416 



The pair of circles (66) correspond to the circles A, A' of Art. 14; 

 and the circles corresponding to the pairs of circles B, B', C, C, D, D' } 

 of the same Article are 



U= j X sin r cos (B - C) + fi sin/ cos (C+A) 



+ vsinr"cos(A + B}\ (67) 



U= { X sin r cos (B + C) + fi sin r f cos C - A 



+ v smr'' cos(A + B} 2 , (68) 



TJ = j \ sin r cos (B + C) + p sin / cos ( C + A) 



+ vsinr"cos (^L-£)} 2 . (69) 



36. It can be seen precisely in the same way as in the analogous 

 case on the plane (Art. 6), that the points of contact of three circles, 

 S, S 1 , S", on the sphere with their four pairs of tangential circles ar 

 given by constructing the circles, 



IS 



cos r 



IS 



cos r 



VS i 

 cos r 



I'S 

 cos r 



Also, that if A, A', A", denote the radical circles of S, S', S", taken 

 in pairs, then the equations of the great circles passing through the 

 points of contact on S } S', S", are for the four pairs of tangential 

 circles 



A cos r A' cos r' 

 I m 



A cos r A' cos r 

 I m' 



A cos r A' cos r' 



V m 



A cos r A' cos r' 



V = m'~ 



mS' 

 cos r 



m'S' 

 cos r 



mS' 

 cos r' 



m'S' 

 cos r' 



nS" 

 cos r ,f1 



n'S" [ 

 cos r" 1 



n'S" m 

 cos r" ' 



nS" 



COS 1 



(70 

 (71) 

 (72) 

 (73) 



A" cos r' f 

 n 



A" cos v" 



n' : 



A" cos r ' 



A' cos r" 

 n 



(74) 

 (75) 

 (76) 

 (77) 



