Bernoulli, Daniel - Hydrodynamica, sive De viribus et motibus fluidorum commentarii

Scan	Original
111	97
112	98
113	99
114	100
115	101
116	102
117	103
118	104
119	105
120	106
121	107
122	108
123	109
124	110
125	111
126	112
127	113
128	114
129	115
130	116
131	117
132	118
133	119
134	120
135	121
136	122
137	123
138
139	125
140	126

11298HYDRODYNAMICÆ ctum in motum aquarum exerere debeat, quiſque videt ex eo, quod in utro-
que modo omnis aquæ tubum ingredientis inertia ſit ab aqua inferiore ſupe-
randa. Sed idem etiam à priori demonſtrari poterit inquirendo in motum, qui
inde oriri debeat, ſecundum æquationem paragraphi octavi Sect. III. quæ hæc eſt:
Ndv - {mmvydx/nn} + {mmvdx/y} = - yxdx;
accommodabitur autem ad præſentem caſum, ſi pro m, x & - d x ſubſtituas re-
ſpective n, a, & {ndx/y}, (cujus rei ratio patebit, ſi hæc cum illis contuleris) ſi-
mulque y infinitum ponas; tunc enim evaneſcit tertius æquationis terminus,
fitque omnino, ut pro præſenti negotio ſupra invenimus,
Ndv + nvdx = nadx.

Poſtquam in his ſcholiis motus utriuſque indolem, quantum ſimplexrei
conſideratio phyſica permittit, eorumque differentiam oſtendimus, ſimulque
modum illos producendi ad legem hypotheſeos mechanicum tradidimus, ſu-
pereſt, ut reliqua phænomena notabiliora etiam indicentur, quod nunc faciam.

Corollarium 1.

§. 8. Si in vaſe R S N H omnè fundum abſit, erit orificium L M =
orificio R S; poteſt etiam hoc ab illo ſuperari, ſi nempe vaſis divergant late-
ra. In his autem caſibus nullum habet terminum altitudo v in æquatione
v = {mma/mm - nn} X (1 - c{n3 - nmm/mmN} x)
& fit infinita, ſi quantitas aquæ ejectæ indicata per n x eſt infinita.

Id quidem per ſe patet ex æquatione, cum n eſt major quam m; at
cum amplitudines orificiorum ſunt æquales, recurrendum eſt ad æquationem
differentialem paragraphi tertii, ex qua iſta æquatio proxima deducta fuit, nempe
{N/M}dv - {n3/mmM}vdx + {n/M}vdx = {n/M}adx,
quæ poſito n = m dat N d v = n a d x, id eſt, v = {nax/N}, ubi v fit manifeſte in-
finita ſi x eſt infinita.

§. 9. Sin autem vaſi propoſito fundum ſit, atque in eo foramen,

Page concordance

Text layer

Text normalization

Search

Scan	Original
111	97
112	98
113	99
114	100
115	101
116	102
117	103
118	104
119	105
120	106
121	107
122	108
123	109
124	110
125	111
126	112
127	113
128	114
129	115
130	116
131	117
132	118
133	119
134	120
135	121
136	122
137	123
138
139	125
140	126

Scan	Original
111	97
112	98
113	99
114	100
115	101
116	102
117	103
118	104
119	105
120	106
121	107
122	108
123	109
124	110
125	111
126	112
127	113
128	114
129	115
130	116
131	117
132	118
133	119
134	120
135	121
136	122
137	123
138
139	125
140	126

Scan	Original
111	97
112	98
113	99
114	100
115	101
116	102
117	103
118	104
119	105
120	106
121	107
122	108
123	109
124	110
125	111
126	112
127	113
128	114
129	115
130	116
131	117
132	118
133	119
134	120
135	121
136	122
137	123
138
139	125
140	126