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
Table of Notes
<
1 - 3
[out of range]
>
[Note]
Page: 204
[Note]
Page: 207
[Note]
Page: 210
[Note]
Page: 214
[Note]
Page: 218
[Note]
Page: 220
[Note]
Page: 227
[Note]
Page: 229
[Note]
Page: 234
[Note]
Page: 235
[Note]
Page: 236
[Note]
Page: 243
[Note]
Page: 247
[Note]
Page: 248
[Note]
Page: 250
[Note]
Page: 251
[Note]
Page: 258
[Note]
Page: 258
[Note]
Page: 266
[Note]
Page: 267
[Note]
Page: 268
[Note]
Page: 268
[Note]
Page: 272
[Note]
Page: 277
[Note]
Page: 279
[Note]
Page: 279
[Note]
Page: 287
[Note]
Page: 289
[Note]
Page: 290
[Note]
Page: 293
<
1 - 3
[out of range]
>
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
>