QUADRATURE of the CONIC SECTIONS, &c. 30? 

 known formulae 



r I 



2 ab - = (ab s -f- ord j)" + (ab j — ord *)*, 



2 ord- 3 (ab j -f- ord *)* — (ab j — ord s)", 



n 



by proceeding as follows. Let each fide of the latter of thefe 

 equations be divided by the correfponding fide of the former, 

 the refult is 



d s l i 



n __ (ab s -f- ord x) — (ab s — ord s) , 



n (ab s -f- ord s)" + (ab s — ord s) 

 which expreflion is equivalent to this other one, 



, s /ab s 4- ord s\" 



ord - (— - 1 t-/ — - 1 



n v abj — ord s' , 



"TT- i 



aD « / ab j + ordj\ w 



*ab j — ord j' ~*~ 



Let us now put p for the fraction a s -r ord J then, re- 



abj — ord j 



ord- 



n s 



marking that = tan -, we have 



ab- n 



n 



J* 

 s p — 1 

 tan - = c. > 



n i 



P + 1 

 Vo.VI.~P.II. Qjj aa 



