Bernoulli, Daniel, Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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            <s xml:id="echoid-s8518" xml:space="preserve">
              <pb o="287" file="0301" n="301" rhead="SECTIO DECIMA TERTIA."/>
            lis rectis, in quibus nempe uniuscujuſque guttulæ vis motrix, indeque ori-
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            unda vis repellens, inter ſe ſingulæ conſpirant, communemque habent dire-
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            ctionem: </s>
            <s xml:id="echoid-s8519" xml:space="preserve">at cum fiſtulæ vaſi implantatæ, per quas aquæ effluunt, ſunt incur-
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            vatæ, alius adhibendus eſt demonſtrandi modus: </s>
            <s xml:id="echoid-s8520" xml:space="preserve">Ut nihil in iſto argumento
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            prorſus novo omittamus, hunc quoque caſum docebimus: </s>
            <s xml:id="echoid-s8521" xml:space="preserve">nec erit, quod
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            laboris pœniteat, cum inde veræ preſſionum leges, quas natura non ſolum in
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            his caſibus, ſed & </s>
            <s xml:id="echoid-s8522" xml:space="preserve">multis aliis ſequatur, apparebunt.</s>
            <s xml:id="echoid-s8523" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8524" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8525" xml:space="preserve">13. </s>
            <s xml:id="echoid-s8526" xml:space="preserve">Concipiamus itaque vaſi infinito fiſtulam implantatam eſſe uni-
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            formis quidem amplitudinis, ſed incurvatam ſecundum curvaturam qualem-
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            cunque A S (Fig. </s>
            <s xml:id="echoid-s8527" xml:space="preserve">83.) </s>
            <s xml:id="echoid-s8528" xml:space="preserve">ita ut A locus ſit inſertionis, S locus effluxus: </s>
            <s xml:id="echoid-s8529" xml:space="preserve">Du-
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              <note position="right" xlink:label="note-0301-01" xlink:href="note-0301-01a" xml:space="preserve">Fig. 83.</note>
            cantur tangentes in A & </s>
            <s xml:id="echoid-s8530" xml:space="preserve">S, nempe A R & </s>
            <s xml:id="echoid-s8531" xml:space="preserve">S B, ſitque A B ad S B perpendi-
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            cularis: </s>
            <s xml:id="echoid-s8532" xml:space="preserve">fuerit velocitas aquæ per fiſtulam transfluentis uniformis & </s>
            <s xml:id="echoid-s8533" xml:space="preserve">talis,
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            quæ debeatur altitudini A; </s>
            <s xml:id="echoid-s8534" xml:space="preserve">amplitudo fiſtulæ ubique = 1: </s>
            <s xml:id="echoid-s8535" xml:space="preserve">Dico totam vim
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            repellentem in directione S B ſumtam fore rurſus = 2 A, hancque ſolam adfore.</s>
            <s xml:id="echoid-s8536" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8537" xml:space="preserve">Demonſtrationis gratia ducantur infinite propinquæ nq, ep ad S B per-
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            pendiculares; </s>
            <s xml:id="echoid-s8538" xml:space="preserve">n m parallela eidem S B; </s>
            <s xml:id="echoid-s8539" xml:space="preserve">ſit S q = x, qp = dx; </s>
            <s xml:id="echoid-s8540" xml:space="preserve">qn = y;
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            </s>
            <s xml:id="echoid-s8541" xml:space="preserve">e m = dy: </s>
            <s xml:id="echoid-s8542" xml:space="preserve">erit radius oſculi in e n = {- dsdy/ddx}, ſumtis elementis en quæ
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            vocabo ds pro conſtantibus; </s>
            <s xml:id="echoid-s8543" xml:space="preserve">habet autem columella aquæ intercepta inter e & </s>
            <s xml:id="echoid-s8544" xml:space="preserve">n
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            vim centrifugam, ſic determinandam: </s>
            <s xml:id="echoid-s8545" xml:space="preserve">gravitas columellæ eſt = ds (quia
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            baſis ejus = 1 & </s>
            <s xml:id="echoid-s8546" xml:space="preserve">altitudo = ds) atque ſi radius oſculi foret = 2 A, ha-
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            beretur per theorema Hugenianum vis centrifuga particulæ æqualis ejusdem
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            gravitati, & </s>
            <s xml:id="echoid-s8547" xml:space="preserve">ſunt vires centrifugæ cæteris paribus in reciproca ratione radio-
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            rum: </s>
            <s xml:id="echoid-s8548" xml:space="preserve">eſt igitur vis centrifuga columellæ = {- 2 Addx/dy}: </s>
            <s xml:id="echoid-s8549" xml:space="preserve">exprimatur hæc vis
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            centrifuga per ec ad curvam perpendicularem, ducaturque co ipfi B S paral-
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            lela: </s>
            <s xml:id="echoid-s8550" xml:space="preserve">reſolvatur vis e c in oc & </s>
            <s xml:id="echoid-s8551" xml:space="preserve">eo; </s>
            <s xml:id="echoid-s8552" xml:space="preserve">erit (ob ſimilitudinem triangulorum eoc
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            & </s>
            <s xml:id="echoid-s8553" xml:space="preserve">nme) vis oc = {- 2 Addx/ds}, vis eo = {- 2 Adxddx/dyds} = (ob d s conſtans)
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            {2 Addy/ds}.</s>
            <s xml:id="echoid-s8554" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s8555" xml:space="preserve">Sed vis elementaris oc agit ſola in directione S B, dum altera e o pro
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            hac directione eſt negligenda: </s>
            <s xml:id="echoid-s8556" xml:space="preserve">ſumatur integrale vis elementaris oc cum con-
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            ſtanti tali, ut integrale una cum abſciſſa evaneſcat: </s>
            <s xml:id="echoid-s8557" xml:space="preserve">integrale hoc eſt = </s>
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