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
>
51
(37)
52
(38)
53
(39)
54
(40)
55
(41)
56
(42)
57
(43)
58
(44)
59
(45)
60
(46)
<
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
|<
<
(42)
of 361
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div55
"
type
="
section
"
level
="
1
"
n
="
40
">
<
p
>
<
s
xml:id
="
echoid-s1112
"
xml:space
="
preserve
">
<
pb
o
="
42
"
file
="
0056
"
n
="
56
"
rhead
="
HYDRODYNAMICÆ.
"/>
z = [{10000/9998} ({999/1000} - ({999/1000})
<
emph
style
="
super
">9999</
emph
>
) + 4({999/1000})
<
emph
style
="
super
">9999</
emph
>
] a,
<
lb
/>
ſive z = {99915/100000}a + {18/100000}a, in poſteriori caſu autem fit z = {99915/100000}a,
<
lb
/>
ex quo exemplo patet, quam exiguus & </
s
>
<
s
xml:id
="
echoid-s1113
"
xml:space
="
preserve
">plane inſenſibilis ſit exceſſus prio-
<
lb
/>
ris altitudinis ſupra alteram, & </
s
>
<
s
xml:id
="
echoid-s1114
"
xml:space
="
preserve
">quam cito diminuatur jactus ille aqueus,
<
lb
/>
quandoquidem tota mutatio fiat, dum ſuperficies aquæ per milleſimem par-
<
lb
/>
tem altitudinis a deſcendit, quod tempus in machinis hydraulicis ſolitis non
<
lb
/>
poteſt non eſſe admodum breve. </
s
>
<
s
xml:id
="
echoid-s1115
"
xml:space
="
preserve
">Tum etiam confirmatur, quod ſupra Pa-
<
lb
/>
ragrapho 17. </
s
>
<
s
xml:id
="
echoid-s1116
"
xml:space
="
preserve
">dictum fuit, eſſe ſcilicet proxime z = x, quando foramen eſt
<
lb
/>
vel mediocriter parvum, cum in præſenti caſu, ubi motus à quiete incipit,
<
lb
/>
differentia inter z & </
s
>
<
s
xml:id
="
echoid-s1117
"
xml:space
="
preserve
">x ſit tantum quindecim centies milleſimarum partium
<
lb
/>
ipſius altitudinis a; </
s
>
<
s
xml:id
="
echoid-s1118
"
xml:space
="
preserve
">quoniam interim paululum major eſt altitudo z quamx,
<
lb
/>
patet ad majorem altitudinem aſcendere poſſe aquam effluentem, poſtquam
<
lb
/>
aliquantiſper effluxit aqua, quam eſt altitudo aquæ ſupra foramen.</
s
>
<
s
xml:id
="
echoid-s1119
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1120
"
xml:space
="
preserve
">§. </
s
>
<
s
xml:id
="
echoid-s1121
"
xml:space
="
preserve
">19. </
s
>
<
s
xml:id
="
echoid-s1122
"
xml:space
="
preserve
">Poſtquam ſic ex Theoria noſtra generali deduximus, quæ mo-
<
lb
/>
tum fluidorum ex cylindris verticaliter poſitis ſpectant, jam etiam conſi-
<
lb
/>
derabimus tubos oblique poſitos, qui prælongi eſſe ſolent in fontibus ſali-
<
lb
/>
entibus. </
s
>
<
s
xml:id
="
echoid-s1123
"
xml:space
="
preserve
">In his enim id ſingulare eſt, quod acceleratio motus non ita repen-
<
lb
/>
te fiat, veluti cum Cylindri ſunt verticales atque ſic liceat ſenſibus percipe-
<
lb
/>
re conſenſum Theoriæ, cum motu aquarum reali.</
s
>
<
s
xml:id
="
echoid-s1124
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1125
"
xml:space
="
preserve
">§. </
s
>
<
s
xml:id
="
echoid-s1126
"
xml:space
="
preserve
">20. </
s
>
<
s
xml:id
="
echoid-s1127
"
xml:space
="
preserve
">Fingamus canalem utcunque incurvum, ſed tamen Cylindri-
<
lb
/>
cum, cujus amplitudo habeatrurſus ad amplitudinem foraminis rationem m ad n-
<
lb
/>
Incipiat motus à quiete, ſitque altitudo verticalis aquæ ſupra foramen ab initio
<
lb
/>
motus = a; </
s
>
<
s
xml:id
="
echoid-s1128
"
xml:space
="
preserve
">Effluxerit certa aquæ quantitas, ponaturque altitudo verticalis aquæ
<
lb
/>
reſiduæ ſupra foramen = x, longitudo canalis, quæ eo ipſo momento plena eſt
<
lb
/>
= ξ, habeatque tunc aqua interna (cujus ſingulas particulas motu axi canalis pa-
<
lb
/>
rallelo feri hîc aſſumo) velocitatem, quæ reſpondeat altitudini v; </
s
>
<
s
xml:id
="
echoid-s1129
"
xml:space
="
preserve
">His ita poſitis,
<
lb
/>
ſi ſimili ratiocinio utamur quo ſupra, quærendo nimirum incrementum aſcenſus
<
lb
/>
potentialis dum guttula effluit, uti paragrapho 6. </
s
>
<
s
xml:id
="
echoid-s1130
"
xml:space
="
preserve
">fecimus, idemque ponen-
<
lb
/>
do = deſcenſui actuali, obtinetur nunc talis æquatio
<
lb
/>
ξdv - {mm/nn} vdξ + vdξ = - xdξ, </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>