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

Page concordance

< >
Scan Original
121 107
122 108
123 109
124 110
125 111
126 112
127 113
128 114
129 115
130 116
131 117
132 118
133 119
134 120
135 121
136 122
137 123
138
139 125
140 126
141 127
142 128
143 129
144 130
145 131
146 132
147 133
148 134
149 135
150 136
< >
page |< < (135) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div150" type="section" level="1" n="118">
          <pb o="135" file="0149" n="149" rhead="SECTIO SEPTIMA."/>
          <p>
            <s xml:id="echoid-s3884" xml:space="preserve">Idem vero aliter ſic invenitur.</s>
            <s xml:id="echoid-s3885" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3886" xml:space="preserve">Conſideretur ſcilicet guttulæ L O N P quaſi nullam velocitatem fuiſſe,
              <lb/>
            priuſquam influere inciperet, eandem vero ſtatim atque influere incipiat, ac-
              <lb/>
            quirere aſcenſum potentialem, qui ſit = n n v, quamvis mox poſt ſui influxum
              <lb/>
            (per annot. </s>
            <s xml:id="echoid-s3887" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s3888" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3889" xml:space="preserve">2.) </s>
            <s xml:id="echoid-s3890" xml:space="preserve">cenſenda ſit motum continuare velocitate communi
              <lb/>
            √ v. </s>
            <s xml:id="echoid-s3891" xml:space="preserve">Quo facto ſic erit ratiocinandum. </s>
            <s xml:id="echoid-s3892" xml:space="preserve">Ante influxum guttulæ, eſt aſcenſus
              <lb/>
            potent. </s>
            <s xml:id="echoid-s3893" xml:space="preserve">aquæ c d M L P I c (cujus maſſa = n ξ) = v. </s>
            <s xml:id="echoid-s3894" xml:space="preserve">& </s>
            <s xml:id="echoid-s3895" xml:space="preserve">aſcenſ. </s>
            <s xml:id="echoid-s3896" xml:space="preserve">potent. </s>
            <s xml:id="echoid-s3897" xml:space="preserve">guttulæ
              <lb/>
            L O N P (cujus maſſa = n d ξ) = o; </s>
            <s xml:id="echoid-s3898" xml:space="preserve">ergo aſcenſus potentialis omnis aquæ
              <lb/>
            c d M L O N P I c = {nξv/nξ = ndξ} = {ξv/ξ + dξ}.</s>
            <s xml:id="echoid-s3899" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3900" xml:space="preserve">At vero poſtquam guttula L O N P influxit ſitumque aſſumſit L on P,
              <lb/>
            eſt ejus aſcenſ. </s>
            <s xml:id="echoid-s3901" xml:space="preserve">potent. </s>
            <s xml:id="echoid-s3902" xml:space="preserve">= n n v, reliquæ autem aquæ e f M L o n P I e (cujus
              <lb/>
            quidem maſſa rurſus = n ξ) aſcenſus potent. </s>
            <s xml:id="echoid-s3903" xml:space="preserve">eſt = v + d v; </s>
            <s xml:id="echoid-s3904" xml:space="preserve">igitur aſcenſus
              <lb/>
            potent. </s>
            <s xml:id="echoid-s3905" xml:space="preserve">omnis aquæ hic conſideratæ poſt influxum guttulæ eſt
              <lb/>
            = {ndξ x nnv + nξx(v + dv)/nξ + ndξ} = {ξv + ξdv + nnvdξ/ξ + dξ}, cum ante eundem influ-
              <lb/>
            xum fuerit {ξv/ξ + dξ}: </s>
            <s xml:id="echoid-s3906" xml:space="preserve">cepit igitur incrementum {ξdv + nnvdξ/ξ + dξ}, vel ſimplicius
              <lb/>
            {ξdv + nnvdξ/ξ}. </s>
            <s xml:id="echoid-s3907" xml:space="preserve">Iſtud vero incrementum æquandum eſt cum deſcenſu actuali
              <lb/>
            quem aqua facit mutando ſitum c d M L O N P I c ſitu e f M L O N P I e, qui
              <lb/>
            deſcenſus æqualis eſt quartæ proportionali ad maſſam aquæ internæ n ξ, ad
              <lb/>
            guttulam n d ξ & </s>
            <s xml:id="echoid-s3908" xml:space="preserve">altitudinem V f vel b - ξ, ſic ut præfatus deſcenſus ſit =
              <lb/>
            {(b - ξ)dξ/ξ}: </s>
            <s xml:id="echoid-s3909" xml:space="preserve">unde iterum habetur talis æquatio
              <lb/>
            ξdv + nnvdξ = (b - ξ)dξ;</s>
            <s xml:id="echoid-s3910" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3911" xml:space="preserve">Hujus vero integralis poſt debitæ conſtantis additionem talis fit
              <lb/>
            v = {b/nn} (1 - ({α/ξ})
              <emph style="super">nn</emph>
            ) - {1/nn + 1} (ξ - ({α/ξ})
              <emph style="super">nn</emph>
            α),
              <lb/>
            quam nunc pro diverſis ejus circumſtantiis perpendemus.</s>
            <s xml:id="echoid-s3912" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3913" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3914" xml:space="preserve">15. </s>
            <s xml:id="echoid-s3915" xml:space="preserve">Et quidem cum fuerit amplitudo tubi infinities major, quam
              <lb/>
            amplitudo foraminis; </s>
            <s xml:id="echoid-s3916" xml:space="preserve">patet fieri v = {b - ξ/nn}, & </s>
            <s xml:id="echoid-s3917" xml:space="preserve">irruere proinde aquam velo-
              <lb/>
            citate quæ debeatur altitudini ſuperficiei externæ fuper internam, neque
              <lb/>
            tunc ultra ſuperficiem aquæ externæ fiet aſcenſus.</s>
            <s xml:id="echoid-s3918" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum