[ 219 ] 



V 



Whence a ~ the arc, the cofine of which is — X i — ^' and rad. 



I — e' 



unity = the arc, the cofine of which is — — . This fluent 



e X 



requires no corredion, becaufe when a = 0, — X i ^^ _ i; And 



, which is the well 



I I — e^ I — e 



becaufe cs, a = — — > v *= 



e e X \, I — e cs, a 



known equation; of the ellipfe, in which x is the diftance from 



the focus and a the true anomaly Q^E I. 



For the fubfequent propofitions it is neceffary to folve the 

 following problem : 



Problem. Let the greateft diflance S A from 

 the focus S of the ellipfe A P B = i -j- e, the leaft 

 diftance 8 6= I — e, any other diftance SP=: i -fj, 

 and the angle ASP = ^, it is required to ex- 

 prefs, the different integral powers of jf by a feries 

 of cofines of multiple arcs and powers of the ex- 

 centricity. 



Solution. The equation of the ellipfe gives. 



cs, a — e 



I — e 



t cs, a 



•.■y — eX 



or 



