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

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              <pb o="42" file="0056" n="56" rhead="HYDRODYNAMICÆ."/>
            z = [{10000/9998} ({999/1000} - ({999/1000})
              <emph style="super">9999</emph>
            ) + 4({999/1000})
              <emph style="super">9999</emph>
            ] a,
              <lb/>
            ſive z = {99915/100000}a + {18/100000}a, in poſteriori caſu autem fit z = {99915/100000}a,
              <lb/>
            ex quo exemplo patet, quam exiguus & </s>
            <s xml:id="echoid-s1113" xml:space="preserve">plane inſenſibilis ſit exceſſus prio-
              <lb/>
            ris altitudinis ſupra alteram, & </s>
            <s xml:id="echoid-s1114" xml:space="preserve">quam cito diminuatur jactus ille aqueus,
              <lb/>
            quandoquidem tota mutatio fiat, dum ſuperficies aquæ per milleſimem par-
              <lb/>
            tem altitudinis a deſcendit, quod tempus in machinis hydraulicis ſolitis non
              <lb/>
            poteſt non eſſe admodum breve. </s>
            <s xml:id="echoid-s1115" xml:space="preserve">Tum etiam confirmatur, quod ſupra Pa-
              <lb/>
            ragrapho 17. </s>
            <s xml:id="echoid-s1116" xml:space="preserve">dictum fuit, eſſe ſcilicet proxime z = x, quando foramen eſt
              <lb/>
            vel mediocriter parvum, cum in præſenti caſu, ubi motus à quiete incipit,
              <lb/>
            differentia inter z & </s>
            <s xml:id="echoid-s1117" xml:space="preserve">x ſit tantum quindecim centies milleſimarum partium
              <lb/>
            ipſius altitudinis a; </s>
            <s xml:id="echoid-s1118" xml:space="preserve">quoniam interim paululum major eſt altitudo z quamx,
              <lb/>
            patet ad majorem altitudinem aſcendere poſſe aquam effluentem, poſtquam
              <lb/>
            aliquantiſper effluxit aqua, quam eſt altitudo aquæ ſupra foramen.</s>
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            <s xml:id="echoid-s1120" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1121" xml:space="preserve">19. </s>
            <s xml:id="echoid-s1122" xml:space="preserve">Poſtquam ſic ex Theoria noſtra generali deduximus, quæ mo-
              <lb/>
            tum fluidorum ex cylindris verticaliter poſitis ſpectant, jam etiam conſi-
              <lb/>
            derabimus tubos oblique poſitos, qui prælongi eſſe ſolent in fontibus ſali-
              <lb/>
            entibus. </s>
            <s xml:id="echoid-s1123" xml:space="preserve">In his enim id ſingulare eſt, quod acceleratio motus non ita repen-
              <lb/>
            te fiat, veluti cum Cylindri ſunt verticales atque ſic liceat ſenſibus percipe-
              <lb/>
            re conſenſum Theoriæ, cum motu aquarum reali.</s>
            <s xml:id="echoid-s1124" xml:space="preserve"/>
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            <s xml:id="echoid-s1125" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1126" xml:space="preserve">20. </s>
            <s xml:id="echoid-s1127" xml:space="preserve">Fingamus canalem utcunque incurvum, ſed tamen Cylindri-
              <lb/>
            cum, cujus amplitudo habeatrurſus ad amplitudinem foraminis rationem m ad n-
              <lb/>
            Incipiat motus à quiete, ſitque altitudo verticalis aquæ ſupra foramen ab initio
              <lb/>
            motus = a; </s>
            <s xml:id="echoid-s1128" xml:space="preserve">Effluxerit certa aquæ quantitas, ponaturque altitudo verticalis aquæ
              <lb/>
            reſiduæ ſupra foramen = x, longitudo canalis, quæ eo ipſo momento plena eſt
              <lb/>
            = ξ, habeatque tunc aqua interna (cujus ſingulas particulas motu axi canalis pa-
              <lb/>
            rallelo feri hîc aſſumo) velocitatem, quæ reſpondeat altitudini v; </s>
            <s xml:id="echoid-s1129" xml:space="preserve">His ita poſitis,
              <lb/>
            ſi ſimili ratiocinio utamur quo ſupra, quærendo nimirum incrementum aſcenſus
              <lb/>
            potentialis dum guttula effluit, uti paragrapho 6. </s>
            <s xml:id="echoid-s1130" xml:space="preserve">fecimus, idemque ponen-
              <lb/>
            do = deſcenſui actuali, obtinetur nunc talis æquatio
              <lb/>
            ξdv - {mm/nn} vdξ + vdξ = - xdξ, </s>
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