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

Table of figures

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            <s xml:id="echoid-s3713" xml:space="preserve">
              <pb o="129" file="0143" n="143" rhead="SECTIO SEPTIMA."/>
            expertus ſum cylindrum eodem tempore evacuari, ſive aquæ in aërem eji-
              <lb/>
            ciantur, ſive fundum aquæ ſtagnanti tantillum ſubmergatur. </s>
            <s xml:id="echoid-s3714" xml:space="preserve">Docet hæc ex-
              <lb/>
            perientia parum aut nihil obſtare aërem externum effluxui, cum reſiſtentia
              <lb/>
            plus quam octingenties major notabiliorem effectum non exerat. </s>
            <s xml:id="echoid-s3715" xml:space="preserve">Quia adeo-
              <lb/>
            que iſte caſus nihil particulare habet, quod non loco citato monitum fuerit,
              <lb/>
            huic non ulterius immorabimur: </s>
            <s xml:id="echoid-s3716" xml:space="preserve">Inquiremus potius, quid fieri debeat, cum
              <lb/>
            elevatio aquæ internæ ſuper externam, quanta ab initio deſcenſus eſt, ſumi-
              <lb/>
            tur valde parva & </s>
            <s xml:id="echoid-s3717" xml:space="preserve">negligenda præ immerſione cylindri; </s>
            <s xml:id="echoid-s3718" xml:space="preserve">cui hypotheſi ſatisfit,
              <lb/>
            cum exceſſus altitudinis a ſuper altitudinem b (quem exceſſum rurſus vocabi-
              <lb/>
            mus (ut §. </s>
            <s xml:id="echoid-s3719" xml:space="preserve">7.) </s>
            <s xml:id="echoid-s3720" xml:space="preserve">c) eſt admodum parvus.</s>
            <s xml:id="echoid-s3721" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3722" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3723" xml:space="preserve">10. </s>
            <s xml:id="echoid-s3724" xml:space="preserve">Cum itaque ponitur a - b = c, ponendum etiam erit a - x = z,
              <lb/>
            tumque utraque quantitas, nempe c & </s>
            <s xml:id="echoid-s3725" xml:space="preserve">z, erunt negligendæ præ quantitatibus
              <lb/>
            a & </s>
            <s xml:id="echoid-s3726" xml:space="preserve">b, ſed ſi a - x = z, erit x = a - z & </s>
            <s xml:id="echoid-s3727" xml:space="preserve">x
              <emph style="super">nn - 1</emph>
            = (a - z)
              <emph style="super">nn - 1</emph>
            =
              <lb/>
            a
              <emph style="super">nn - 1</emph>
            - (nn - 1)a
              <emph style="super">nn - 2</emph>
            z + ({
              <emph style="ol">nn - 1. nn -2</emph>
            /2})a
              <emph style="super">nn - 3</emph>
            zz
              <lb/>
            - ({
              <emph style="ol">nn - 1. nn - 2. nn - 3</emph>
            /2. </s>
            <s xml:id="echoid-s3728" xml:space="preserve">3.</s>
            <s xml:id="echoid-s3729" xml:space="preserve">})a
              <emph style="super">nn - 4</emph>
            z
              <emph style="super">3</emph>
            + &</s>
            <s xml:id="echoid-s3730" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3731" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3732" xml:space="preserve">Hæc ſeries quantum ad inſtitutum noſtrum ſufficit eſt continuanda;
              <lb/>
            </s>
            <s xml:id="echoid-s3733" xml:space="preserve">ſufficiet autem ad tres usque terminos. </s>
            <s xml:id="echoid-s3734" xml:space="preserve">Igitur in æquatione integrata quam
              <lb/>
            dedimus §. </s>
            <s xml:id="echoid-s3735" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3736" xml:space="preserve">ponemus, x = a - z & </s>
            <s xml:id="echoid-s3737" xml:space="preserve">
              <lb/>
            x
              <emph style="super">nn - 1</emph>
            = a
              <emph style="super">nn - 1</emph>
            - (nn - 1)a
              <emph style="super">nn - 2</emph>
            z + ({
              <emph style="ol">nn - 1. nn - 2</emph>
            /2})a
              <emph style="super">nn - 3</emph>
            zz & </s>
            <s xml:id="echoid-s3738" xml:space="preserve">
              <lb/>
            ſic erit
              <lb/>
            v = {1/nn -2} [a - z - a + (nn - 1) z - ({
              <emph style="ol">nn - 1. nn -2</emph>
            /2}){zz/a}]
              <lb/>
            - {b/nn - 1}[1 - 1 + (nn - 1){z/a} - ({
              <emph style="ol">nn - 1. nn - 2</emph>
            /2}){zz/aa}]</s>
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          <p>
            <s xml:id="echoid-s3739" xml:space="preserve">In qua æquatione ſi termini ſe deſtruentes deleantur, atque ponatur a - c
              <lb/>
            pro b, rejiciaturque terminus qui affectatur quantitate {czz/aa}, prodit ſimpliciter
              <lb/>
            v = {2cz - zz/2a}.
              <lb/>
            </s>
            <s xml:id="echoid-s3740" xml:space="preserve">ex quâ formula, cum littera n evanuerit, indicium habemus, nihil </s>
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