Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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131
117
SECTIO SEXTA.
v
= {(
b
-
β
+
f
-
φ
)
gx
-
({
bg
/
2a
} + {
bgg
/
2αγ
)}
xx
/
ga
-
gx
+ {
αgg
/
γ
} + {
g
3
/
γ
} {
x
/
γ
} +
MN
}
Q
.
E
.
I
.
Corollarium
1
.
§
.
8
.
Quia
linea
mn
=
mg
-
nh
+
gh
=
h
-
β
+
f
-
m
,
ponemus
mn
=
c
,
ſimulque
multiplicabimus
denominatorem
&
numeratorem
per
2γγαα
:
Ita
vero
habebimus
v
= {
2gγγaαcx
-
(
gγγαb
+
ggγaß
)
xx
/
2gγγaaα
-
2gγγaαx
+
2ggγaαα
+
2g
3
aαx
+
2γγaαMN
}
Corollarium
2
.
§
.
9
.
Si
fiat
v
=
o
,
patet
tunc
valorem
x
denotare
totam
fluidi
ſuper-
ficiei
excurſionem
in
tubo
ac
,
quæ
ſic
invenitur
æqualis
{
2γaαc
/
γαb
+
gαβ
},
in
altero
vero
tubo
fit
= {
2gaαc
/
γαb
+
gαβ
}.
Igitur
poterit
aqua
in
tubo
ſtrictiori
ad
quamcunque
elevari
altitudi-
nem
,
ſi
modo
ratio
amplitudinum
g
&
γ
ſat
magna
ſumatur
.
Corollarium
3
.
§
.
10
.
Pars
illa
vaſis
c
A
d
,
quam
neutra
ſuperficierum
unquam
attin-
gi
ponimus
,
nihil
pertinet
ad
iſtas
fluidi
excurſiones
ſive
augendas
ſive
dimi-
nuendas
:
facere
tamen
poteſt
,
ut
inferius
oſtendetur
,
ad
accelerandas
retar-
dandaſque
oſcillationes
.
Corollarium
4
.
§
.
11
.
Ponatur
uterque
tubus
communis
amplitudinis
,
erit
,
poſito
nempe
g
=
γ
,
v
=
2gaαcx
-
(
gαb
+
gaβ
)
xx
/
2gaaα
+
2gaαα
+
2aαMN
}.
In
hoc
caſu
maxima
ſuperficiei
utriuſque
velocitas
eſt
,
cum
in
medio
totius
excurſionis
poſitæ
ſunt
,
ſecus
ac
fit
,
cum
tubi
ſunt
inæqualis
amplitu-
dinis
.
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