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
>
161
(147)
162
(148)
163
(149)
164
(150)
165
(151)
166
(152)
167
(153)
168
(154)
169
(155)
170
(156)
<
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
|<
<
(169)
of 361
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div194
"
type
="
section
"
level
="
1
"
n
="
151
">
<
p
>
<
s
xml:id
="
echoid-s4901
"
xml:space
="
preserve
">
<
pb
o
="
169
"
file
="
0183
"
n
="
183
"
rhead
="
SECTIO NONA.
"/>
erit diſpendium potentiæ abſolutæ ad integram hanc potentiam ut F G ad alti-
<
lb
/>
tudinem G ſupra A B.</
s
>
<
s
xml:id
="
echoid-s4902
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div195
"
type
="
section
"
level
="
1
"
n
="
152
">
<
head
xml:id
="
echoid-head199
"
xml:space
="
preserve
">Demonſtratio.</
head
>
<
p
>
<
s
xml:id
="
echoid-s4903
"
xml:space
="
preserve
">Fingamus augeri admodum orificium F diminuta in eadem ratione ve-
<
lb
/>
locitate aquarum effluentium in F; </
s
>
<
s
xml:id
="
echoid-s4904
"
xml:space
="
preserve
">ſic non mutabitur quantitas aquæ dato
<
lb
/>
tempore effluentis, ſi velocitas potentiæ moventis eadem ſit, atque proinde idem
<
lb
/>
erit effectus. </
s
>
<
s
xml:id
="
echoid-s4905
"
xml:space
="
preserve
">Sed ſi velocitas ita diminuatur, ut altitudo ipſi debita ſit inſenſi-
<
lb
/>
bilis, exprimetur potentia movens per altitudinem F ſupra A B, cum antea po-
<
lb
/>
tentia movens erat æqualis altitudini G ſupra A B; </
s
>
<
s
xml:id
="
echoid-s4906
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4907
"
xml:space
="
preserve
">cum in utroque caſu ea-
<
lb
/>
dem ſit velocitas potentiæ moventis, erunt potentiæ abſolutæ pro iiſdem tempori-
<
lb
/>
bus ut altitudo G ad altitudinem F ſupra communem A B. </
s
>
<
s
xml:id
="
echoid-s4908
"
xml:space
="
preserve
">Igitur differentia
<
lb
/>
altitudinum G & </
s
>
<
s
xml:id
="
echoid-s4909
"
xml:space
="
preserve
">F exprimet diſpendium, cum integra altitudo G ſupra A B
<
lb
/>
repræſentat totam potentiam abſolutam.</
s
>
<
s
xml:id
="
echoid-s4910
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4911
"
xml:space
="
preserve
">§. </
s
>
<
s
xml:id
="
echoid-s4912
"
xml:space
="
preserve
">12. </
s
>
<
s
xml:id
="
echoid-s4913
"
xml:space
="
preserve
">Idem ratiocinium valet pro omni machinationum genere: </
s
>
<
s
xml:id
="
echoid-s4914
"
xml:space
="
preserve
">Quo-
<
lb
/>
ties nempe aquæ in locum, ad quem elevandæ ſunt, evectæ notabilem habent
<
lb
/>
velocitatem, magnum fit potentiæ abſolutæ diſpendium: </
s
>
<
s
xml:id
="
echoid-s4915
"
xml:space
="
preserve
">poſita enim altitudine
<
lb
/>
elevationis = A; </
s
>
<
s
xml:id
="
echoid-s4916
"
xml:space
="
preserve
">altitudine debita velocitati aquarum in loco quo effundun-
<
lb
/>
tur = B, integra potentia abſoluta = P, perdetur {B/A + B} X P.</
s
>
<
s
xml:id
="
echoid-s4917
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4918
"
xml:space
="
preserve
">Notari etiam poteſt, cum aquæ trans altitudinem aliquam, cujus cul-
<
lb
/>
men in F poſitum ſit, fundi debent ope antliæ tubo inſtructæ, continuandum
<
lb
/>
eſſe tubum D F inferiora verſus quantum id liceat, nec abrumpendum in F,
<
lb
/>
prouti id apparet ex Fig. </
s
>
<
s
xml:id
="
echoid-s4919
"
xml:space
="
preserve
">49. </
s
>
<
s
xml:id
="
echoid-s4920
"
xml:space
="
preserve
">Nam ſi v. </
s
>
<
s
xml:id
="
echoid-s4921
"
xml:space
="
preserve
">gr. </
s
>
<
s
xml:id
="
echoid-s4922
"
xml:space
="
preserve
">punctum F duplo altius poſitum ſit,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0183-01
"
xlink:href
="
note-0183-01a
"
xml:space
="
preserve
">Fig. 49</
note
>
quam extremitas tubi G, duplo major potentia abſoluta requiritur pro transfun-
<
lb
/>
dendis aquis per canalem abruptum in F, quam per continuatum uſque in G;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4923
"
xml:space
="
preserve
">ſi parvula utrobique velocitate effluant, cujus nempe altitudo genitrix parva
<
lb
/>
ſit ratione altitudinum F D vel G D.</
s
>
<
s
xml:id
="
echoid-s4924
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div197
"
type
="
section
"
level
="
1
"
n
="
153
">
<
head
xml:id
="
echoid-head200
"
xml:space
="
preserve
">Regula 6.</
head
>
<
p
>
<
s
xml:id
="
echoid-s4925
"
xml:space
="
preserve
">§. </
s
>
<
s
xml:id
="
echoid-s4926
"
xml:space
="
preserve
">13. </
s
>
<
s
xml:id
="
echoid-s4927
"
xml:space
="
preserve
">Cum in antliis quas hucusque conſideravimus opercula A B
<
lb
/>
ſeu potius emboli non bene lateribus machinarum reſpondent, hiatus relin-
<
lb
/>
quitur, & </
s
>
<
s
xml:id
="
echoid-s4928
"
xml:space
="
preserve
">ab hoc aliud diſpendii genus in potentiis abſolutis oritur, quod
<
lb
/>
in antliis, in quibus altitudo orificii ſuprà embolum negligi </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>