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

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          <p>
            <s xml:id="echoid-s1053" xml:space="preserve">
              <pb o="39" file="0053" n="53" rhead="SECTIO TERTIA."/>
            {mma/mm - 2nn} X [({nn/mm - nn})
              <emph style="super">nn: (mm - 2nn)</emph>
            - ({nn/mm - nn})
              <emph style="super">(mm - nn): (mm - 2nn)</emph>
            ]
              <lb/>
            quæ quantitas reducta fit =
              <lb/>
            {mma/mm - nn}({nn/mm - nn})
              <emph style="super">nn: (mm - 2nn)</emph>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s1054" xml:space="preserve">Intelligitur ex iſtis formulis tempus, quo velocitas à nihilo in maxi-
              <lb/>
            mam vertitur, plane imperceptibile eſſe, quando foramen vel mediocriter
              <lb/>
            parvum tubusque non admodum longus eſt: </s>
            <s xml:id="echoid-s1055" xml:space="preserve">notabile autem fieri, cum res
              <lb/>
            ſecus ſe habet, quod videmus in fontibus ſalientibus, ad quos aquæ per
              <lb/>
            longos tractus vehuntur; </s>
            <s xml:id="echoid-s1056" xml:space="preserve">hæc vero quæ ad tempora pertinent, magis in
              <lb/>
            ſequenti ſectione explicabuntur, atque ſimul oſtendetur, quam parum aquæ
              <lb/>
            ex vaſis ampliſſimis ejiciatur, priusquam maxima velocitate effluant.</s>
            <s xml:id="echoid-s1057" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1058" xml:space="preserve">Natura velocitatum melius intelligitur ex appoſita Figura decima ſepti-
              <lb/>
              <note position="right" xlink:label="note-0053-01" xlink:href="note-0053-01a" xml:space="preserve">Fig. 17.</note>
            ma, in quâ ſi A B repræſentet totam altitudinem fluidi ſupra foramen ab initio
              <lb/>
            fluxus, expriment curvæ A 1 C B, A 2 C B, A 3 C B, A 4 C B, ſcalas altitudi-
              <lb/>
            num reſpondentium, ad quas fluidum effluens ſua velocitate aſcendere poſſit in
              <lb/>
            diverſis foraminum magnitudinibus: </s>
            <s xml:id="echoid-s1059" xml:space="preserve">nempe ſcala accedet ad figuram A 1 C B, ſi
              <lb/>
            foramen habeat exiguam rationem ad vaſis amplitudinem & </s>
            <s xml:id="echoid-s1060" xml:space="preserve">ad figuram A 2 C B,
              <lb/>
            cum aſſumitur fundum majori lumine perforatum; </s>
            <s xml:id="echoid-s1061" xml:space="preserve">& </s>
            <s xml:id="echoid-s1062" xml:space="preserve">ſi jam ratio foraminis
              <lb/>
            ſit ad amplitudinem vaſis ut 1 ad √ 2, erit ſcala illa ut A 3 C B (quo in caſu
              <lb/>
            minor fit maxima velocitas quam in quocunque alio, eſtque nominatim ea
              <lb/>
            quæ debetur altitudini {2a/c}, intelligendo per c numerum cujus Logarithmus
              <lb/>
            eſt unitas, id eſt, altitudini paulo minori quam {3/4}a) ac denique erit ſcala ut
              <lb/>
            A 4 C B cum fere nihil fundi ſupereſt.</s>
            <s xml:id="echoid-s1063" xml:space="preserve"/>
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            <s xml:id="echoid-s1064" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1065" xml:space="preserve">17. </s>
            <s xml:id="echoid-s1066" xml:space="preserve">Jam vero exemplo quodam illuſtrabimus, quod ſupra §. </s>
            <s xml:id="echoid-s1067" xml:space="preserve">10.
              <lb/>
            </s>
            <s xml:id="echoid-s1068" xml:space="preserve">indicatum fuit, nempe niſi foramen ſit ampliſſimum, poſſe id ſine valde
              <lb/>
            ſenſibili errore in calculo conſiderari ut infinitè parvum, atque adeo aſſumi
              <lb/>
            z = x, ut §. </s>
            <s xml:id="echoid-s1069" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1070" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1071" xml:space="preserve">& </s>
            <s xml:id="echoid-s1072" xml:space="preserve">15. </s>
            <s xml:id="echoid-s1073" xml:space="preserve">dictum fuit. </s>
            <s xml:id="echoid-s1074" xml:space="preserve">Videtur id tantum apud nonnullos
              <lb/>
            Auctores valuiſſe, ut cenſuerint, nullam magnitudinis in foramine rationem
              <lb/>
            unquam eſſe habendam, quantumvis magnum ponatur foramen, quæ res
              <lb/>
            certe ridicula eſt: </s>
            <s xml:id="echoid-s1075" xml:space="preserve">faltem nemo hactenus quod ſciam magnitudinem forami-
              <lb/>
            nis pro hoc negotio recte conſideravit. </s>
            <s xml:id="echoid-s1076" xml:space="preserve">Ponamus igitur cylindrum, cujus
              <lb/>
            diameter quadrupla tantum ſit diametri foraminis, cujusmodi magna </s>
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