Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO DECIMA.
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que ponatur pondus columnæ mercurii (cujus baſis eſt C D & </
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<
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xml:space
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eadem ſit quæ in barometro) = P. </
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<
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xml:space
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">Utemur autem hypotheſi, ſive globus pro-
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pellatur ab aëre condenſato ſive à pulveris pyrii aura, potentiam illius fluidi
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propellentis proportionalem eſſe denſitati.</
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<
s
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xml:space
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">His ad calculum præparatis, globum conſiderabimus in ſitu e, poneu-
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do A c = x, velocitatemque globi in hoc ſitu = v, ſic erit potentia globum
<
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in ſitu e propellens = ({nb/x} - 1) X P, quæ diviſa per maſſam 1 ductaque in ele-
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mentum ſpatii d x dat incrementum dimidium quadrati velocitatis; </
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<
s
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xml:space
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">unde fit v d v
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= ({nb/x} - 1) X P d x, ſive {1/2} v v = (b - x + nb log. </
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<
s
xml:id
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xml:space
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">{x/b})P. </
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<
s
xml:id
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xml:space
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">Ponatur x = a,
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habetur altitudo debita velocitati, quacum globus exploditur; </
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<
s
xml:id
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xml:space
="
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">vocetur iſta
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altitudo α & </
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<
s
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xml:space
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">erit
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α = (b - a + nb log. </
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<
s
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xml:space
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">{a/b}) X P.</
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<
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</
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<
s
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">(II) Sit v. </
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<
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xml:space
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">in ſclopeto pneumatico longitudo animæ ſeu a = 3 ped.
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</
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<
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xml:space
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<
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">longitudo A C = 4 poll. </
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<
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xml:space
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">fueritque aër captus in A D naturali decies den-
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ſior ſeu n = 10, diameter animæ ſeu globuli ejiciendi trium linearum ejus-
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que gravitas ſpecifica ratione mercurii ut 10 ad 17. </
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<
s
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xml:space
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">Erit P præterpropter =
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286; </
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<
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xml:space
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">indeque invenitur α = 2788, indicio globum ejectum iri velocitate
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qua in vacuo ad altitudinem 2788 ped. </
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<
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">aſcendere poſſit. </
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<
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xml:space
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">Ex præcedente for-
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mula colligitur jactum globi vehementiſſimum fore pro eadem auræ elaſticæ
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quantitate, ſi longitudo animæ fiat = n b. </
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<
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xml:space
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">Si vero animus ad impedimenta
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alia, quæ globus præter inertiam ſuam & </
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<
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xml:space
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">reſiſtentiam aëris externi in tranſitu
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ſuo per Sclopeti animam patitur, advertatur, apparet longitudinem animæ
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ad jactum vehementiſſimum producendum requiri longe minorem. </
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<
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xml:space
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">Si longi-
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tudo n b admodum major ſit longitudine a, quod ita eſt in jactibus fortiori-
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bus, erit ſine ſenſibili errore α = n b P log. </
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<
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xml:space
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">{a/b}.</
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<
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</
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<
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xml:space
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">Si tormentum ſit verticaliter erectum, fit aliquantum diverſus calculus
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ſed pro vehementioribus jactibus differentia nequit eſſe ſenſibilis. </
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<
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">Igitur quia
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jactus deinceps conſiderabimus tantum vehementiſſimos, brevitatis ergo po-
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nemus a = nb P X log. </
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<
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">(III) Prouti in præcedentibus altitudinem determinavimus debitam </
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