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

Table of Notes

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            <s xml:id="echoid-s4264" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4265" xml:space="preserve">10. </s>
            <s xml:id="echoid-s4266" xml:space="preserve">Indicat porro formula noſtra, quod multis fortaſſe nondum
              <lb/>
            perſpectâ hâc theoriâ ſatis paradoxum videri potuiſſet, ſitum diaphragmatis
              <lb/>
            E F ſive altiorem ſive humiliorem nullo modo mutare impetum ſive veloci-
              <lb/>
            tatem aquæ effluentis; </s>
            <s xml:id="echoid-s4267" xml:space="preserve">ratio autem iſtius phænomeni omnibus nunc, puto,
              <lb/>
            manifeſta eſt.</s>
            <s xml:id="echoid-s4268" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4269" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4270" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4271" xml:space="preserve">Jam vero examinabimus inſuper motum aquarum, cum plura
              <lb/>
            ſunt diaphragmata foraminibus pertuſa, per quæ aquæ tranſire cogantur, ut
              <lb/>
            effluxus per foramen D fieri poſſit. </s>
            <s xml:id="echoid-s4272" xml:space="preserve">Poterit id eodem abſolvi modo, quo uſi
              <lb/>
            ſumus in problemate §. </s>
            <s xml:id="echoid-s4273" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4274" xml:space="preserve">Ita autem inſtituto recte calculo retentisque deno-
              <lb/>
            minationibus ibidem adhibitis apparebit eſſe
              <lb/>
            v = x: </s>
            <s xml:id="echoid-s4275" xml:space="preserve">(1 + {nn/αα} + {nn/ββ} + {nn/γγ} + &</s>
            <s xml:id="echoid-s4276" xml:space="preserve">c.)
              <lb/>
            </s>
            <s xml:id="echoid-s4277" xml:space="preserve">ubi per α, β, γ &</s>
            <s xml:id="echoid-s4278" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4279" xml:space="preserve">intelliguntur amplitudines foraminum, quæ ſunt in dia-
              <lb/>
            phragmatibus, dum n exprimit ut antea amplitudinem foraminis D, per quod
              <lb/>
            aquæ effluunt.</s>
            <s xml:id="echoid-s4280" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4281" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4282" xml:space="preserve">12. </s>
            <s xml:id="echoid-s4283" xml:space="preserve">Si proinde loco unius diaphragmatis ſint in ſimili vaſe, quale
              <lb/>
            (Fig. </s>
            <s xml:id="echoid-s4284" xml:space="preserve">39.) </s>
            <s xml:id="echoid-s4285" xml:space="preserve">repræſentat, plura diaphragmata veluti in B, C, R &</s>
            <s xml:id="echoid-s4286" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4287" xml:space="preserve">per quæ
              <lb/>
              <note position="left" xlink:label="note-0162-01" xlink:href="note-0162-01a" xml:space="preserve">Fig. 39.</note>
            aqua transfluat, dum per infimum foramen D effluit, mutabitur & </s>
            <s xml:id="echoid-s4288" xml:space="preserve">augebi-
              <lb/>
            tur confeſtim velocitas aquæ effluentis, quoties aliqua cavitas depletur: </s>
            <s xml:id="echoid-s4289" xml:space="preserve">talis
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            autem eſſe poteſt proportio inter altitudines A B, B C, C R, R E &</s>
            <s xml:id="echoid-s4290" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s4291" xml:space="preserve">atque amplitudines foraminum D, G, F, H &</s>
            <s xml:id="echoid-s4292" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4293" xml:space="preserve">ut ſemper, quoties
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            nova depleri incipit concameratio, vena effluens ad eandem altitudinem
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            O aſſurgat, ſeu eadem velocitate effluat. </s>
            <s xml:id="echoid-s4294" xml:space="preserve">Id vero obtinetur (deſignatis am-
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            plitudinibus foraminum D, G, F, H &</s>
            <s xml:id="echoid-s4295" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4296" xml:space="preserve">per n, α, β, γ, &</s>
            <s xml:id="echoid-s4297" xml:space="preserve">c.) </s>
            <s xml:id="echoid-s4298" xml:space="preserve">faciendo
              <lb/>
            B C = {nn/αα} A B; </s>
            <s xml:id="echoid-s4299" xml:space="preserve">C R = {nn/ββ} A B; </s>
            <s xml:id="echoid-s4300" xml:space="preserve">R E = {nn/γγ} A B &</s>
            <s xml:id="echoid-s4301" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4302" xml:space="preserve">
              <lb/>
            ita ut poſitis ſoraminibus inter ſe æqualibus ſint pariter lineæ A B, B C, C R,
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            R E &</s>
            <s xml:id="echoid-s4303" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4304" xml:space="preserve">inter ſe æquales faciendæ. </s>
            <s xml:id="echoid-s4305" xml:space="preserve">Facile quoque erit in vaſe cylindrico
              <lb/>
            eam conciliare foraminibus magnitudinem, ut ſuperficies fluidi eodem tem-
              <lb/>
            pore ab uno diaphragmate ad ſubſequens quodcunque deſcendat, & </s>
            <s xml:id="echoid-s4306" xml:space="preserve">cum
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            hæc diaphragmata æqualiter à ſe invicem & </s>
            <s xml:id="echoid-s4307" xml:space="preserve">à fundo diſtant, uniformis clep-
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            ſydrarum ſtructura excogitari poteſt.</s>
            <s xml:id="echoid-s4308" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4309" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4310" xml:space="preserve">13. </s>
            <s xml:id="echoid-s4311" xml:space="preserve">Si vero omnia diaphragmata altiſſime poſita ſint, jucundus </s>
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