MtfceUaneci Curio fa. ill 



is lefs than the lean: of the 3, or than the 

 one as often as there is but one. Now it 

 remains for us to inquire of what kind thi§ 

 Space is, by what Limits 'tis di fling mined, 

 and under what Conditions the Radius, of 

 the Circle is lefs or greater than the fore- 

 mentionM Perpendiculars. And firfl of all, 

 we muft mew how a Perpendicular is to be 

 let fall upon the Parabola. Let (Fig. 3.) 

 ABC be a Parabola, AE its Axis, AV i 

 the Parameter, G the point from whence 

 the Perpendicular is to be let fall. Let GE 

 be drawn perpendicular to the Axis, and 

 VE be bife&ed in F, and ere&ing the Per- 

 pendicular FH on the fame fide of the Axis, 

 let F H = i G E } I fay that a Circle de- 

 fcrib'd on the Center H, with the Radius 

 HA, will interfect the Parabola in three 

 points, or one, the right Lines GZ drawn 

 to which, will be perpendicular to the Curve 

 of the Parabola. But now that there may be 

 3 fuch Interferons, the Center H ought to 

 be fo pofited, as that it may be within the 

 fpace included by the Paraboloids (in Fig. 1.) 



that is, that FH may be lefs than V§ r FV% 

 or FH* lefs than the Cube of f VF j and 



fo GE = 4FH will be lefs than 4 \/§ 7 VF ? , 

 that is, the fquare of GE will be lefs than 

 ji VE 3 . Therefore thefe Limits coincide 

 with two Paraboloids of the fame kind with 

 thofe which were ufed in Cubical Equati- 

 ons, but whofe Parameter is twice lefs, viz. 

 fi of the Parameter of the Parabola, that is 

 'f of A V. And therefore it is that very 



Curve 



