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
>
71
(57)
72
(58)
73
(59)
74
(60)
75
76
(62)
77
(63)
78
(64)
79
(65)
80
(66)
<
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
|<
<
(281)
of 361
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div292
"
type
="
section
"
level
="
1
"
n
="
221
">
<
pb
o
="
281
"
file
="
0295
"
n
="
295
"
rhead
="
SECTIO DECIMA TERTIA.
"/>
<
p
>
<
s
xml:id
="
echoid-s8320
"
xml:space
="
preserve
">At ut rem plane in apricum ponamus, eam generalius nunc proſe-
<
lb
/>
quemur, idque tentabimus, ut vim repellentem à fluxus initio, dum veloci-
<
lb
/>
tates continue mutantur, determinemus: </
s
>
<
s
xml:id
="
echoid-s8321
"
xml:space
="
preserve
">neque enim primum noſtrum theo-
<
lb
/>
rema aliter quam cum velocitas invariata manet locum habet. </
s
>
<
s
xml:id
="
echoid-s8322
"
xml:space
="
preserve
">Ut in quæſtio-
<
lb
/>
ne hâc paullo intricatiore pertractanda eo intelligibiliores ſimus, hîc quædam
<
lb
/>
generaliora præmonuiſſe juvabit.</
s
>
<
s
xml:id
="
echoid-s8323
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8324
"
xml:space
="
preserve
">§. </
s
>
<
s
xml:id
="
echoid-s8325
"
xml:space
="
preserve
">7. </
s
>
<
s
xml:id
="
echoid-s8326
"
xml:space
="
preserve
">Quantit{as} mot{us} eſt factum ex velocitate in maſſam: </
s
>
<
s
xml:id
="
echoid-s8327
"
xml:space
="
preserve
">ſi velocitates
<
lb
/>
ſint inæquales, habebitur quantitas mot{us} abſoluta, ſi ſingulæ particulæ per ſuam
<
lb
/>
reſpective velocitatem multiplicentur productorumque fumma accipiatur.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s8328
"
xml:space
="
preserve
">Quantitas mot{us} generatur à preſſionibus motricibus dato tempore urgentibus & </
s
>
<
s
xml:id
="
echoid-s8329
"
xml:space
="
preserve
">
<
lb
/>
effectus cauſæ eſt æqualis cenſendus: </
s
>
<
s
xml:id
="
echoid-s8330
"
xml:space
="
preserve
">Igitur ſumma preſſionum motricium per
<
lb
/>
ſua tempuſcula multiplicatorum æſtimanda eſt ex genita quantitate motus. </
s
>
<
s
xml:id
="
echoid-s8331
"
xml:space
="
preserve
">Et
<
lb
/>
quia quælibet preſſio motrix reagit in vas, ex quo aquæ effluunt, erit tota vis re-
<
lb
/>
pellens pro quovis momento æqualis novæ quantitati motus diviſæ per tempuſ-
<
lb
/>
culum, quo generatur. </
s
>
<
s
xml:id
="
echoid-s8332
"
xml:space
="
preserve
">His præmonitis ad quæſtionem ipſam progredior.</
s
>
<
s
xml:id
="
echoid-s8333
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8334
"
xml:space
="
preserve
">§. </
s
>
<
s
xml:id
="
echoid-s8335
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s8336
"
xml:space
="
preserve
">Sit igitur vas infinitæ amplitudinis A C D B (Fig. </
s
>
<
s
xml:id
="
echoid-s8337
"
xml:space
="
preserve
">82.) </
s
>
<
s
xml:id
="
echoid-s8338
"
xml:space
="
preserve
">eique ho-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0295-01
"
xlink:href
="
note-0295-01a
"
xml:space
="
preserve
">Fig. 82.</
note
>
rizontaliter infixa fiſtula E H I D, cujus amplitudines utcunque inæquales po-
<
lb
/>
nuntur: </
s
>
<
s
xml:id
="
echoid-s8339
"
xml:space
="
preserve
">amplitudo orificii H I fuerit = 1, longitudo fiftulæ = m; </
s
>
<
s
xml:id
="
echoid-s8340
"
xml:space
="
preserve
">velocitas
<
lb
/>
utcunque variabilis in H I = √ 2 v, ſeu talis, quæ debeatur altitudini v: </
s
>
<
s
xml:id
="
echoid-s8341
"
xml:space
="
preserve
">dico
<
lb
/>
primo, fore quantitatem motus abſolutam aquæ in fiſtula contentæ æqualem
<
lb
/>
m√2v, id eſt, talem ac ſi fiſtula eſſet cylindrica ſuaque amplitudine orificium
<
lb
/>
H I exæquaret, quia nempe cujuslibet ſtrati F G gf velocitas eſt maſſæ reci-
<
lb
/>
proce proportionalis.</
s
>
<
s
xml:id
="
echoid-s8342
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8343
"
xml:space
="
preserve
">Jam vero fingamus dato tempuſculo infinite parvo exilire per orificium
<
lb
/>
H I columellam H L M I, cujus longitudinem H L vel I M ponemus = a:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s8344
"
xml:space
="
preserve
">erit maſſa hujus columellæ = a, habebitque quantitatem motus = a√2v: </
s
>
<
s
xml:id
="
echoid-s8345
"
xml:space
="
preserve
">
<
lb
/>
fed eodem tempore maſſa aquæ in fiſtula contentæ acquiſivit quantitatem mo-
<
lb
/>
tus {mdv/√2v} (habuit enim m√2v); </
s
>
<
s
xml:id
="
echoid-s8346
"
xml:space
="
preserve
">eſt igitur quantitas motus abſoluta dato tem-
<
lb
/>
puſculo genita = a√2v + {mdv/√2v}; </
s
>
<
s
xml:id
="
echoid-s8347
"
xml:space
="
preserve
">hæc vero ſi dividatur per idem tempuſ-
<
lb
/>
culum (quod exprimendum eſt per {a/√2v}) habebitur, ut vidimus §. </
s
>
<
s
xml:id
="
echoid-s8348
"
xml:space
="
preserve
">7. </
s
>
<
s
xml:id
="
echoid-s8349
"
xml:space
="
preserve
">preſſio
<
lb
/>
quæſita vas repellens, quæ proinde ſi vocetur p, </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>