[ 222 ] 



diftance i-fcr and any diftance x. In this cllipfe (fee the pre- 

 ceding prop.) a —- 



X 2 X X 



I— f' 





r 

 ■'■ ■''■■ ^ +"2^' x'— x^— I— g' - (P) ' • Vj„^ hecaufe two 



\ : I— ^X- 



2X— X— I— e' (Q)' 



roots of the equation P = 0, viz. i +e and i— <r are the roots of 

 the equation Q,= 0, it follows that O^ muft be a divifor of P; 



p 



accordingly we find __=:;(. ^ i ,' — f'= 2 -j^j^ ' —e\ putting i+y^x 





'7 'i — 4f+rfM 



Hence A = a 



-4 f+rf ' 



r: J , 3^V 



4. i — -^^ 4- &c. re- 



2B 



carding only the 2d power of the eccentricity, which is fufii- 

 cient for the purpofe for which the propofition was defigncd. 

 Next fubftituttng for j-, y\ &c. the values found in the preceding 

 problem, and taking the fluent, we have 



C €"■ % 



— c e s^a i- c c^ s, 1 a 



A = 4 '. X I ■ + 



u I — ^c-\-ce^ I, — 4£'4.cf* 



^_tf» c» 4^ ^f* c^ s, 2a 



4 4 , &c.. 



1 — 4 c-^ce^ Y 



where 



