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
|<
<
(114)
of 361
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div119
"
type
="
section
"
level
="
1
"
n
="
92
">
<
p
>
<
s
xml:id
="
echoid-s3250
"
xml:space
="
preserve
">
<
pb
o
="
114
"
file
="
0128
"
n
="
128
"
rhead
="
HYDRODYNAMICÆ
"/>
ximas hanc legem ſervare. </
s
>
<
s
xml:id
="
echoid-s3251
"
xml:space
="
preserve
">Cum itaque talis caſus occurrit, eo magis con-
<
lb
/>
veniet motus realis cum theoria, quo longior fuerit pars b m & </
s
>
<
s
xml:id
="
echoid-s3252
"
xml:space
="
preserve
">quo paucio-
<
lb
/>
ra adfuerint obſtacula.</
s
>
<
s
xml:id
="
echoid-s3253
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3254
"
xml:space
="
preserve
">§. </
s
>
<
s
xml:id
="
echoid-s3255
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s3256
"
xml:space
="
preserve
">Quod ſi nunc canalis fuerit non horizontaliter ſed oblique ad
<
lb
/>
horizontem poſitus, apparet omnia ſimiliter ſe habere, niſi quod aſcenſus potent.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3257
"
xml:space
="
preserve
">aquæ in omni ſitu æquandus ſit aſcenſui potent. </
s
>
<
s
xml:id
="
echoid-s3258
"
xml:space
="
preserve
">initiali aucto deſcenſu actuali, id
<
lb
/>
eſt, deſcenſui verticali centri gravitatis. </
s
>
<
s
xml:id
="
echoid-s3259
"
xml:space
="
preserve
">Atque ſi nullo impulſu aqua ſua ſponte
<
lb
/>
ſe movere incipiat, erit ſimpliciter deſcenſus actualis æqualis aſcenſui potent.</
s
>
<
s
xml:id
="
echoid-s3260
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3261
"
xml:space
="
preserve
">Igitur aqua continue progredi perget, quamdiu centrum gravitatis lo-
<
lb
/>
co humiliori poſitum eſt, ac fuit ab initio motus. </
s
>
<
s
xml:id
="
echoid-s3262
"
xml:space
="
preserve
">At vero cum tubus ita
<
lb
/>
fuerit formatus & </
s
>
<
s
xml:id
="
echoid-s3263
"
xml:space
="
preserve
">inflexus eaque fluidi quantitate repletus, ut centrum gravi-
<
lb
/>
tatis priſtinam altitudinem reaſſumere poſſit, tunc fluidum motum obtinebit
<
lb
/>
retrogradum & </
s
>
<
s
xml:id
="
echoid-s3264
"
xml:space
="
preserve
">ſine fine oſcillabitur. </
s
>
<
s
xml:id
="
echoid-s3265
"
xml:space
="
preserve
">De iſto motu præcipuam huj
<
unsure
/>
us ſectionis
<
lb
/>
partem faciente mox dicemus. </
s
>
<
s
xml:id
="
echoid-s3266
"
xml:space
="
preserve
">Interea obſervare licet, fieri poſſe, ut aqua
<
lb
/>
omnis ex loco humiliore per altiorem ſua ſponte ſine prævia ſuctione præter-
<
lb
/>
fluat, ſi modo omnia debito modo ſe habeant.</
s
>
<
s
xml:id
="
echoid-s3267
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div121
"
type
="
section
"
level
="
1
"
n
="
93
">
<
head
xml:id
="
echoid-head122
"
style
="
it
"
xml:space
="
preserve
">De oſcillationibus fluidorum in tubisrecurvis.</
head
>
<
head
xml:id
="
echoid-head123
"
xml:space
="
preserve
">Caſus II.</
head
>
<
p
>
<
s
xml:id
="
echoid-s3268
"
xml:space
="
preserve
">§. </
s
>
<
s
xml:id
="
echoid-s3269
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s3270
"
xml:space
="
preserve
">Dedit Pater meus in Comm. </
s
>
<
s
xml:id
="
echoid-s3271
"
xml:space
="
preserve
">Acad. </
s
>
<
s
xml:id
="
echoid-s3272
"
xml:space
="
preserve
">Scient. </
s
>
<
s
xml:id
="
echoid-s3273
"
xml:space
="
preserve
">Petrop. </
s
>
<
s
xml:id
="
echoid-s3274
"
xml:space
="
preserve
">tom. </
s
>
<
s
xml:id
="
echoid-s3275
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s3276
"
xml:space
="
preserve
">theore-
<
lb
/>
mata quædam, quæ inſignem manifeſtant uſum quem theoria virium vivarum
<
lb
/>
habet in rebus mechanicis. </
s
>
<
s
xml:id
="
echoid-s3277
"
xml:space
="
preserve
">Illud vero quod tertio loco poſitum eſt ita ſe
<
lb
/>
habet.</
s
>
<
s
xml:id
="
echoid-s3278
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s3279
"
xml:space
="
preserve
">Sit tubus cylindricus A B C H (Fig. </
s
>
<
s
xml:id
="
echoid-s3280
"
xml:space
="
preserve
">33.) </
s
>
<
s
xml:id
="
echoid-s3281
"
xml:space
="
preserve
">utrobi{q́ue} apertus at{q́ue} infle-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0128-01
"
xlink:href
="
note-0128-01a
"
xml:space
="
preserve
">Fig. 33.</
note
>
xus in duo crura B A & </
s
>
<
s
xml:id
="
echoid-s3282
"
xml:space
="
preserve
">C H ad partem horizontalem B C; </
s
>
<
s
xml:id
="
echoid-s3283
"
xml:space
="
preserve
">ſit ſinus anguli
<
lb
/>
A B C = p, & </
s
>
<
s
xml:id
="
echoid-s3284
"
xml:space
="
preserve
">ſinus anguli H C B = q; </
s
>
<
s
xml:id
="
echoid-s3285
"
xml:space
="
preserve
">exiſtente nimirum ſinu toto = 1;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3286
"
xml:space
="
preserve
">ſit porro ille tubus aqua plenus uſ{q́ue} ad horizontalem M N; </
s
>
<
s
xml:id
="
echoid-s3287
"
xml:space
="
preserve
">vocetur{q́ue} L longi-
<
lb
/>
tudo partis tubi M B C N aqua plenæ: </
s
>
<
s
xml:id
="
echoid-s3288
"
xml:space
="
preserve
">Erunt agitati liquoris in hoc tubo oſ-
<
lb
/>
cillationes tam majores, quam minores omnes tautochronæ at{q́ue} ejuſdem duratio-
<
lb
/>
nis cum oſcillationibus minimis penduli alicujus ſimplicis, cujus longitudo
<
lb
/>
= {L/p + q}.</
s
>
<
s
xml:id
="
echoid-s3289
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3290
"
xml:space
="
preserve
">Huic theoremati eodem auctore ſubnectitur tale corollarium.</
s
>
<
s
xml:id
="
echoid-s3291
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>