </s>
            <s xml:id="echoid-s16009" xml:space="preserve">ejus axis A B, ordinatæ B I, F H, B I. </s>
            <s xml:id="echoid-s16010" xml:space="preserve">di-
              <lb/>
            co quodlibet priſma longitudinis ejuſdem ac eſt ordinata quælibet
              <lb/>
            B I aut F H, & </s>
            <s xml:id="echoid-s16011" xml:space="preserve">altitudinis B A vel F A, atque datæ conſtantis la-
              <lb/>
            titudinis ſatisfacere propoſito: </s>
            <s xml:id="echoid-s16012" xml:space="preserve">nam ob naturam parabolæ eſt A B,
              <lb/>
            A F:</s>
            <s xml:id="echoid-s16013" xml:space="preserve">:
              <emph style="ol">I B</emph>
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s16014" xml:space="preserve">
              <emph style="ol">H F</emph>
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s16015" xml:space="preserve">eſtque ſoliditas priſmatis ex longitudine I B, & </s>
            <s xml:id="echoid-s16016" xml:space="preserve">
              <lb/>
            altitudine A B, uti I B X A B. </s>
            <s xml:id="echoid-s16017" xml:space="preserve">& </s>
            <s xml:id="echoid-s16018" xml:space="preserve">ſoliditas alterius priſmatis = A F
              <lb/>
            X F H. </s>
            <s xml:id="echoid-s16019" xml:space="preserve">ſed I B X A B. </s>
            <s xml:id="echoid-s16020" xml:space="preserve">A F X H F:</s>
            <s xml:id="echoid-s16021" xml:space="preserve">:
              <emph style="ol">I B</emph>
              <emph style="super">c</emph>
            . </s>
            <s xml:id="echoid-s16022" xml:space="preserve">
              <emph style="ol">H F</emph>
              <emph style="super">c</emph>
            . </s>
            <s xml:id="echoid-s16023" xml:space="preserve">momenta gravita-
              <lb/>
            tis horum priſmatum ſunt
              <emph style="ol">I B</emph>
              <emph style="super">c</emph>
            X I B. </s>
            <s xml:id="echoid-s16024" xml:space="preserve">
              <emph style="ol">H F</emph>
              <emph style="super">c</emph>
            X H F. </s>
            <s xml:id="echoid-s16025" xml:space="preserve">verum Cohæren-
              <lb/>
            tiæ eorundem ſunt
              <emph style="ol">A B</emph>
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s16026" xml:space="preserve">
              <emph style="ol">A F</emph>
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s16027" xml:space="preserve">quæ ſunt
              <emph style="ol">I B</emph>
              <emph style="super">qq</emph>
            . </s>
            <s xml:id="echoid-s16028" xml:space="preserve">
              <emph style="ol">H F</emph>
              <emph style="super">qq</emph>
            . </s>
            <s xml:id="echoid-s16029" xml:space="preserve">quæ ſunt uti
              <lb/>
            momenta gravitatis, adeoque demonſtrato Cohærentias eſſe uti ſunt
              <lb/>
            gravitates, erunt hæc ſolida æqualis Cohærentiæ.</s>
            <s xml:id="echoid-s16030" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16031" xml:space="preserve">Coroll. </s>
            <s xml:id="echoid-s16032" xml:space="preserve">Hinc ungula ſolida parabolica erecta ex Cylindro ſuper
              <lb/>
            parabola A I B, eademve ad alteram diametri partem duplicata,
              <lb/>
            erecto, per planum baſi, utcunque inclinatum, & </s>
            <s xml:id="echoid-s16033" xml:space="preserve">per verticem A
              <lb/>
            tranſiens, foret ſolidum reſpectu ſui ponderis in qualibet ſui parte
              <lb/>
            æqualiter reſiſtens: </s>
            <s xml:id="echoid-s16034" xml:space="preserve">ſive ſuſtineretur in linea A B, ſive fulcris ſub
              <lb/>
            ejus perimetro circumpoſitis fulciretur: </s>
            <s xml:id="echoid-s16035" xml:space="preserve">nam diametro A B diviſa
              <lb/>
            in quotlibet æquales partes, erectiſque planis per omnia diviſionum
              <lb/>
            puncta, & </s>
            <s xml:id="echoid-s16036" xml:space="preserve">correſpondentes ordinatas parabolæ, haberentur toti-
              <lb/>
            dem priſmata, huic ungulæ inſcripta, quæ ſui ponderis reſpectu,
              <lb/>
            juxta hanc Propoſitionem, æqualis eſſent Cohærentiæ, & </s>
            <s xml:id="echoid-s16037" xml:space="preserve">quæ
              <lb/>
            ungulæ ipſius ſoliditatem, aucto omnium numero, & </s>
            <s xml:id="echoid-s16038" xml:space="preserve">diminuta
              <lb/>
            ſingulorum latitudine, facile exhaurirent: </s>
            <s xml:id="echoid-s16039" xml:space="preserve">quemadmodum deduxit
              <lb/>
            Cl. </s>
            <s xml:id="echoid-s16040" xml:space="preserve">Grandi.</s>
            <s xml:id="echoid-s16041" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div612" type="section" level="1" n="612">
          <head xml:id="echoid-head731" xml:space="preserve">PROPOSITIO CIX.</head>
          <p style="it">
            <s xml:id="echoid-s16042" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s16043" xml:space="preserve">XXVII. </s>
            <s xml:id="echoid-s16044" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s16045" xml:space="preserve">12. </s>
            <s xml:id="echoid-s16046" xml:space="preserve">Dato cuneo A B P C D, & </s>
            <s xml:id="echoid-s16047" xml:space="preserve">pondere maxi-
              <lb/>
            mo, quod extremo C D appendi poſſit, cum Cunei baſis A B P </s>
          </p>
        </div>
      </text>
    </echo>
Impressum