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
|<
<
(44)
of 361
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div55
"
type
="
section
"
level
="
1
"
n
="
40
">
<
pb
o
="
44
"
file
="
0058
"
n
="
58
"
rhead
="
HYDRODYNAMICÆ
"/>
</
div
>
<
div
xml:id
="
echoid-div57
"
type
="
section
"
level
="
1
"
n
="
41
">
<
head
xml:id
="
echoid-head51
"
style
="
it
"
xml:space
="
preserve
">De Effluxu Aquarum ex Cylindris verticaliter po-
<
lb
/>
ſitis, qui in alios tubos ſtrictiores pariter
<
lb
/>
verticales deſinunt.</
head
>
<
head
xml:id
="
echoid-head52
"
xml:space
="
preserve
">§. 21.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1143
"
xml:space
="
preserve
">COnſtat experientia, inter duos Cylindros omnino æquales ſimiliterque
<
lb
/>
poſitos, quorum alterius foramini tubus ſtrictior reſpondeat, hunc
<
lb
/>
citius depleri, qui tubum appenſum habet, & </
s
>
<
s
xml:id
="
echoid-s1144
"
xml:space
="
preserve
">quidem eo citius, quo
<
lb
/>
magis tubus à loco inſertionis verſus extremitatem amplitudine creſcit, quæ
<
lb
/>
pluribus expoſuit D. </
s
>
<
s
xml:id
="
echoid-s1145
"
xml:space
="
preserve
">s’Graveſande in Phyſ. </
s
>
<
s
xml:id
="
echoid-s1146
"
xml:space
="
preserve
">Elem. </
s
>
<
s
xml:id
="
echoid-s1147
"
xml:space
="
preserve
">Math. </
s
>
<
s
xml:id
="
echoid-s1148
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s1149
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s1150
"
xml:space
="
preserve
">cap. </
s
>
<
s
xml:id
="
echoid-s1151
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s1152
"
xml:space
="
preserve
">Totam rem
<
lb
/>
ſequenti Problemate comprehendemus.</
s
>
<
s
xml:id
="
echoid-s1153
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div58
"
type
="
section
"
level
="
1
"
n
="
42
">
<
head
xml:id
="
echoid-head53
"
xml:space
="
preserve
">Problema.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1154
"
xml:space
="
preserve
">§. </
s
>
<
s
xml:id
="
echoid-s1155
"
xml:space
="
preserve
">22. </
s
>
<
s
xml:id
="
echoid-s1156
"
xml:space
="
preserve
">Fuerit vas cylindricum A E H B (Fig. </
s
>
<
s
xml:id
="
echoid-s1157
"
xml:space
="
preserve
">18.) </
s
>
<
s
xml:id
="
echoid-s1158
"
xml:space
="
preserve
">verticaliter poſi-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0058-01
"
xlink:href
="
note-0058-01a
"
xml:space
="
preserve
">Fig 18.</
note
>
tum perforatum in F G, quo lumine communicet cum tubo conico F M N G,
<
lb
/>
per cujus demum orificium M N aquæ effiuant. </
s
>
<
s
xml:id
="
echoid-s1159
"
xml:space
="
preserve
">Quæritur velocitas ſuperfi-
<
lb
/>
ciei aqueæ C D, poſtquam à quiete deſcendit per A C vel B D.</
s
>
<
s
xml:id
="
echoid-s1160
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div60
"
type
="
section
"
level
="
1
"
n
="
43
">
<
head
xml:id
="
echoid-head54
"
xml:space
="
preserve
">Solutio.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1161
"
xml:space
="
preserve
">Sit altitudo aquæ ſupra M N initialis, nempe N G + H B = a, altitu-
<
lb
/>
do ſuperficiei aqueæ in ſitu C D ſupra M N, id eſt, N G + H D = x; </
s
>
<
s
xml:id
="
echoid-s1162
"
xml:space
="
preserve
">lon-
<
lb
/>
gitudo tubi annexi ſeu N G = b; </
s
>
<
s
xml:id
="
echoid-s1163
"
xml:space
="
preserve
">amplitudo orificii M N = n; </
s
>
<
s
xml:id
="
echoid-s1164
"
xml:space
="
preserve
">amplitudo
<
lb
/>
orificii F G = g, amplitudo Cylindri ſuperioris = m; </
s
>
<
s
xml:id
="
echoid-s1165
"
xml:space
="
preserve
">ſit velocitas ſuperficiei
<
lb
/>
aqueæ in C D talis quæ debeatur altitudini v, erit in æquatione generali §. </
s
>
<
s
xml:id
="
echoid-s1166
"
xml:space
="
preserve
">8.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1167
"
xml:space
="
preserve
">y = m & </
s
>
<
s
xml:id
="
echoid-s1168
"
xml:space
="
preserve
">N = m (x - b) + {bmm/√gn}, quæ ſubſtitutiones inſtituto calculo con-
<
lb
/>
formes eſſe patebunt cum §. </
s
>
<
s
xml:id
="
echoid-s1169
"
xml:space
="
preserve
">6. </
s
>
<
s
xml:id
="
echoid-s1170
"
xml:space
="
preserve
">reliquæ autem poſitiones eædem ſunt quæ an-
<
lb
/>
te. </
s
>
<
s
xml:id
="
echoid-s1171
"
xml:space
="
preserve
">Abit igitur æquatio paragraphi 8 in hanc
<
lb
/>
m(x - b)dv + {bmm/√gn}dv - {m
<
emph
style
="
super
">3</
emph
>
vdx/nn} + mvdx = - mxdx
<
lb
/>
quæ porro diviſa per m factoque x - b + {mb/√gn} = z, </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>