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
Table of Notes
<
1 - 3
[out of range]
>
<
1 - 3
[out of range]
>
page
|<
<
(190)
of 361
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div227
"
type
="
section
"
level
="
1
"
n
="
180
">
<
p
>
<
s
xml:id
="
echoid-s5472
"
xml:space
="
preserve
">
<
pb
o
="
190
"
file
="
0204
"
n
="
204
"
rhead
="
HYDRODYNAMICÆ
"/>
cæ indirectis; </
s
>
<
s
xml:id
="
echoid-s5473
"
xml:space
="
preserve
">placet tamen hujus rei demonſtrationem dare ex natura vectis
<
lb
/>
petitam, quia mechanici eo omnia reducere amant.</
s
>
<
s
xml:id
="
echoid-s5474
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s5475
"
xml:space
="
preserve
">Helicem conſiderabimus a 1 b ex figura quinquageſima ſecunda ſeor-
<
lb
/>
ſim deſumtam, ad evitandam linearum confuſionem, conſervatis denomi-
<
lb
/>
nationibus art. </
s
>
<
s
xml:id
="
echoid-s5476
"
xml:space
="
preserve
">IV. </
s
>
<
s
xml:id
="
echoid-s5477
"
xml:space
="
preserve
">adhibitis. </
s
>
<
s
xml:id
="
echoid-s5478
"
xml:space
="
preserve
">Sic igitur in Figura 53. </
s
>
<
s
xml:id
="
echoid-s5479
"
xml:space
="
preserve
">erit rurſus angulus
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0204-01
"
xlink:href
="
note-0204-01a
"
xml:space
="
preserve
">Fig. 53.</
note
>
N M G angulus quem facit nucleus cum horizonte, cujus ſinus = N, ſi-
<
lb
/>
nusque anguli a M H = n; </
s
>
<
s
xml:id
="
echoid-s5480
"
xml:space
="
preserve
">a 1 b eſt una ſpiralis circumvolutio: </
s
>
<
s
xml:id
="
echoid-s5481
"
xml:space
="
preserve
">baſis nuclei
<
lb
/>
eſt circulus a c M p a; </
s
>
<
s
xml:id
="
echoid-s5482
"
xml:space
="
preserve
">ſinus anguli p a l eſt ut ante = m, ejusque coſinus M;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s5483
"
xml:space
="
preserve
">puncta vero l & </
s
>
<
s
xml:id
="
echoid-s5484
"
xml:space
="
preserve
">o ſunt extremitates aquæ in ſpirali quieſcentis & </
s
>
<
s
xml:id
="
echoid-s5485
"
xml:space
="
preserve
">in ea-
<
lb
/>
dem altitudine ab horizonte poſita, ex iſtis punctis ductæ ſunt ad periphe-
<
lb
/>
riam baſis rectæ l c & </
s
>
<
s
xml:id
="
echoid-s5486
"
xml:space
="
preserve
">o p ad baſin perpendiculares. </
s
>
<
s
xml:id
="
echoid-s5487
"
xml:space
="
preserve
">In parte helicis quam
<
lb
/>
aqua occupat ſumta ſunt duo puncta infinite propinqua m & </
s
>
<
s
xml:id
="
echoid-s5488
"
xml:space
="
preserve
">n & </
s
>
<
s
xml:id
="
echoid-s5489
"
xml:space
="
preserve
">per hæc du-
<
lb
/>
ctæ ſunt rectæ n f & </
s
>
<
s
xml:id
="
echoid-s5490
"
xml:space
="
preserve
">m g rurſus ad baſin perpendiculares. </
s
>
<
s
xml:id
="
echoid-s5491
"
xml:space
="
preserve
">Denique ex pun-
<
lb
/>
ctis c, f, g, p ductæ ſunt ad diametrum a M perpendiculares c d, f h, g i & </
s
>
<
s
xml:id
="
echoid-s5492
"
