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
|<
<
(39)
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-s1053
"
xml:space
="
preserve
">
<
pb
o
="
39
"
file
="
0053
"
n
="
53
"
rhead
="
SECTIO TERTIA.
"/>
{mma/mm - 2nn} X [({nn/mm - nn})
<
emph
style
="
super
">nn: (mm - 2nn)</
emph
>
- ({nn/mm - nn})
<
emph
style
="
super
">(mm - nn): (mm - 2nn)</
emph
>
]
<
lb
/>
quæ quantitas reducta fit =
<
lb
/>
{mma/mm - nn}({nn/mm - nn})
<
emph
style
="
super
">nn: (mm - 2nn)</
emph
>
</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1054
"
xml:space
="
preserve
">Intelligitur ex iſtis formulis tempus, quo velocitas à nihilo in maxi-
<
lb
/>
mam vertitur, plane imperceptibile eſſe, quando foramen vel mediocriter
<
lb
/>
parvum tubusque non admodum longus eſt: </
s
>
<
s
xml:id
="
echoid-s1055
"
xml:space
="
preserve
">notabile autem fieri, cum res
<
lb
/>
ſecus ſe habet, quod videmus in fontibus ſalientibus, ad quos aquæ per
<
lb
/>
longos tractus vehuntur; </
s
>
<
s
xml:id
="
echoid-s1056
"
xml:space
="
preserve
">hæc vero quæ ad tempora pertinent, magis in
<
lb
/>
ſequenti ſectione explicabuntur, atque ſimul oſtendetur, quam parum aquæ
<
lb
/>
ex vaſis ampliſſimis ejiciatur, priusquam maxima velocitate effluant.</
s
>
<
s
xml:id
="
echoid-s1057
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1058
"
xml:space
="
preserve
">Natura velocitatum melius intelligitur ex appoſita Figura decima ſepti-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0053-01
"
xlink:href
="
note-0053-01a
"
xml:space
="
preserve
">Fig. 17.</
note
>
ma, in quâ ſi A B repræſentet totam altitudinem fluidi ſupra foramen ab initio
<
lb
/>
fluxus, expriment curvæ A 1 C B, A 2 C B, A 3 C B, A 4 C B, ſcalas altitudi-
<
lb
/>
num reſpondentium, ad quas fluidum effluens ſua velocitate aſcendere poſſit in
<
lb
/>
diverſis foraminum magnitudinibus: </
s
>
<
s
xml:id
="
echoid-s1059
"
xml:space
="
preserve
">nempe ſcala accedet ad figuram A 1 C B, ſi
<
lb
/>
foramen habeat exiguam rationem ad vaſis amplitudinem & </
s
>
<
s
xml:id
="
echoid-s1060
"
xml:space
="
preserve
">ad figuram A 2 C B,
<
lb
/>
cum aſſumitur fundum majori lumine perforatum; </
s
>
<
s
xml:id
="
echoid-s1061
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1062
"
xml:space
="
preserve
">ſi jam ratio foraminis
<
lb
/>
ſit ad amplitudinem vaſis ut 1 ad √ 2, erit ſcala illa ut A 3 C B (quo in caſu
<
lb
/>
minor fit maxima velocitas quam in quocunque alio, eſtque nominatim ea
<
lb
/>
quæ debetur altitudini {2a/c}, intelligendo per c numerum cujus Logarithmus
<
lb
/>
eſt unitas, id eſt, altitudini paulo minori quam {3/4}a) ac denique erit ſcala ut
<
lb
/>
A 4 C B cum fere nihil fundi ſupereſt.</
s
>
<
s
xml:id
="
echoid-s1063
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1064
"
xml:space
="
preserve
">§. </
s
>
<
s
xml:id
="
echoid-s1065
"
xml:space
="
preserve
">17. </
s
>
<
s
xml:id
="
echoid-s1066
"
xml:space
="
preserve
">Jam vero exemplo quodam illuſtrabimus, quod ſupra §. </
s
>
<
s
xml:id
="
echoid-s1067
"
xml:space
="
preserve
">10.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1068
"
xml:space
="
preserve
">indicatum fuit, nempe niſi foramen ſit ampliſſimum, poſſe id ſine valde
<
lb
/>
ſenſibili errore in calculo conſiderari ut infinitè parvum, atque adeo aſſumi
<
lb
/>
z = x, ut §. </
s
>
<
s
xml:id
="
echoid-s1069
"
xml:space
="
preserve
">§. </
s
>
<
s
xml:id
="
echoid-s1070
"
xml:space
="
preserve
">10. </
s
>
<
s
xml:id
="
echoid-s1071
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1072
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s1073
"
xml:space
="
preserve
">dictum fuit. </
s
>
<
s
xml:id
="
echoid-s1074
"
xml:space
="
preserve
">Videtur id tantum apud nonnullos
<
lb
/>
Auctores valuiſſe, ut cenſuerint, nullam magnitudinis in foramine rationem
<
lb
/>
unquam eſſe habendam, quantumvis magnum ponatur foramen, quæ res
<
lb
/>
certe ridicula eſt: </
s
>
<
s
xml:id
="
echoid-s1075
"
xml:space
="
preserve
">faltem nemo hactenus quod ſciam magnitudinem forami-
<
lb
/>
nis pro hoc negotio recte conſideravit. </
s
>
<
s
xml:id
="
echoid-s1076
"
xml:space
="
preserve
">Ponamus igitur cylindrum, cujus
<
lb
/>
diameter quadrupla tantum ſit diametri foraminis, cujusmodi magna </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>