76

I. A

II

III

Libe. I. Sect. II.

■ sin co cos u + cos co sin u cos isin a sin u + cos co cos u cos i

■ cos co sm u sm i

'(4f)=- sir

&_ / d i \

• r \d«/

A^ /_d l \ _

• r V dr A '

IV. (j = 1 + -g- COS {L — & — co) = 1 +^-cos(Z,—/)

/db\ , . . . . , . . .. ,

. A f J = — cos co cos u sin b — sin co sin u cos i sm b + sm u sm i cos b

_ T A /d b\ . . , ...

I. — 1 \ = cos (o sin u sin b — sin a cos u cos i sm b -f cos u sm ? cos b

, r A /d b\ . . , .

VII. -p- i -jj- J — sm co sm u sin i sm b -f- sm u cos i cos b

V.

VI

VIII.

A_

R

(1L)

\d&J

: sin b sin ( Z >—Q — co) — sin b sin {JL — T)

Formulae IV et VIII liic iam In forma ad calculum commodissima apparent; for-mulae I, III, V autem per substitutiones obuias ad formam concinniorem redigun-tur, puta

I*

HI*

(*■)= ,T' ! '

■m-

cos co tang bR

R

V * ("dr) = —"72T cos ( L ~ l ) sin5 = —7^- cos (£ — /) tang/

Denique formulae reliquae quoque II, VI, VII per introductionem quorundam an-gulorum auxiliarium in formam simpliciorem abeunt: quod commodissime fit se-

. tang co

quenti modo. Determinentur anguli auxiliares M, N per formulas tang./!/ =-

cos l

tang N — sin co tang i = tang M cos co sin i. Tunc simul fitcos i 2 -}- sin co 2 sin i

cos M 2cos JV 2

i 2

i -f tang A ?i -f tang M z

cos i 2 -ftang co z — = cos : ^ am fi uum ambiguitatem in determinatione ipso-

rum M i N per tangentes suas remanentem ad lubitum decidere liceat, hoc ita

e • x . , , cos M sin IV , . .

heri pos e patet, vt habeatur - -r-— — -j- cos co , ac proin—:—— = 4- sm i. Qui-

COS iV j r gjjj jyi

bus ita factis, formulae II, VI, VII transeunt in sequentes: