RELATIONES INTER LOCOS PLVRES IN ORBITA.

85

fieri posse ad normam lemmatis III in art. praec. Habemus itaque

Si angulus 77 datus est, p et e determinabuntur per aequationes

D en omi n at orem communem in his formulis reducere licet sub formam a cos (yi—77,

adeoque = acos(^7~ 77), si a et A determinantur per aequationesr cos ( A — 77) — / cos (A' — JI)=acos(A — 77)r sin ( N—H)~r sin(A'-//)=« sin (A— II)

Hoc modo llt

_ 2 it' sin -I (N' — A T ) sin ( A r + IN' — II)

1 a cos (A — II)

Hae formulae imprimis sunt commodae, quoties p et e pro pluribus valoribus ipsiusn computandae sunt, manentibus r, r, N, A — Quum ad calculum quantita~tum auxiliarium a, A angulum II ad libitum assumere liceat, e re erit statuere

tang(A—77) = co!ang(A'—A) —

r) sin ( N'

N+iN

(/— r)cotang£ (7? — A)2 rr

8o.

rr (cos( N — II) — cos( N' —77))

rcos(A r 77) — /cos (A 1 ' — 77)

f

r — r

r cos (N — 77) — r cos (A' — II)

ita vt a et A a 77 sint independentes. Designante scilicet 77 angulum arbitrarium,

fit

j (reos (A—77)

(A'—77)) cos (77—77)

r cos (A — 77) — / cos (A' — 77)

{—(r sin (A—77)

(A—77)) sin(77—77)

r — r

a cos ( A —77)

77= |(A 7 +A / ), quo pacto formulae abeunt in has

(/— r) cos i (N' — A ) = — a cos ( A — \ N — \ A ’’)(/ -f r) sin § (A'— A) = — a sin {A—\ N — i- A')

Determinato itaque angulo A per aequationem tang (A —\ A—j- N ')

tang^(A'—A), statim habetur e

cos i- (A'—A~) cos (A — 77)