172158HYDRODYNAMICÆ
(B) ααy + (β√x + γ√y)2 = αα X (a + b).
Subtractâ æquatione (B) ab æquatione (A) prodity = x + b, ex quo
ſequitur, ſi venæ ambæ verticaliter ſurſum dirigantur, utramque ad eundem lo-
cum aſſilire. Deinde ſi in æquatione (A) ſubſtituatur pro y valor ejus x + b,
erit
(C) ααx + (β√x + γ√x + b)2 = ααa,
unde deducitur valor ipſius x æquatione quadrata.
ſequitur, ſi venæ ambæ verticaliter ſurſum dirigantur, utramque ad eundem lo-
cum aſſilire. Deinde ſi in æquatione (A) ſubſtituatur pro y valor ejus x + b,
erit
(C) ααx + (β√x + γ√x + b)2 = ααa,
unde deducitur valor ipſius x æquatione quadrata.
§.
27.
Ex præcedentis paragraphi æquationibus ſequentes fluunt affe-
ctiones.
ctiones.
I.
Quia velocitas aquæ per M transfluentis eſt = {β√x + γ√y/α}, eritalti-
tudo generans hanc velocitatem = ({β√x + γ√y/α})2; ſed ſi addantur æqua-
tiones (A) & (B) fit:
({β√x + γ√y/α})2 = {2a + b - x - y/2} = ob(y = x + b)a - x.
tudo generans hanc velocitatem = ({β√x + γ√y/α})2; ſed ſi addantur æqua-
tiones (A) & (B) fit:
({β√x + γ√y/α})2 = {2a + b - x - y/2} = ob(y = x + b)a - x.
II.
Si foramen H ſit valde exiguum ratione foraminum M &
N, id eſt, ſi
β poſſit cenſeri nulla ratione α & γ, abit æquatio (C) in hanc
ααx + γγx + γγb = ααa, ſeu
x = {ααa - γγb/αα + γγ};
β poſſit cenſeri nulla ratione α & γ, abit æquatio (C) in hanc
ααx + γγx + γγb = ααa, ſeu
x = {ααa - γγb/αα + γγ};
Id vero egregie convenit cum paragrapho decimo nono, cum manife-
ſtum ſit aquam per foramen valde exiguum ad eandem altitudinem aſſilire,
quam haberet aqua, ſi hæc laminam L Q tantum deorſum premat, quantum
ab aqua interna ſurſum premitur; Iſta vero præfata altitudo vi paragraphi 19.
eſt {ααa - γγb/αα + γγ}; Eſt porro in iſta hypotheſi altitudo velocitatis aquarum in N
ſeu x + b = {ααa + ααb/αα + γγ}
& denique altitudo velocitatis aquarum in M, ſeu
a - x = {γγa + γγb/αα + γγ};
quæ poſteriores æquationes in iſto caſu particulari pariter ex §. 19. immediate
colligi aut prævideri potuiſſent.
ſtum ſit aquam per foramen valde exiguum ad eandem altitudinem aſſilire,
quam haberet aqua, ſi hæc laminam L Q tantum deorſum premat, quantum
ab aqua interna ſurſum premitur; Iſta vero præfata altitudo vi paragraphi 19.
eſt {ααa - γγb/αα + γγ}; Eſt porro in iſta hypotheſi altitudo velocitatis aquarum in N
ſeu x + b = {ααa + ααb/αα + γγ}
& denique altitudo velocitatis aquarum in M, ſeu
a - x = {γγa + γγb/αα + γγ};
quæ poſteriores æquationes in iſto caſu particulari pariter ex §. 19. immediate
colligi aut prævideri potuiſſent.
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