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 |< < (152) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div167" type="section" level="1" n="134">
          <p>
            <s xml:id="echoid-s4399" xml:space="preserve">
              <pb o="152" file="0166" n="166" rhead="HYDRODYNAMICÆ"/>
            natis amplitudinibus foraminum M, N, R, per m, n, p, fore L P
              <lb/>
            = {mm/nn} X B H; </s>
            <s xml:id="echoid-s4400" xml:space="preserve">Q R = {mm/pp} X B H: </s>
            <s xml:id="echoid-s4401" xml:space="preserve">Eſt vero B H + L P + Q R æqualis al-
              <lb/>
            titudini ſuperficiei A B ſupra foramen ultimum R ſeu D R; </s>
            <s xml:id="echoid-s4402" xml:space="preserve">erit igitur
              <lb/>
            B H + {mm/nn} X B H + {mm/pp} X B H = D R,
              <lb/>
            & </s>
            <s xml:id="echoid-s4403" xml:space="preserve">proinde B H = D R: </s>
            <s xml:id="echoid-s4404" xml:space="preserve">(1 + {mm/nn} + {mm/pp}); </s>
            <s xml:id="echoid-s4405" xml:space="preserve">pariterque
              <lb/>
            L P = {mm/nn} X D R: </s>
            <s xml:id="echoid-s4406" xml:space="preserve">(1 + {mm/nn} + {mm/pp}) atque
              <lb/>
            Q R = {mm/pp} X D R: </s>
            <s xml:id="echoid-s4407" xml:space="preserve">(1 + {mm/nn} + {mm/pp}), ſeu
              <lb/>
            B H = D R: </s>
            <s xml:id="echoid-s4408" xml:space="preserve">(1 + {mm/nn} + {mm/pp})
              <lb/>
            L P = D R: </s>
            <s xml:id="echoid-s4409" xml:space="preserve">(1 + {nn/mm} + {nn/pp})
              <lb/>
            Q R = D R: </s>
            <s xml:id="echoid-s4410" xml:space="preserve">(1 + {pp/nn} + {pp/mm})
              <lb/>
            atque ſic determinantur ſitus invariabiles ſuperficierum H L, P Q, &</s>
            <s xml:id="echoid-s4411" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4412" xml:space="preserve">At
              <lb/>
            quanto tempore id fiat, ſi aliter ſuperficies illæ ſint poſitæ & </s>
            <s xml:id="echoid-s4413" xml:space="preserve">quænam inte-
              <lb/>
            rea aquæ quantitas per ſingula foramina fluat, inferius examinabimus unà cum
              <lb/>
            aliis quæſtionibus eo pertinentibus: </s>
            <s xml:id="echoid-s4414" xml:space="preserve">Jam vero ex allatis valoribus altitudi-
              <lb/>
            num B H, L P, Q R &</s>
            <s xml:id="echoid-s4415" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4416" xml:space="preserve">præcipuas affectiones deducemus.</s>
            <s xml:id="echoid-s4417" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4418" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4419" xml:space="preserve">20. </s>
            <s xml:id="echoid-s4420" xml:space="preserve">I. </s>
            <s xml:id="echoid-s4421" xml:space="preserve">Cum ſingula foramina ſunt inter ſe æque ampla, erit B H =
              <lb/>
            L P = Q R &</s>
            <s xml:id="echoid-s4422" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4423" xml:space="preserve">& </s>
            <s xml:id="echoid-s4424" xml:space="preserve">quævis iſtarum altitudinum toties continebitur in altitu-
              <lb/>
            dine D R, quoties vaſa replicantur.</s>
            <s xml:id="echoid-s4425" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4426" xml:space="preserve">II. </s>
            <s xml:id="echoid-s4427" xml:space="preserve">Si vero aliquod foraminum ſit infinite parvum ratione reliquorum,
              <lb/>
            erunt omnes ſuperficies, quæ ſunt cis foramen poſitæ, in eadem altitudine
              <lb/>
            cum prima ſuperficie A B: </s>
            <s xml:id="echoid-s4428" xml:space="preserve">reliquæ autem fundo G R erunt proximæ.</s>
            <s xml:id="echoid-s4429" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4430" xml:space="preserve">III. </s>
            <s xml:id="echoid-s4431" xml:space="preserve">Si canalis fingatur continuus per ſingula foramina M, N, R &</s>
            <s xml:id="echoid-s4432" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s4433" xml:space="preserve">tranſiens, intelligitur, aquam per orificium canalis effluere debere velocitate,
              <lb/>
            quæ debeatur toti altitudini D R. </s>
            <s xml:id="echoid-s4434" xml:space="preserve">In noſtro vero caſu ea velocitas reſpondet
              <lb/>
            tantum altitudini Q R, cujus rei ratio & </s>
            <s xml:id="echoid-s4435" xml:space="preserve">origo eſt, quod aſcenſus pot ntialis ſin-
              <lb/>
            gularum guttularum per foramina, excepto ſolo foramine effluxus, </s>
          </p>
        </div>
      </text>
    </echo>