ISS ANALYTICAL FORMUf-iE. 



Analytical Bv multiplying this last equation by 2, and subtracting 



formula for i— — i ° 



the targcut, |_L| from it, we obtain 



cetangent 



Ac 



1 



J cot. 

 1 



•n 



1 

 ' 2^-a 



-/« + 



+ 3- 



tan. 



1 

 2a 



1 



a 





1 



+ 



1 

 2a 



&c. 





TT 





4' 



— *a 



2 



TT 



a/c 





2v/a 



X 





«in. 9 



W' 



c 



|3| 



(A \* 

 —J write a ; and, transposing — - , 



multiply by y^; and for A write its value w -/ a 

 we get 



^ I 7 11 



(l»_a} (2^-0)^ (3*-. a) |4'-^a) + (fi-^^.^) (62_^ 



tical with the value of \—r\ 



\±\ 



lira- d:-a^dra-zira^ ^'' ^'^""'^ ^^^°^^- 



Should you think. these trifles worthy of insertion in 

 your excellent publication, they are entirely at your dis- 

 posal; andatsonae future time it is not impossible, fbat 

 1 may again intrude myself on the notice of your readers 

 through the same medium. 



I remain. Sir, 

 Your most obedient humble servant, 



A LovE» er the modern Analysis. 



IX. 



