Z22 A NEW and UNIVERSAL SOLUTION 



Suppofe cof 4* =r '£ V^f a : ^ n > finCe l ~~ cof * = 2 fin » | 



r A 

 A i— cofA fin2 7 A 



we have 2 fin 2 - — ; ^—- zz 1 — tan * - therefore 



2 1-f-cofA ,A 2 , mererore 



cof - 



2 



fin - - tan <- x -^ - tan - x fin 45 ° : We fhall alfo have 



, fin » * - '—cof A _ (1 — cof A)' _ (1 — cof A)' 



2 fm 2 ~ i + cofA - 1 -cof A ~ fin » A ; whence 



fin ^ — —r — : — x -= • Subftitute now, for cof -J/, its value 

 2 fin A \/2 



2 cof A , _ r -0/ , 1— cof A 1 



1 + cof A ' and f0r fm 2' ltS ValUC fm A X 75 ; and W€ 

 fhall eafily obtain, 



e v/2 x fin <p x cof A = cof ^ ~ m - x fin A, 



. finA t A fin <2> _ 



whence —~-r = tan A — * x • £ — X v/2. 



cof A cof ^~ w 



2 



Hence we have another general rule for computing 4, when <z> 

 is given, which is this : Take tan A z= e x ft X fee 4c ' 



cof^i? 



2 



4- A 



then fin - rz tan -• X 45 °. 

 2 2 



Taking w* rr 90 °, and <p r= 90 °, this rule coincides with 

 that already given in Art. 1 o. : And it may be of ufe, not only 

 when m is exactly a right angle, but alfo when it is very nearly 

 fo. 



The detail with which we have difcuffed the rules and for- 

 mulas of computation that have been deduced from the analyfis, 

 leaves no difficulty in applying them to practice. Thefe rules 



are 



