JMifcellanea Curio fa. a 55 



notes only the place of the point R, with 



refpeft to F, to be oppofite to the place of 



the point F, with refped to B, when the 



Curve AFQ. is concave towards the Axis 



' ■ • 



AB.) And Ff (by Prop. II.) = . 



-XX 



Wherefore (by the foregoing Lemma) FR = 



(F f % a-\-'X xx 2 iax-\- xx x V lax -\~ xx 

 y iax~\-xx a—\-x x ax % 



— ) *+* * V \ax-\ z xx t Again, becaufe of 

 a 



the Redangular Triangles Fsf, FRU, ha- 

 ving the Angles fFs, UFR, equal to one 

 another (becaufe UFs is the Complement of 

 either to a right Angle) we have F s : s f : : 



ax a-\ x x V 2ax-\-xx 



F R : UR, or x : - — : : ~- ; 



/- ■ " a 



V 2ax-\-xx 



UR, which therefore is ab a*-\-x. Therefore 

 the Nature of the Curve KU is fuch, that if 



a-\-x x V 2ax-\-xx 



AB = x^ FR lhall == ■ : , and 



a 



UR = a\x. d: E : I. 



COROL 



