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

Table of handwritten notes

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            natis amplitudinibus foraminum M, N, R, per m, n, p, fore L P
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            = {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-
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            titudini ſuperficiei A B ſupra foramen ultimum R ſeu D R; </s>
            <s xml:id="echoid-s4402" xml:space="preserve">erit igitur
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            B H + {mm/nn} X B H + {mm/pp} X B H = D R,
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            & </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
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            L P = {mm/nn} X D R: </s>
            <s xml:id="echoid-s4406" xml:space="preserve">(1 + {mm/nn} + {mm/pp}) atque
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            Q R = {mm/pp} X D R: </s>
            <s xml:id="echoid-s4407" xml:space="preserve">(1 + {mm/nn} + {mm/pp}), ſeu
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            B H = D R: </s>
            <s xml:id="echoid-s4408" xml:space="preserve">(1 + {mm/nn} + {mm/pp})
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            L P = D R: </s>
            <s xml:id="echoid-s4409" xml:space="preserve">(1 + {nn/mm} + {nn/pp})
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            Q R = D R: </s>
            <s xml:id="echoid-s4410" xml:space="preserve">(1 + {pp/nn} + {pp/mm})
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            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
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            quanto tempore id fiat, ſi aliter ſuperficies illæ ſint poſitæ & </s>
            <s xml:id="echoid-s4413" xml:space="preserve">quænam inte-
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            rea aquæ quantitas per ſingula foramina fluat, inferius examinabimus unà cum
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            aliis quæſtionibus eo pertinentibus: </s>
            <s xml:id="echoid-s4414" xml:space="preserve">Jam vero ex allatis valoribus altitudi-
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            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"/>
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            <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 =
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            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-
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            dine D R, quoties vaſa replicantur.</s>
            <s xml:id="echoid-s4425" xml:space="preserve"/>
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            <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,
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            erunt omnes ſuperficies, quæ ſunt cis foramen poſitæ, in eadem altitudine
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            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"/>
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            <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.
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            </s>
            <s xml:id="echoid-s4433" xml:space="preserve">tranſiens, intelligitur, aquam per orificium canalis effluere debere velocitate,
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            quæ debeatur toti altitudini D R. </s>
            <s xml:id="echoid-s4434" xml:space="preserve">In noſtro vero caſu ea velocitas reſpondet
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            tantum altitudini Q R, cujus rei ratio & </s>
            <s xml:id="echoid-s4435" xml:space="preserve">origo eſt, quod aſcenſus pot ntialis ſin-
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            gularum guttularum per foramina, excepto ſolo foramine effluxus, </s>
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