126 Mr WALLACE, ON GEOMETRICAL THEOREMS, AND FORMULA, 



Hence, by compounding these equal ratios, 



A 

 sinca; 



A 

 c' sin /3 _ sin ex _ h sin 7 _ sin E sin 7 



'■'■-=" ~ ' . J^ ~ c' sin /3 ~ sin C sin /3 ' 

 sin ox 



. f^ ' b' ' sin 7 

 sm ox 



Fig. 5. No. 1. 



Fig. 5. No. 2. 



Thus, to determine the angles ex, bx, we have their sum and the ratio 

 of their sines. 



Again, by Trigonometry and Formulae IV, 



sin ay _^ _i c _ ^ sin C 



A ~ y ~ c ' b' ~ e sm B' 

 sm a% 



A A 

 , also ay+a% = ir — a; 



A A 



hence, as before, the sum of the angles ay, az is given; also, the ratio 

 of their sines, to determine the angles. 



A a; . -, ■ 1^ X . ^ 



Lastly, smce sm ey = - sm 7, and sm Ois = ^ sm /i ; 



A A A 



^ sin cy 5 sin 7 , ,1. ,i a< 



therefore a ="-~\rA' also cy + 6s! = a-^ = ^. 



sm b% 

 By these cy and &» may be found. 



26. The results which have been obtained may be applied to the 

 pairs of like angles and tabulated for use as follows : 



