( 721 ) 
sin A, BC, cot AC B + cos A. BC 
cot A,B = — noche Si ait od eek : 
sin BC, 
COS BC, 
sin (90 —0) cot a, + cos (90 — 5) cos (9 —90) 
sin (o—90) 
— cot h, = 
or 
cot h, cos 9 = cos Goot a, + sinosing. … … . . (I) 
Now is ~ C\Cy=vy a constant that can be calculated with the 
help of the given angles «u, and 8 from AC,C,D and that is 
measured from C, positively in a direction opposite to the hands of 
a clock. In ABA,C, is then: 
sin A, BC, cot A,C,B + cos A, BC, cos BC, 
cot a —— 
: sin BC, 
sin (90 —9) cot a, + cos (90 — 5) cos (g—90 —y) 
— cot h, = — ne enn ee 
sin (0— 90 —y) 
cos O cot dt, + sin 6 sin (0—y) 
— coth, = 
2408 (0) 
sot h, (cos 9 cos y + sin Q sin y) = cos 6 cot a, + sin G sin (0 —y) 
cot h, cos Q cos y = cos 6 cot a, J- sin O sin (9—y) —coth, sinasiny . . (2) 
If one divides (2) by (1), then becomes 
cot h, cos y (cos 6 cot a, + sin 6 sin 0) = 
= cot h, {cos 5 cot a, + sin 6 sin (vy —y) — cot h, sin g sin yh 
cos G (cot a, cot h, cos y — cot a, cot h,) + sin 6 {sin @ (cot h,—cot h,) cos y + 
+ cot h, cos 9 sin yj -+ cot h, vot h, sin 9 sin w= |, 
If one supposes 
cot a, cot h, cos Y — cot a, cot h, Sasi 
(cot h, — cot h,) (os ¥ = 6 
cot hy sin y= t | 
cot h, cot h, nd . 
then the formula changes into 
acos 6 + sin a (b sing + ¢cos 9) 4+ d sin =0 
b sin QO + ¢ COSO , d 
cos G6 = — — —— sin 6 — — sing 
a a 
REDEN 
If one substitutes this value of cos 5 in (1), one obtains: 
— 
«cot h, cos gp = — cot a, \(b sin 9 + ec cos 0) sino + d sin of + a sin 6 sin C= 
= sin Of— (b sin + © cos 9) cot a, + a sin 0} — d cot a, sin 0 
from which follows: 
47* 
