JProsthaphaeresis in hyperbolic trigonometry. 
We have cosh a A ß B = cosh A cosh B -f- sinh A sinh B cos aß; 
and Sinh a A ß B = / cosh A sinh B • /5 + cosh B sinh A * a 
+]/—1 sinh A sinh B sin aß • aß | 
By putting in — sinh B instead of sinh B we get 
^ ß 
cosh aß == cosh A cosh B — sinh A sinh B cos aß; 
Sinh a A ß~ B — — cosh A sinh B * ß + cosh B sinh A • a 
Therefore cosh a A ß B -(- cosh a A ß B 
—]/—1 sinh A sinh B sin aß • aß. 
2 cosh A cosh B ; 
cosh a A ß B — cosh a A ß B — 2 sinh A sinh B cos aß;