Bernoulli, Daniel, Hydrodynamica, sive De viribus et motibus fluidorum commentarii

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        <div xml:id="echoid-div24" type="section" level="1" n="20">
          <p>
            <s xml:id="echoid-s574" xml:space="preserve">
              <pb o="22" file="0036" n="36" rhead="HYDRODYNAMICÆ"/>
            demum attolletur pondus; </s>
            <s xml:id="echoid-s575" xml:space="preserve">erit autem æquilibrium, cum locus contactus
              <lb/>
            c d ſe habet ad orificium o, ut pondus B ad pondus cylindri aquei altitudi-
              <lb/>
            nis FR ſuper baſi o inſiſtentis. </s>
            <s xml:id="echoid-s576" xml:space="preserve">Pendet itaque abſoluta elevationis determi-
              <lb/>
            natio à ſtructura veſicæ, quæ ſi exempli gratia compoſita fuerit ex filamen-
              <lb/>
            tis perfecte flexibilibus, extenſionemque nullam admittentibus, ſimulque
              <lb/>
            figuram naturalem habuerit Sphæricam, facile apparet, fore ſpatia conta-
              <lb/>
            ctus cnd & </s>
            <s xml:id="echoid-s577" xml:space="preserve">gpe æqualia & </s>
            <s xml:id="echoid-s578" xml:space="preserve">corrugata, partemque reliquam expanſam,
              <lb/>
            habituram eſſe formam Zonæ ſphæricæ; </s>
            <s xml:id="echoid-s579" xml:space="preserve">Atque hinc per Geometriam dedu-
              <lb/>
            citur quantitas elevationis np, quæ nulla erit, quamdiu circulus maximus
              <lb/>
            veſicæ minorem habuerit rationem ad orificium o illa, quæ eſt inter pon-
              <lb/>
            dus B & </s>
            <s xml:id="echoid-s580" xml:space="preserve">pondus præfati cylindri aquei, nec prius tota explicabitur veſi-
              <lb/>
            ca quam altitudo fuerit infinita, id eſt, nunquam. </s>
            <s xml:id="echoid-s581" xml:space="preserve">Si vero fibræ alius ſunt
              <lb/>
            indolis, aliter ſe res habet, quod multi non ſatis conſiderarunt, quibus de
              <lb/>
            figura veſicæ inflatæ ſermo fuit, eamque cavernulis muſcularibus in œcono-
              <lb/>
            mia animali applicare voluerunt, quâ de re nunc paullo fuſius agam.</s>
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          </p>
          <p>
            <s xml:id="echoid-s583" xml:space="preserve">§. </s>
            <s xml:id="echoid-s584" xml:space="preserve">10. </s>
            <s xml:id="echoid-s585" xml:space="preserve">Fuerit vèſica DC (Fig. </s>
            <s xml:id="echoid-s586" xml:space="preserve">6.) </s>
            <s xml:id="echoid-s587" xml:space="preserve">eidemque appenſum pondus P, ſi-
              <lb/>
              <note position="left" xlink:label="note-0036-01" xlink:href="note-0036-01a" xml:space="preserve">Fig. 6.</note>
            mulque alligata tubulo DA, cujus rurſus longitudinem compendii ergo in
              <lb/>
            comparabiliter majorem longitudine DC fingemus. </s>
            <s xml:id="echoid-s588" xml:space="preserve">His poſitis facile qui-
              <lb/>
            dem quivis perſpicit, repletis veſica & </s>
            <s xml:id="echoid-s589" xml:space="preserve">tubulo fore, ut illa intumeſcat,
              <lb/>
            pondusque appenſum P elevet: </s>
            <s xml:id="echoid-s590" xml:space="preserve">nemo autem intelliget ſtatum æquilibrii,
              <lb/>
            figuramque ventricoſam, niſi plane intelligatur ſtructura veſicæ ejusdemque
              <lb/>
            fibrarum, quæ cum ita ſint, caſus aliquot ſingulares examinabimus, qui
              <lb/>
            frequentius occurrere poſſunt.</s>
            <s xml:id="echoid-s591" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div27" type="section" level="1" n="21">
          <head xml:id="echoid-head27" xml:space="preserve">Caſus I.</head>
          <p>
            <s xml:id="echoid-s592" xml:space="preserve">§. </s>
            <s xml:id="echoid-s593" xml:space="preserve">11. </s>
            <s xml:id="echoid-s594" xml:space="preserve">Si veſica compoſita fuerit ex fibris longitudinalibus DpC,
              <lb/>
            DmC &</s>
            <s xml:id="echoid-s595" xml:space="preserve">c. </s>
            <s xml:id="echoid-s596" xml:space="preserve">inſtar meridianorum in punctis D & </s>
            <s xml:id="echoid-s597" xml:space="preserve">C, ceu Polis concurren-
              <lb/>
            tibus æqualibus, perfecte flexibilibus & </s>
            <s xml:id="echoid-s598" xml:space="preserve">uniformibus, quarum ſingu-
              <lb/>
            læ inter ſe proximæ minimis connectantur fibrillis transverſalibus, hisque ita
              <lb/>
            laxis, ut minima vel quaſi nulla vi ſufficientem extenſionem admittant. </s>
            <s xml:id="echoid-s599" xml:space="preserve">Sic
              <lb/>
            quælibet fibra DpC incurvabitur in figuram elaſticæ, totaque veſica formam
              <lb/>
            aſſumet ſolidi, quod generatur ex revolutione iſtius curvæ circa axem DC.
              <lb/>
            </s>
            <s xml:id="echoid-s600" xml:space="preserve">Si porro altitudo AD eſt infinita, fit elaſtica DpC rectangula & </s>
            <s xml:id="echoid-s601" xml:space="preserve">tunc eſt
              <lb/>
            graſſities maxima veſicæ ad longitudinem axis DC ut 25 ad 11 præter </s>
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