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

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210196HYDRODYNAMICÆ ad √ 3; Si vero vena fluidi eadem atque tota excipiatur ab ala, modo ſic mo-
do aliter ad directionem fluidi inclinatâ, maximam preſſionem ſuſtinebit in
directione rotationis ala, quæ facit angulum ſemirectum cum directione fluidi.

Prima Regula pertinet ad machinas quæ à vento omnia ambiente cir-
cumaguntur: altera ad illas, quæ à vena ſolitaria & à certa determinataque flui-
di quantitate moventur. Utraque vero hypotheſi innititur, quod motus ala-
rum admodum parvus ſit reſpectu motus fluidi, ſi enim ad motum alarum re-
ſpicias, ambæ regulæ falſæ ſunt; neque profecto iſte motus negligendus eſt, in
moletrinis enim ſæpe obſervavi, extremitates alarum velocitate ferri, ipſam
fere venti velocitatem exæquante.

Hæc cum ita ſint, calculum nunc ita ponemus, ut utriuſque motus
rationem habeamus.

§. 39. Sit igitur fluidum D E B A (Fig. 55.) quod ſub directione E B
11Fig. 55. impingit in totum planum A B: moveri autem ponitur planum motu paral-
lelo in directione B b ad E B perpendiculari: Sint porro velocitates ejusmo-
di, ut dum particula fluidi percurrit lineam E B, punctum plani B abſol-
vat lineam B b. His poſitis fingere licet totum ſyſtema, fluidum nempe
cum plano moveri à b verſus B & quidem velocitate b B: Ita vero fiet, ut
planum A B quieſcat, particula autem fluidi in punctum B incidens cenſen-
da ſit veniſſe expuncto e, ſumta E e = B b, & ſic de omnibus guttulis.
Igitur loco fluidi D E B A in planum motum A B incidentis velocitate E B
concipiendum erit fluidum d e B A in idem planum A B ſed immotum inci-
dens velocitate e B: Producatur jam A B usque in b agaturque D E d e b per-
pendicularis ad E B, erit motus particulæ fluidi repræſentatus per e B reſol-
vendus in e g & g B, ſibi invicem perpendiculariter inſiſtentes, quorum po-
ſterior nihil in planum A B agit, alter vero e g rurſus ex duobus compoſi-
tus eſt motibus e f & f g, quorum poſterior f g planum A B inutiliter in di-
rectione E B propellere tentat; dum prior e f ſolus idem planum in dire-
ctione B b propellit. Demonſtratum itaque eſt, quamlibet particulam face-
re impulſum proportionalem lineæ e f: Dein patet quoque, ſi linea A B
repræſentet totum planum, fore numerum particularum dato tempore in
planum impingentium repræſentandum per lineam B N perpendicularem ad
A d ſeu B e. Unde tandem niſus aquarum ad movendum planum in dire-
ctione B b eſt proportionalis lineæ e f ductæ in B N.

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Scan	Original
101	87
102	88
103	89
104
105	91
106	92
107	93
108	94
109	95
110	96
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

Scan	Original
101	87
102	88
103	89
104
105	91
106	92
107	93
108	94
109	95
110	96
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

Scan	Original
101	87
102	88
103	89
104
105	91
106	92
107	93
108	94
109	95
110	96
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