Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 361
>
51
(37)
52
(38)
53
(39)
54
(40)
55
(41)
56
(42)
57
(43)
58
(44)
59
(45)
60
(46)
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 361
>
page
|<
<
(37)
of 361
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div54
"
type
="
section
"
level
="
1
"
n
="
39
">
<
pb
o
="
37
"
file
="
0051
"
n
="
51
"
rhead
="
SECTIO TERTIA.
"/>
</
div
>
<
div
xml:id
="
echoid-div55
"
type
="
section
"
level
="
1
"
n
="
40
">
<
head
xml:id
="
echoid-head49
"
style
="
it
"
xml:space
="
preserve
">De his quæ pertinent ad effluxum aquarum ex Cy-
<
lb
/>
lindris verticaliter poſitis, per Lumen quod-
<
lb
/>
cunque, quod eſt in fundo horizontali.</
head
>
<
head
xml:id
="
echoid-head50
"
xml:space
="
preserve
">§. 13.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1003
"
xml:space
="
preserve
">GEometræ, quibus de aquis ex vaſe erumpentibus ſermo fuit, con-
<
lb
/>
ſiderare potiſſimum ſolent cylindros verticaliter poſitos: </
s
>
<
s
xml:id
="
echoid-s1004
"
xml:space
="
preserve
">Igitur haud
<
lb
/>
abs re erit ex theoria noſtra generali conſectaria illa, quæ huc per-
<
lb
/>
tinent, deducere. </
s
>
<
s
xml:id
="
echoid-s1005
"
xml:space
="
preserve
">Sit amplitudo cylindri ad amplitudinem foraminis ut m
<
lb
/>
ad n; </
s
>
<
s
xml:id
="
echoid-s1006
"
xml:space
="
preserve
">altitudo aquæ ſupra foramen, cum fluxus incipit = a; </
s
>
<
s
xml:id
="
echoid-s1007
"
xml:space
="
preserve
">altitudo aquæ
<
lb
/>
reſiduæ = x, altitudo velocitati aquæ internæ debita = v; </
s
>
<
s
xml:id
="
echoid-s1008
"
xml:space
="
preserve
">erit in æquatio-
<
lb
/>
ne canonica paragraphi octavi y = m, N = mx (per §. </
s
>
<
s
xml:id
="
echoid-s1009
"
xml:space
="
preserve
">6.) </
s
>
<
s
xml:id
="
echoid-s1010
"
xml:space
="
preserve
">quæ adeoque
<
lb
/>
abit in hanc æquationem.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1011
"
xml:space
="
preserve
">mxdv - {m
<
emph
style
="
super
">3</
emph
>
/nn}vdx + mvdx = - mxdx, vel
<
lb
/>
(1 - {mm/nn})vdx + xdv = - xdx
<
lb
/>
multiplicetur hæc poſterior æquatio per x
<
emph
style
="
super
">{- mm/nn}</
emph
>
, ut habeatur
<
lb
/>
(1 - {mm/nn})x
<
emph
style
="
super
">- {mm/nn}</
emph
>
vdx + x
<
emph
style
="
super
">1 - {mm/nn}</
emph
>
dv = - x
<
emph
style
="
super
">1 - {mm/nn}</
emph
>
dx.</
s
>
<
s
xml:id
="
echoid-s1012
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1013
"
xml:space
="
preserve
">Poteſt jam hæc æquatio integrari: </
s
>
<
s
xml:id
="
echoid-s1014
"
xml:space
="
preserve
">obſervanda autem eſt in Integratio-
<
lb
/>
ne conſtantis additio, talis nempe, ut a fluxus initio, id eſt, cum x = a,
<
lb
/>
ſit velocitas fluidi nulla, ipſaque proin v pariter = o: </
s
>
<
s
xml:id
="
echoid-s1015
"
xml:space
="
preserve
">ita vero oritur:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1016
"
xml:space
="
preserve
">x
<
emph
style
="
super
">1 - {mm/nn}</
emph
>
v = {nn/2nn - mm}(a
<
emph
style
="
super
">2 - {mm/nn}</
emph
>
- x
<
emph
style
="
super
">2 - {mm/nn}</
emph
>
) vel
<
lb
/>
v = {nna/2nn - mm}(({a/x})
<
emph
style
="
super
">1 - {mm/nn}</
emph
>
- {x/a})</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1017
"
xml:space
="
preserve
">§. </
s
>
<
s
xml:id
="
echoid-s1018
"
xml:space
="
preserve
">14. </
s
>
<
s
xml:id
="
echoid-s1019
"
xml:space
="
preserve
">Ex hâc igitur æquatione cognoſcitur altitudo generans velocita-
<
lb
/>
tem aquæ internæ; </
s
>
<
s
xml:id
="
echoid-s1020
"
xml:space
="
preserve
">ubi notari meretur, ſi vas ſit ampliſſimum, mox poſſe
<
lb
/>
cenſeri v = {nn/mm}x, poſtquam ſcilicet vel tantillum deſcendit aqua, id </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>