ALGEBRAIC FORMULA. 



257 



,andofcof(/>+i)<p-fcof(/> — i)<p 



and fubftitution of A for - 



for 2 cof <p cof p<p> we get the following equation, 



A A' -f AB'"] 

 --2 A' 



-f-AC 

 — B' 



+ AD' 



— C 



-n/ q/ j»Cof£> jy ^COf2<£> ry J> Cof 3<£>, &C. = O 



A B 



ab ~ ab J 



ab J 



ab. -> 



Hence it follows, that, 



B' = AA' — 4 



C = AB' 



ab 



E' = AD'— C —5- 

 &c. &c. 



It yet remains to determine A', the firft coefficient ; but that, 

 as well as B', may be readily found by confidering that we have 

 already found (Art 4.) 



C = -£-B+-2f-A 



therefore, 'fubftituting n — 1 for #,. and C for C, for the very 

 fame reafon we get 



C'=4-B' + -^A'. 

 »+ 1 ' » •+ 1 



. By comparing together this value of C, and the values of B' 

 and C as given in the laft feries of equations, and fubftituting, 



for A its value ab , we get, 



A '--£-til A 4- Q+'> 3 B 



» — (V— 3 1 )* ^~ »(«* — * 2 )* 



6* It 



