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

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        <div xml:id="echoid-div65" type="section" level="1" n="46">
          <pb o="50" file="0064" n="64" rhead="HYDRODYNAMICÆ."/>
          <p>
            <s xml:id="echoid-s1287" xml:space="preserve">Denique punctum E maximo reſpondens deſcenſui obtinetur ope hu-
              <lb/>
            jus æquationis,
              <lb/>
            ξ - αlog.</s>
            <s xml:id="echoid-s1288" xml:space="preserve">ξ = β - αlog.</s>
            <s xml:id="echoid-s1289" xml:space="preserve">β</s>
          </p>
          <p>
            <s xml:id="echoid-s1290" xml:space="preserve">Alter caſus ſeorſim ſubducendus calculo eſt, cum mm = 2nn, ubi
              <lb/>
            oritur
              <lb/>
            v = {αξ - αβ - ξβlog.</s>
            <s xml:id="echoid-s1291" xml:space="preserve">ξ + ξβlog.</s>
            <s xml:id="echoid-s1292" xml:space="preserve">β/gβ}
              <lb/>
            atque ſi capiatur, poſito c pro numero, cujus logarithmus eſt unitas,
              <lb/>
            ξ = c
              <emph style="super">{α - β/β}</emph>
            β determinabitur ſic locus maximæ velocitatis, cujus altitudo
              <lb/>
            generatrix eſt = c
              <emph style="super">{α - β/β}</emph>
            β - α, dum maximus deſcenſus, qui proportiona-
              <lb/>
            lis eſt toti aquæ effluenti, definitur faciendo
              <lb/>
            αξ - αβ - ξβlog.</s>
            <s xml:id="echoid-s1293" xml:space="preserve">ξ + ξβlog.</s>
            <s xml:id="echoid-s1294" xml:space="preserve">β = o</s>
          </p>
          <p>
            <s xml:id="echoid-s1295" xml:space="preserve">Non dubito, quin hæc ad amuſſim experientiæ eſſent reſponſura, ſi
              <lb/>
            modo adhæſio aquæ ad latera tubi motum non retardaret; </s>
            <s xml:id="echoid-s1296" xml:space="preserve">puto tamen, even-
              <lb/>
            tum experimentorum talem eſſe poſſe, ut intelligenti, qui horum impedi-
              <lb/>
            mentorum rationem habeat, ſatis @ſtendant propoſitionum veritatem.</s>
            <s xml:id="echoid-s1297" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1298" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1299" xml:space="preserve">28. </s>
            <s xml:id="echoid-s1300" xml:space="preserve">Ultimo loco communicabo veram ſolutionem phænomeni ali-
              <lb/>
            cujus, quod primo aſpectu valde videtur paradoxon. </s>
            <s xml:id="echoid-s1301" xml:space="preserve">Poſtquam enim ex
              <lb/>
            omnibus hactenus dictis luculenter apparet fieri non poſſe, ut aquæ multo
              <lb/>
            majori velocitate effluant quam qualis altitudini aquæ ſupra foramen debetur,
              <lb/>
            (poſſunt tamen aliquanto majori, præſertim ſi foramina ſunt magna, con-
              <lb/>
            fer ea quæ dixi de velocitatibus maximis §. </s>
            <s xml:id="echoid-s1302" xml:space="preserve">16.) </s>
            <s xml:id="echoid-s1303" xml:space="preserve">multis mirum fortaſſe videbitur,
              <lb/>
            contingere aliquando in fontibus ſalientibus, ut aqua ad temporis momen-
              <lb/>
            ium jactum faciat longe altiorem, quam ſecundum regulas noſtras fieri poſſe
              <lb/>
            videtur. </s>
            <s xml:id="echoid-s1304" xml:space="preserve">Verum tantum abeſt, ut hæ inde aliquid roboris perdant, quin
              <lb/>
            potius egregie confirmentur. </s>
            <s xml:id="echoid-s1305" xml:space="preserve">Solutio autem paradoxi in eo conſiſtit, quod
              <lb/>
            nos hactenus aquas conſideraverimus continuas, & </s>
            <s xml:id="echoid-s1306" xml:space="preserve">nullo vacuo aëreo ſepara-
              <lb/>
            tas: </s>
            <s xml:id="echoid-s1307" xml:space="preserve">Recteque obſervavit D
              <emph style="super">us</emph>
            . </s>
            <s xml:id="echoid-s1308" xml:space="preserve">De la Hire non fieri hujusmodi ſaltus irrregu-
              <lb/>
            lares, niſi aër una cum aqua tubum prope ſcaturiginem fuerit ingreſſus,
              <lb/>
            quod ſæpe fieri indicavi §. </s>
            <s xml:id="echoid-s1309" xml:space="preserve">25. </s>
            <s xml:id="echoid-s1310" xml:space="preserve">Iſte vero aër ſimul cum aqua fertur usque ad
              <lb/>
            orificium effluxus, per quod mox erumpit: </s>
            <s xml:id="echoid-s1311" xml:space="preserve">id dum fit, maſſa aquea </s>
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