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

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            <s xml:id="echoid-s2079" xml:space="preserve">
              <pb o="76" file="0090" n="90" rhead="HYDRODYNAMICÆ"/>
            ximam velocitatem fiunt: </s>
            <s xml:id="echoid-s2080" xml:space="preserve">Dico autem poſſe in calculo hujusmodi tempo-
              <lb/>
            rum ſimpliciter poni v = {nn/mm}a; </s>
            <s xml:id="echoid-s2081" xml:space="preserve">Reliquæ enim quantitates in æquatione ul-
              <lb/>
            tima §. </s>
            <s xml:id="echoid-s2082" xml:space="preserve">16. </s>
            <s xml:id="echoid-s2083" xml:space="preserve">evaneſcunt, quantumlibet parva ſumatur altitudo z, modo ha-
              <lb/>
            beat rationem vel minimam aſſignabilem ad altitudinem illam infinite par-
              <lb/>
            vam, quæ reſpondet maximæ velocitati, nempe ad {nb/m}√{n/g} X log.</s>
            <s xml:id="echoid-s2084" xml:space="preserve">({ma/nb}√{g/n}).
              <lb/>
            </s>
            <s xml:id="echoid-s2085" xml:space="preserve">Sequitur exinde eſſe prædictum tempus, quod vocabo
              <lb/>
            t = {b√n/√ga} X log.</s>
            <s xml:id="echoid-s2086" xml:space="preserve">({ma/nb}√{g/n})
              <lb/>
            & </s>
            <s xml:id="echoid-s2087" xml:space="preserve">proinde infinitum, quamvis idem tempus admodum exiguum ſit, quum
              <lb/>
            amplitudo vaſis non eſt infinita, ſed utcunque magna, quod rurſus ex na-
              <lb/>
            tura infiniti logarithmicalis eſt deducendum.</s>
            <s xml:id="echoid-s2088" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2089" xml:space="preserve">§. </s>
            <s xml:id="echoid-s2090" xml:space="preserve">19. </s>
            <s xml:id="echoid-s2091" xml:space="preserve">Quia altitudo velocitatis, ut vidimus in proximo paragrapho, poteſt
              <lb/>
            ſtatim cenſeri = {nn/mm}a, id eſt, æqualis maximæ, cum ſuperficies per minimam
              <lb/>
            partem aſſignabilem deſcenſus infinite parvi, poſt quem velocitas maxima
              <lb/>
            plena adeſt, deſcendit, ſequitur mutationes plerasque à quiete usque ad ſta-
              <lb/>
            tum maximæ velocitatis eſſe inſenſibiles, id eſt, infinite parvas, imo non
              <lb/>
            ſolum plerasque, ſed & </s>
            <s xml:id="echoid-s2092" xml:space="preserve">omnes præter particulam infinite parvam: </s>
            <s xml:id="echoid-s2093" xml:space="preserve">res ſci-
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            licet ſic ſe habet: </s>
            <s xml:id="echoid-s2094" xml:space="preserve">velocitas à primo initio plane nulla eſt, & </s>
            <s xml:id="echoid-s2095" xml:space="preserve">poſtquam aqua
              <lb/>
            per ſpatiolum infinite parvum deſcendit, jam eſt tantum non maxima; </s>
            <s xml:id="echoid-s2096" xml:space="preserve">dein
              <lb/>
            dum per aliud ſpatiolum rurſus quidem infinite parvum priori tamen infinite
              <lb/>
            majus, deſcendit, pergit velocitate ſua moveri, incrementa ſumens infinitè
              <lb/>
            parva, & </s>
            <s xml:id="echoid-s2097" xml:space="preserve">tunc demum vere maximam velocitatem attingit: </s>
            <s xml:id="echoid-s2098" xml:space="preserve">Cum vero po-
              <lb/>
            ſteriores illæ mutationes ceu infinite parvæ non poſſint ſenſibus percipi, aliter
              <lb/>
            pertractabimus ea quæ à §. </s>
            <s xml:id="echoid-s2099" xml:space="preserve">17. </s>
            <s xml:id="echoid-s2100" xml:space="preserve">dedimus theoremata, conſiderando loco mu-
              <lb/>
            tationum à quiete usque ad punctum maximæ velocitatis, easdem mutatio-
              <lb/>
            nes usque ad datum gradum velocitatis.</s>
            <s xml:id="echoid-s2101" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2102" xml:space="preserve">§. </s>
            <s xml:id="echoid-s2103" xml:space="preserve">20. </s>
            <s xml:id="echoid-s2104" xml:space="preserve">Indagabimus itaque, per quantum ſpatiolum z ſuperficies aquæ
              <lb/>
            à ſtatu quietis deſcendere, quantaque aqua effluere, ac denique quantum
              <lb/>
            tempus præterire debeat, ut aqua interna velocitate moveatur, quæ gene-
              <lb/>
            retur lapſu libero per datam altitudinem, quam vocabimus {nn/mm}e, ita ut ip-
              <lb/>
            fa e denotet ſimilem altitudinem pro velocitate aquæ effluentis. </s>
            <s xml:id="echoid-s2105" xml:space="preserve">Ad hoc </s>
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