QUADRATURE of the CONIC SECTIONS, &c. 331 



61. That we may inveftigate a fecond feries, we muft take 

 the fquare of the formula, (Art. 58.), which will be 



f *' + iV - (x+i)' , 1 f x - 1 y , 1 



From this exprefiion, proceeding exactly as in Art. 58. we form 

 the following feries of equations, 



+ i) 2 (*t + 1) 



(# — i) 2 4 (V 



+ \ ( ~ ) + "' 



(* T +iy (*« + i) a 



(x T — i) 2 4*0* — i) 2 ^ V X 4 + I / 2.4. 



= . j- I f \ _j_ j_ y 



i. 2 (^ — i) 2 43 (*$-!» 1) 9 4 3 \* + I / 2.4? 



4 (* + 0* O 4- 1) 



2 

 2 /■ '" 



I / X I \ 2 1 



+ ? VI — v + 2 -4" _I 



2 /■ '" _\2 2 /■ '" \2 f/l , 



tfZ (X 1) W2 (X i) X -J- I 



Here « denotes the number of equations, and m is put for 2*. 

 Let the fum of the correfponding fides of thefe equations be ta- 

 ken, and the quantities common to each rejected, as ufual, and 

 Vol. VI.— P. II. Tie the 



