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

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              <pb o="283" file="0297" n="297" rhead="SECTIO DECIMA TERTIA."/>
            rit fiſtula, eo tardius accelerantur aquæ & </s>
            <s xml:id="echoid-s8379" xml:space="preserve">viciſſim, ſic ut in inſtanti à quiete
              <lb/>
            maximum ſuum celeritatis gradum acquirant, ſi longitudo fiſtulæ nulla fue-
              <lb/>
            rit; </s>
            <s xml:id="echoid-s8380" xml:space="preserve">at ſi infinitæ fuerit eadem hæc fiſtula longitudinis, aquæ nonniſi poſt
              <lb/>
            tempus infinitum notab lem celeritatis gradum acquirere poſſunt.</s>
            <s xml:id="echoid-s8381" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8382" xml:space="preserve">(β) Fieri igitur poteſt non mutata aquarum altitudine, ut diſpendio
              <lb/>
            aquarum quantumvis parvo, vis repellens notabilis ſit, eaque pro lubitu
              <lb/>
            duret; </s>
            <s xml:id="echoid-s8383" xml:space="preserve">& </s>
            <s xml:id="echoid-s8384" xml:space="preserve">id quidem duplici obtineri poteſt modo, tum prolongando fiſtu-
              <lb/>
            lam, tum etiam obturando ſæpius orificium, antequam aquæ notabilem ve-
              <lb/>
            locitatis gradum attigerint; </s>
            <s xml:id="echoid-s8385" xml:space="preserve">prior tamen modus liberum aquarum fluxum
              <lb/>
            per fiſtulam ponit: </s>
            <s xml:id="echoid-s8386" xml:space="preserve">retardato enim ab impedimentis extrinſecis, in prælon-
              <lb/>
            gis fiſtulis nunquam vitabilibus, aquarum fluxu, diminuitur quoque vis
              <lb/>
            repellens.</s>
            <s xml:id="echoid-s8387" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8388" xml:space="preserve">(γ) Liceat hic paucis attingere verbis propoſitionem aliquam ex princ.
              <lb/>
            </s>
            <s xml:id="echoid-s8389" xml:space="preserve">math. </s>
            <s xml:id="echoid-s8390" xml:space="preserve">phil. </s>
            <s xml:id="echoid-s8391" xml:space="preserve">nat. </s>
            <s xml:id="echoid-s8392" xml:space="preserve">edit. </s>
            <s xml:id="echoid-s8393" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8394" xml:space="preserve">Newtoni: </s>
            <s xml:id="echoid-s8395" xml:space="preserve">Auctor hic poſtquam ſententiam ſuam de ve-
              <lb/>
            locitate aquarum ex vaſe effluentium in prima citati operis editione exhibi-
              <lb/>
            tam mutaſſet, easque, ſi verticaliter ſurſum ejiciantur, ad integram ſuper-
              <lb/>
            ficiei aquæ altitudinem aſcendere agnoviſſet in editione ſecunda, talia ſubje-
              <lb/>
            cit verba in libro ſecundo propos. </s>
            <s xml:id="echoid-s8396" xml:space="preserve">36. </s>
            <s xml:id="echoid-s8397" xml:space="preserve">coroll. </s>
            <s xml:id="echoid-s8398" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8399" xml:space="preserve">Vis qua totus aquæ exilientis
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            motus generari poteſt, æqualis eſt ponderi cylindricæ columellæ aquæ, cujus
              <lb/>
            baſis eſt for amen E F (vid. </s>
            <s xml:id="echoid-s8400" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s8401" xml:space="preserve">Nevvt.) </s>
            <s xml:id="echoid-s8402" xml:space="preserve">& </s>
            <s xml:id="echoid-s8403" xml:space="preserve">cujus altitudo eſt 2 G I vel 2 C K. </s>
            <s xml:id="echoid-s8404" xml:space="preserve">
              <lb/>
            Iſta ſententia à me olim & </s>
            <s xml:id="echoid-s8405" xml:space="preserve">ab aliis fuit impugnata, ab aliis rurſus confirma-
              <lb/>
            ta. </s>
            <s xml:id="echoid-s8406" xml:space="preserve">Nunc autem poſtquam hanc aquarum motarum theoriam medita-
              <lb/>
            tus ſum, lis ita dirimenda mihi videtur, ut cum aquæ ad motum unifor-
              <lb/>
            mem pervenerint, quæ quidem hypotheſis eſt Newtoni, tunc recte altitu-
              <lb/>
            dine 2 G I vis illa definiatur, ſed ab initio fluxus, ubi velocitas adhuc nulla
              <lb/>
            eſt, vis ſimplici altitudini G I reſpondeat, moxque creſcente velocitate ſi-
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            mul vis aquam ad effluxum animans creſcat, & </s>
            <s xml:id="echoid-s8407" xml:space="preserve">tandem ad eam magnitudi-
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            nem exſurgat, quam Newtonus aſſignavit. </s>
            <s xml:id="echoid-s8408" xml:space="preserve">Hæc nunc ſunt unicuique ob-
              <lb/>
            via, quia vis motum aquæ generans, de qua Newtonus loquitur, non po-
              <lb/>
            teſt non eſſe æqualis vi repellenti, quam vidimus eſſe æqualem a + v. </s>
            <s xml:id="echoid-s8409" xml:space="preserve">Re-
              <lb/>
            cte etiam Jll. </s>
            <s xml:id="echoid-s8410" xml:space="preserve">Riccatus, cum quo mihi de hoc argumento res erat interro-
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            gatus, unde vis illa duplæ aquarum altitudini conveniens oriri po{ſsi}t, </s>
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