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
Page concordance
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 361
>
Scan
Original
11
12
13
14
15
16
2
17
3
18
4
19
5
20
6
21
7
22
8
23
9
24
10
25
11
26
12
27
13
28
14
29
15
30
16
31
17
32
18
33
19
34
20
35
21
36
22
37
23
38
24
39
25
40
26
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 361
>
page
|<
<
(32)
of 361
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div40
"
type
="
section
"
level
="
1
"
n
="
27
">
<
pb
o
="
32
"
file
="
0046
"
n
="
46
"
rhead
="
HYDRODYNAMICÆ.
"/>
</
div
>
<
div
xml:id
="
echoid-div41
"
type
="
section
"
level
="
1
"
n
="
28
">
<
head
xml:id
="
echoid-head37
"
xml:space
="
preserve
">Solutio.</
head
>
<
p
>
<
s
xml:id
="
echoid-s883
"
xml:space
="
preserve
">Sit ſpatium A E G B = M, ſpatium A E Z U = N, qs = v, erit
<
lb
/>
aſcenſus potent. </
s
>
<
s
xml:id
="
echoid-s884
"
xml:space
="
preserve
">= {Nv/M}: </
s
>
<
s
xml:id
="
echoid-s885
"
xml:space
="
preserve
">quia vero quantitas aquæ in canali conſtanter eadem
<
lb
/>
ponitur, erit ſpatium A E G B invariabile, adeoque d M = o ita ut diffe-
<
lb
/>
rentiale aſcenſus potent. </
s
>
<
s
xml:id
="
echoid-s886
"
xml:space
="
preserve
">ſit ſimpliciter = {Ndv + vdN/M}, habetur autem d N
<
lb
/>
ex variatione ſitus aquæ. </
s
>
<
s
xml:id
="
echoid-s887
"
xml:space
="
preserve
">Patet igitur propoſitum. </
s
>
<
s
xml:id
="
echoid-s888
"
xml:space
="
preserve
">Q. </
s
>
<
s
xml:id
="
echoid-s889
"
xml:space
="
preserve
">E. </
s
>
<
s
xml:id
="
echoid-s890
"
xml:space
="
preserve
">I.</
s
>
<
s
xml:id
="
echoid-s891
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div42
"
type
="
section
"
level
="
1
"
n
="
29
">
<
head
xml:id
="
echoid-head38
"
xml:space
="
preserve
">Scholion.</
head
>
<
p
>
<
s
xml:id
="
echoid-s892
"
xml:space
="
preserve
">§. </
s
>
<
s
xml:id
="
echoid-s893
"
xml:space
="
preserve
">5. </
s
>
<
s
xml:id
="
echoid-s894
"
xml:space
="
preserve
">Poterunt hæ propoſitiones inſervire pro motu |fluidi intra vaſa
<
lb
/>
moti, id eſt, non effluentis definiendo, uti ſuo loco oſtendam: </
s
>
<
s
xml:id
="
echoid-s895
"
xml:space
="
preserve
">at ve-
<
lb
/>
ro cum fluidum per foramen effluit, aptius inſtituetur aliter calculus,
<
lb
/>
nempe ut ſequitur.</
s
>
<
s
xml:id
="
echoid-s896
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div43
"
type
="
section
"
level
="
1
"
n
="
30
">
<
head
xml:id
="
echoid-head39
"
xml:space
="
preserve
">Problema.</
head
>
<
p
>
<
s
xml:id
="
echoid-s897
"
xml:space
="
preserve
">§. </
s
>
<
s
xml:id
="
echoid-s898
"
xml:space
="
preserve
">6. </
s
>
<
s
xml:id
="
echoid-s899
"
xml:space
="
preserve
">Invenire differentiam aſcenſus potentialis poſtquam guttula
<
lb
/>
per foramen effluxit.</
s
>
<
s
xml:id
="
echoid-s900
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div44
"
type
="
section
"
level
="
1
"
n
="
31
">
<
head
xml:id
="
echoid-head40
"
xml:space
="
preserve
">Solutio.</
head
>
<
p
>
<
s
xml:id
="
echoid-s901
"
xml:space
="
preserve
">Fingamus aquam effluere ex vaſe aimb (Fig. </
s
>
<
s
xml:id
="
echoid-s902
"
xml:space
="
preserve
">15.) </
s
>
<
s
xml:id
="
echoid-s903
"
xml:space
="
preserve
">utcunque for-
<
lb
/>
mato, fundum ſit im perforatum foramine pl: </
s
>
<
s
xml:id
="
echoid-s904
"
xml:space
="
preserve
">quantitas aquæ, poſtquam
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0046-01
"
xlink:href
="
note-0046-01a
"
xml:space
="
preserve
">Fig. 15.</
note
>
jam data ejus quantitas effluxit, reſidua in vaſe ſit cimd; </
s
>
<
s
xml:id
="
echoid-s905
"
xml:space
="
preserve
">effluat autem
<
lb
/>
tempusculo infinitè parvo guttula pnol, ſuperficie cd deſcendente in ſitum
<
lb
/>
ef: </
s
>
<
s
xml:id
="
echoid-s906
"
xml:space
="
preserve
">concipiatur in medio aquæ ſectio gh parallela ſuperficiebus cd vel ef
<
lb
/>
ipſique fundo im; </
s
>
<
s
xml:id
="
echoid-s907
"
xml:space
="
preserve
">ſitque velocitas unius cujusvis particulæ in gh talis,
<
lb
/>
ut poſſit aſcendere ad altitudinem qs ſeu v, cum nondum effluxit guttula
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s908
"
xml:space
="
preserve
">ad altitudinem qz ſive
<
gap
/>
+ dv, poſtquam ea ipſa guttula effluxit.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s909
"
xml:space
="
preserve
">Omnibus his ita poſitis, quæritur incrementum aſcenſus potentialis aquæ poſt-
<
lb
/>
quam ſitum cimd commutavit cum ſitu eipnolmf, id eſt, poſtquam gut-
<
lb
/>
tula emanavit.</
s
>
<
s
xml:id
="
echoid-s910
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s911
"
xml:space
="
preserve
">Fiat, ut antea, curva C G I (Fig. </
s
>
<
s
xml:id
="
echoid-s912
"
xml:space
="
preserve
">16.) </
s
>
<
s
xml:id
="
echoid-s913
"
xml:space
="
preserve
">ceu ſcala amplitudinum, ubi
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0046-02
"
xlink:href
="
note-0046-02a
"
xml:space
="
preserve
">Fig. 16.</
note
>
adeoque C D vel E F repræſentabunt magnitudinem ſuperficiei aqueæ </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>