QUADRATURE of the CONIC SECTIONS, &c. 285 

 be put under this form 



I = sb + T « + T "> + T ^ + T «> +• &c - 



II T T 



where T(i) Is put for - tan - a, and T( 2 ) for - tan - a, and T( 3 ) 

 for - tan-- a, &c, then, as the formula given at the conclufion 



<J o 



of the laft article, becomes by fubftituting tan* I a for *""" J a . 



4 i-fcoffa 



and tan* \a for ^^j 4 , and fo on, 

 8 1 -{- col ~ a 



f 1 1 + cof a , 1 



T I 4 1 — cof a 6 



it may be otherwife exprefled thus, 



1 1 -j- cof a , 1 

 £_ _ J 41 — cof # 6 



*' { - (T 2 ( 2 ) + T'( 3 ) + T\ 4 ) + T-o) +, &c), 



where it is to be obferved, that the fymbols T( 2 ), T( 3 >, T( 4 ), 

 denote the very fame quantities in both feries. 

 Now, as we have found (Art. 8, and 9.), that each term of 



the feries of quantities T( 2 > T( 3 ), T( 4 ), &c. is lefs than - of the 



4 



term immediately before, but greater than a third proportional 

 to the two terms immediately before it, taken in their order, it 



Nn 2 is 



