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
page |< < (606) of 795 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div565" type="section" level="1" n="565">
          <pb o="606" file="0622" n="623" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
        </div>
        <div xml:id="echoid-div566" type="section" level="1" n="566">
          <head xml:id="echoid-head681" xml:space="preserve">PROPOSITIO LXXXVII.</head>
          <p>
            <s xml:id="echoid-s15121" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s15122" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s15123" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s15124" xml:space="preserve">10. </s>
            <s xml:id="echoid-s15125" xml:space="preserve">Determinare momentum ex gravitate corpo-
              <lb/>
            ris Hyperbolici A B E, ejusque ſegmenti F A G. </s>
            <s xml:id="echoid-s15126" xml:space="preserve">cujus baſis F G pa-
              <lb/>
            rallela eſt ad B E.</s>
            <s xml:id="echoid-s15127" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15128" xml:space="preserve">Momentum integri corporis Hyperbolici determinavimus in
              <lb/>
            Propoſitione LXXXV. </s>
            <s xml:id="echoid-s15129" xml:space="preserve">={a
              <emph style="super">4</emph>
            cr+7a
              <emph style="super">3</emph>
            bcr+12aabbcr.</s>
            <s xml:id="echoid-s15130" xml:space="preserve">/24aa+120ab+144bb} Verum
              <lb/>
            nunc ſegmenti F A G momentum determinandum quoque erit:
              <lb/>
            </s>
            <s xml:id="echoid-s15131" xml:space="preserve">Vocetur A H, x, tum ex natura Hyperbolæ eſt D A X D L, ad
              <lb/>
            H A X H L:</s>
            <s xml:id="echoid-s15132" xml:space="preserve">: B D
              <emph style="super">q</emph>
            , H F
              <emph style="super">q</emph>
            , ſive eſt aa+2ab, xx+2bx:</s>
            <s xml:id="echoid-s15133" xml:space="preserve">: rr,
              <lb/>
            {rrxx+2bxrr:</s>
            <s xml:id="echoid-s15134" xml:space="preserve">/aa+2ab} ut nunc peripheria deſcribenda a puncto F radii
              <lb/>
            H F habeatur, fiat r. </s>
            <s xml:id="echoid-s15135" xml:space="preserve">c:</s>
            <s xml:id="echoid-s15136" xml:space="preserve">: r {xx+2bx.</s>
            <s xml:id="echoid-s15137" xml:space="preserve">/aa+2ab} c{xx+2bx.</s>
            <s xml:id="echoid-s15138" xml:space="preserve">/aa+2ab}
              <lb/>
            ut ſoliditas obtineatur, multiplicanda hæc peripheria per radium,
              <lb/>
            & </s>
            <s xml:id="echoid-s15139" xml:space="preserve">per{xx+3xb.</s>
            <s xml:id="echoid-s15140" xml:space="preserve">/6x+12b} quod dat productum
              <lb/>
            {crx
              <emph style="super">4</emph>
            +5bcrx
              <emph style="super">3</emph>
            +6bbcx
              <emph style="super">3</emph>
            /6aax+12abx+12aab+144abb} = ſoliditati ſegmenti F A G. </s>
            <s xml:id="echoid-s15141" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s15142" xml:space="preserve">quoniam centrum gravitatis in axe H A diſtat a G F, quantitate
              <lb/>
            {xx+4xb.</s>
            <s xml:id="echoid-s15143" xml:space="preserve">/4x+12b} per hanc quantitatem multiplicata ſoliditas dabit
              <lb/>
            productum{crx
              <emph style="super">6</emph>
            +9bcrx
              <emph style="super">5</emph>
            +26bbcrx
              <emph style="super">4</emph>
            +24b
              <emph style="super">3</emph>
            crx
              <emph style="super">3</emph>
            /24aaxx+48abxx+120aabx+720abbx+144aabb+1728ab
              <emph style="super">3</emph>
            .</s>
            <s xml:id="echoid-s15144" xml:space="preserve">}
              <lb/>
            quod eſt æquale momento ſegmenti F A G.</s>
            <s xml:id="echoid-s15145" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div567" type="section" level="1" n="567">
          <head xml:id="echoid-head682" xml:space="preserve">PROPOSITIO LXXXVIII.</head>
          <p style="it">
            <s xml:id="echoid-s15146" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s15147" xml:space="preserve">XXVI fig. </s>
            <s xml:id="echoid-s15148" xml:space="preserve">11. </s>
            <s xml:id="echoid-s15149" xml:space="preserve">Sit Hyperbola AMB, & </s>
            <s xml:id="echoid-s15150" xml:space="preserve">dimidium primi axis
              <lb/>
            A C, & </s>
            <s xml:id="echoid-s15151" xml:space="preserve">dimidium axis conjugati C D, circa C D concipiatur circum-
              <lb/>
            volvi figura B A C D, quæritur ut determinetur momentum ſolidi
              <lb/>
            generati, & </s>
            <s xml:id="echoid-s15152" xml:space="preserve">Cohærentia baſeos B D, affixæ parieti perpendiculari ad
              <lb/>
            borizontem.</s>
            <s xml:id="echoid-s15153" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum