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

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          <pb o="91" file="0105" n="105" rhead="SECTIO QUINTA."/>
          <p>
            <s xml:id="echoid-s2568" xml:space="preserve">Primam igitur ſolam accuratius ſcrutabimur: </s>
            <s xml:id="echoid-s2569" xml:space="preserve">Hic vero memores ſimus
              <lb/>
            eorum, quæ in præcedente ſectione monita fuerunt circa contractionem venæ
              <lb/>
            per ſimplicia orificia, aut tubos convergentes effluentis, & </s>
            <s xml:id="echoid-s2570" xml:space="preserve">dilatationem ejuſ-
              <lb/>
            dem, cum per tubos divergentes ejicitur. </s>
            <s xml:id="echoid-s2571" xml:space="preserve">Indicavimus autem §. </s>
            <s xml:id="echoid-s2572" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2573" xml:space="preserve">Art. </s>
            <s xml:id="echoid-s2574" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2575" xml:space="preserve">Sect.
              <lb/>
            </s>
            <s xml:id="echoid-s2576" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s2577" xml:space="preserve">eò uſque venam conſiderandam eſſe, donec particularum velocitates (ab-
              <lb/>
            ſtrahendo animum à mutationibus quas gravitas in particulis extra vas producit)
              <lb/>
            amplius non mutentur, & </s>
            <s xml:id="echoid-s2578" xml:space="preserve">omnem illam venæ partem ceü intra vas motam
              <lb/>
            æſtimandam eſſe, quaſi ſcilicet ſuperficies venæ eouſque indureſcat. </s>
            <s xml:id="echoid-s2579" xml:space="preserve">Igitur dein-
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            ceps cum de vaſe per quod aquæ effluunt ſermo erit, ſubintelligendum erit
              <lb/>
            vas illud ideale, cujus orificium effluxus ſit ſectio venæ nulli deinceps muta-
              <lb/>
            tioni ſubjectæ, niſi quæ deſcenſui vel aſcenſui venæ debetur.</s>
            <s xml:id="echoid-s2580" xml:space="preserve"/>
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        <div xml:id="echoid-div94" type="section" level="1" n="69">
          <head xml:id="echoid-head94" xml:space="preserve">Problema.</head>
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            <s xml:id="echoid-s2581" xml:space="preserve">§. </s>
            <s xml:id="echoid-s2582" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2583" xml:space="preserve">Invenire velocitatem aquæ effluentis ex vaſe conſtanter pleno, poſtquam
              <lb/>
            jam data aquæ quantitas effluxit.</s>
            <s xml:id="echoid-s2584" xml:space="preserve"/>
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        <div xml:id="echoid-div95" type="section" level="1" n="70">
          <head xml:id="echoid-head95" xml:space="preserve">Solutio.</head>
          <p>
            <s xml:id="echoid-s2585" xml:space="preserve">Duo ſunt modi affundendæ aquæ præcipue conſideratu digni, quorum
              <lb/>
            quivis aliam poſtulat problematis ſolutionem: </s>
            <s xml:id="echoid-s2586" xml:space="preserve">vel enim aqua verticaliter in
              <lb/>
            vas depluere ponitur & </s>
            <s xml:id="echoid-s2587" xml:space="preserve">ita quidem, ut eâdem præciſe affluat velocitate, quam
              <lb/>
            habet aquæ ſuperficies, vel lateraliter affluit aqua, ſicque caret impetu, quo
              <lb/>
            ſua ſponte aquæ ſuperficiem inſequi poſſit & </s>
            <s xml:id="echoid-s2588" xml:space="preserve">in motum demum eſt cienda.</s>
            <s xml:id="echoid-s2589" xml:space="preserve"/>
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        <div xml:id="echoid-div96" type="section" level="1" n="71">
          <head xml:id="echoid-head96" xml:space="preserve">Caſus 1.</head>
          <p>
            <s xml:id="echoid-s2590" xml:space="preserve">Ut pro primo caſu æquationem inveniamus inter quantitatem aquæ
              <lb/>
            ejectæ, velocitatemque reſpondentem, iiſdem unica mutata circumſtantia ve-
              <lb/>
            ſtigiis inſiſtendum erit, quæ in primis paragraphis ſectionis tertiæ ſecuti ſumus.</s>
            <s xml:id="echoid-s2591" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2592" xml:space="preserve">Sit igitur ut in §. </s>
            <s xml:id="echoid-s2593" xml:space="preserve">6. </s>
            <s xml:id="echoid-s2594" xml:space="preserve">Sect. </s>
            <s xml:id="echoid-s2595" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2596" xml:space="preserve">vas propoſitum aimb (Fig. </s>
            <s xml:id="echoid-s2597" xml:space="preserve">15. </s>
            <s xml:id="echoid-s2598" xml:space="preserve">& </s>
            <s xml:id="echoid-s2599" xml:space="preserve">16.)
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            </s>
            <s xml:id="echoid-s2600" xml:space="preserve">quod affuſione aquarum conſtanter plenum ſervatur uſque in c d; </s>
            <s xml:id="echoid-s2601" xml:space="preserve">effluant au-
              <lb/>
            tem aquæ per foramen pl; </s>
            <s xml:id="echoid-s2602" xml:space="preserve">ponaturque eam aquæ quantitatem jam effluxiſſe,
              <lb/>
            quæ contineri poſſit in cylindro ſuper foramine p l erecto altitudinis x, ulti-
              <lb/>
            mam autem guttulam effluxiſſe velocitate, qua aſcendere poſſit ad altitudinem
              <lb/>
            q s ſeu v; </s>
            <s xml:id="echoid-s2603" xml:space="preserve">ſic jam exhibenda erit æquatio inter x & </s>
            <s xml:id="echoid-s2604" xml:space="preserve">v.</s>
            <s xml:id="echoid-s2605" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2606" xml:space="preserve">Sit curva C G I ſcala amplitudinum, talis nempe, ut, denotante H </s>
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