xml:space
="
preserve
">
<
lb
/>
p q; </
s
>
<
s
xml:id
="
echoid-s5493
"
xml:space
="
preserve
">atque centrum baſis ponitur in e, radiusque e a = 1. </
s
>
<
s
xml:id
="
echoid-s5494
"
xml:space
="
preserve
">Sit jam arcus
<
lb
/>
ſpiralis l 1 o aqua plenus = c & </
s
>
<
s
xml:id
="
echoid-s5495
"
xml:space
="
preserve
">conſequenter arcus circularis eidem reſpon-
<
lb
/>
dens c M p = M c; </
s
>
<
s
xml:id
="
echoid-s5496
"
xml:space
="
preserve
">a l = e; </
s
>
<
s
xml:id
="
echoid-s5497
"
xml:space
="
preserve
">a c = M e; </
s
>
<
s
xml:id
="
echoid-s5498
"
xml:space
="
preserve
">a d (ſeu ſinus verſus arcus ac) = f; </
s
>
<
s
xml:id
="
echoid-s5499
"
xml:space
="
preserve
">
<
lb
/>
a q = g; </
s
>
<
s
xml:id
="
echoid-s5500
"
xml:space
="
preserve
">pondus aquæ in l s o = p: </
s
>
<
s
xml:id
="
echoid-s5501
"
xml:space
="
preserve
">arcus a l n = x; </
s
>
<
s
xml:id
="
echoid-s5502
"
xml:space
="
preserve
">n m = d x; </
s
>
<
s
xml:id
="
echoid-s5503
"
xml:space
="
preserve
">a c f = M x; </
s
>
<
s
xml:id
="
echoid-s5504
"
xml:space
="
preserve
">
<
lb
/>
f g = M d x; </
s
>
<
s
xml:id
="
echoid-s5505
"
xml:space
="
preserve
">a b = y; </
s
>
<
s
xml:id
="
echoid-s5506
"
xml:space
="
preserve
">h i = d y; </
s
>
<
s
xml:id
="
echoid-s5507
"
xml:space
="
preserve
">h f = √2y - yy, erit pondus guttulæ in
<
lb
/>
nm = {p d x/c}; </
s
>
<
s
xml:id
="
echoid-s5508
"
xml:space
="
preserve
">ſi vero linea h f multiplicetur per ſinum anguli a M H, divida-
<
lb
/>
turque per ſinum totum, habetur vectis quo particula n m cochleam circum-
<
lb
/>
agere tentat: </
s
>
<
s
xml:id
="
echoid-s5509
"
xml:space
="
preserve
">eſtigitur vectis iſte = n √ (2y - yy) qui multiplicatus per præ-
<
lb
/>
fatum guttulæ pondus {p d x/c} dat ejusdem momentum {n p d x/c} √ (2y - y y)}. </
s
>
<
s
xml:id
="
echoid-s5510
"
xml:space
="
preserve
">
<
lb
/>
Sed ex natura circuli eſt M d x = {dy√ (2y - yy): </
s
>
<
s
xml:id
="
echoid-s5511
"
xml:space
="
preserve
">hoc igitur valore ſubſtituto
<
lb
/>
pro d x, fit idem guttulæ n m momentum = {n p d y/M c}, cujus integralis, ſub-
<
lb
/>
tracta debita conſtante, eſt {n p (y - f)/Mc}, denotatque momentum aquæ in ar-
<
lb
/>
cu l n; </
s
>
<
s
xml:id
="
echoid-s5512
"
xml:space
="
preserve
">hinc igitur momentum omnis aquæ in l 1 o eſt = {n p (g - f)/Mc}: </
s
>
<
s
xml:id
="
echoid-s5513
"
xml:space
="
preserve
">quod
<
lb
/>
diviſum per vectem potentiæ in f applicatæ ſeu per 1 relinquit potentiam
<
lb
/>
iſtam quæſitam pariter = {n p (g - f)/Mc}. </
s
>
<
s
xml:id
="
echoid-s5514
"
xml:space
="
preserve
">Q. </
s
>
<
s
xml:id
="
echoid-s5515
"
xml:space
="
preserve
">E. </
s
>
<
s
xml:id
="
echoid-s5516
"
xml:space
="
preserve
">I.</
s
>
<
s
xml:id
="
echoid-s5517
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>
