MATHEMATICAL SECTION. 97 
hence the values of cos XY, cos YZ, cos ZX furnish the equations 
cos (F' — G) = — cotg f cotg g 
cos (G — H) = — cotg g cotgh (6) 
cos (H — F') = — cotg A cotg f 
Again the triangle X7'Y gives 
cos f = sin g cos TYX, 
and from the triangle 7YX 
sin hsin YTZ= sin TYZ, 
but TYX — TYZ= 90°, 
and YTZ= — (G— B), 
hence these equations and similar ones give 
cos h 
sin f sing 
sin (F — G) = 
cos f 
ain (GH) =" ain gain he (7) 
COs g 
sin A sin f 
sin (H — F)= 
By combining equations (6) and (7), we have 
cotang (fF — G) = — a 
cotang (G — H) = — angen’ 
__ 608 h cos f 
COS J 
cos f? = cotg (F' — G@) cotg (H — F) 
cos g’ = cotg (G— H) cotg (F — @) 
cos h? = cotg (H— F) cote (G — H) 
cotang (H — F’) = 
: cos (G@ — H) 
anf == in (F— Gein (= F+) 
, cos (H — F’) 
ang = an yan (PS G) 
. cos (F — G) 
SMI — = se He Pa GSD) 
