( 722 ) 
| a cot h, cos 9 + d cot a, sin 9 
sin 6 = 
f, 
(a—b cot a@,) sin @ — ccot a, sing 
When worked out this formula furnishes : 
a cos Q + cot a, cot h, sin y sin nQ 
sin 6 = — = : 
cot a, sin 7 cos @ - (cot a, — cot a, cos ¥) cos Q 
If one supposes herein again 
cot a, coth, sin y =e | 
GOLDEN IJ PE en ee a 
cot a, siny =9 | 
then becomes 
acos @ + esino 
sin 6 = — — ete Sanita) ec) ee 
g cos @ + jf sin Q 
We found above 
b sino + ec CCOSO , en 
cos 6 == — ———— — sin 6 — — sino 
a a 
bsing + ccos @\ (4 cos Q + esin Q d's 
COSO a En SS ee — — $n OQ = 
a J COS Q zin f sin QO a 
_ (bs sin O Perle c cos Q) (ac Cos Q zE | e sin 9) — d (7 cos @ + f sin Q) sin Q 
a (g cos O 0 + f sin Q) 
sun’ o (eb — fd) + sin Q cos y (ab + ec — gd) 4+ ac cos” @ 
a(g cos 9 + f sin Q) 
a2 h sin® 9 + b sin 9 cos 9 + ¢ cos* @ 
g cos 9 + f sin 0 
which 
f= Oth, SUEY 4 ate eS Os ee 
The variables g and 5 are consequently separated; the ratio 
sin? 6 + cos° 6 = 1 
furnishes 
(a cosy + esin)" + (hsin® 9 + b sin Q cos Q + c¢cos* 0) = (9 cos 9 + f sing)’ 
? 9 (a?—q") + 2 sin 9 cos 0 (ae—fg) + sin? 0 (2° —f*) + 
| + (h sin® 9 4- b sin @ cos vy + eeos* 0) = 0. 
If one introduces : 
; 1 + cos 29° ent in le LOS EON es Se Ree 
Bs OS =a yt en ar aie sin Q COS 9 = sin 20, 
the latter ratio changes into: 
cos° 20 (ce —h)’ bile B cos dal dd Ten 
Hb + 4+ oS Ae g — fy 
+ 2 sin 20 {2(ae—fg) + b(h He) Hb (c—h) cos Ay} = 0 
