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
>
131
(117)
132
(118)
133
(119)
134
(120)
135
(121)
136
(122)
137
(123)
138
139
(125)
140
(126)
<
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
|<
<
(117)
of 361
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div127
"
type
="
section
"
level
="
1
"
n
="
97
">
<
p
>
<
s
xml:id
="
echoid-s3361
"
xml:space
="
preserve
">
<
pb
o
="
117
"
file
="
0131
"
n
="
131
"
rhead
="
SECTIO SEXTA.
"/>
v = {(b - β + f - φ) gx - ({bg/2a} + {bgg/2αγ)} xx/ga - gx + {αgg/γ} + {g
<
emph
style
="
super
">3</
emph
>
/γ} {x/γ} + MN} Q.</
s
>
<
s
xml:id
="
echoid-s3362
"
xml:space
="
preserve
">E.</
s
>
<
s
xml:id
="
echoid-s3363
"
xml:space
="
preserve
">I.</
s
>
<
s
xml:id
="
echoid-s3364
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div128
"
type
="
section
"
level
="
1
"
n
="
98
">
<
head
xml:id
="
echoid-head128
"
xml:space
="
preserve
">Corollarium 1.</
head
>
<
p
>
<
s
xml:id
="
echoid-s3365
"
xml:space
="
preserve
">§. </
s
>
<
s
xml:id
="
echoid-s3366
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s3367
"
xml:space
="
preserve
">Quia linea mn = mg - nh + gh = h - β + f - m, ponemus
<
lb
/>
mn = c, ſimulque multiplicabimus denominatorem & </
s
>
<
s
xml:id
="
echoid-s3368
"
xml:space
="
preserve
">numeratorem per
<
lb
/>
2γγαα: </
s
>
<
s
xml:id
="
echoid-s3369
"
xml:space
="
preserve
">Ita vero habebimus
<
lb
/>
v = {2gγγaαcx - (gγγαb + ggγaß)xx/2gγγaaα - 2gγγaαx + 2ggγaαα + 2g
<
emph
style
="
super
">3</
emph
>
aαx + 2γγaαMN}</
s
>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div129
"
type
="
section
"
level
="
1
"
n
="
99
">
<
head
xml:id
="
echoid-head129
"
xml:space
="
preserve
">Corollarium 2.</
head
>
<
p
>
<
s
xml:id
="
echoid-s3370
"
xml:space
="
preserve
">§. </
s
>
<
s
xml:id
="
echoid-s3371
"
xml:space
="
preserve
">9. </
s
>
<
s
xml:id
="
echoid-s3372
"
xml:space
="
preserve
">Si fiat v =o, patet tunc valorem x denotare totam fluidi ſuper-
<
lb
/>
ficiei excurſionem in tubo ac, quæ ſic invenitur æqualis {2γaαc/γαb + gαβ}, in altero
<
lb
/>
vero tubo fit = {2gaαc/γαb + gαβ}.</
s
>
<
s
xml:id
="
echoid-s3373
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3374
"
xml:space
="
preserve
">Igitur poterit aqua in tubo ſtrictiori ad quamcunque elevari altitudi-
<
lb
/>
nem, ſi modo ratio amplitudinum g & </
s
>
<
s
xml:id
="
echoid-s3375
"
xml:space
="
preserve
">γ ſat magna ſumatur.</
s
>
<
s
xml:id
="
echoid-s3376
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div130
"
type
="
section
"
level
="
1
"
n
="
100
">
<
head
xml:id
="
echoid-head130
"
xml:space
="
preserve
">Corollarium 3.</
head
>
<
p
>
<
s
xml:id
="
echoid-s3377
"
xml:space
="
preserve
">§. </
s
>
<
s
xml:id
="
echoid-s3378
"
xml:space
="
preserve
">10. </
s
>
<
s
xml:id
="
echoid-s3379
"
xml:space
="
preserve
">Pars illa vaſis c A d, quam neutra ſuperficierum unquam attin-
<
lb
/>
gi ponimus, nihil pertinet ad iſtas fluidi excurſiones ſive augendas ſive dimi-
<
lb
/>
nuendas: </
s
>
<
s
xml:id
="
echoid-s3380
"
xml:space
="
preserve
">facere tamen poteſt, ut inferius oſtendetur, ad accelerandas retar-
<
lb
/>
dandaſque oſcillationes.</
s
>
<
s
xml:id
="
echoid-s3381
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div131
"
type
="
section
"
level
="
1
"
n
="
101
">
<
head
xml:id
="
echoid-head131
"
xml:space
="
preserve
">Corollarium 4.</
head
>
<
p
>
<
s
xml:id
="
echoid-s3382
"
xml:space
="
preserve
">§. </
s
>
<
s
xml:id
="
echoid-s3383
"
xml:space
="
preserve
">11. </
s
>
<
s
xml:id
="
echoid-s3384
"
xml:space
="
preserve
">Ponatur uterque tubus communis amplitudinis, erit, poſito
<
lb
/>
nempe g = γ,
<
lb
/>
v = 2gaαcx - (gαb + gaβ)xx/2gaaα + 2gaαα + 2aαMN}.</
s
>
<
s
xml:id
="
echoid-s3385
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3386
"
xml:space
="
preserve
">In hoc caſu maxima ſuperficiei utriuſque velocitas eſt, cum in medio
<
lb
/>
totius excurſionis poſitæ ſunt, ſecus ac fit, cum tubi ſunt inæqualis amplitu-
<
lb
/>
dinis.</
s
>
<
s
xml:id
="
echoid-s3387
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>