Mifcellanea Curio fa. \oj 



poffible thatHR may fall between the Axis and 

 the Curve UX or UL, viz* if the Cube of f 

 UH or of />, be greater than the Square of \ $ \ 

 that is, if rrp 1 - be greater than \ q 1 \ in which 

 cafe there are three Roots, two Negative, if 

 it be — < ^, and one Affirmative equal to the 

 fum of the others but if it be ~j- then 

 there are two Affirmative ones, and one 

 Negative. But if i 7 p 3 be lefs than % ^% 

 then there is but one Root, Affirmative if it 

 be — • Negative, if -\- q. All which things 

 are taught by thofe that have handled this 

 part of Geometry. 



Now let all the Terms be in, and firft let 

 there be propofed, as an Example, this Equa- 

 tion, zJ r~* zj 2 b-\-z.p*-*q t=zo, to which Fig.n. 

 ferves. Iivthe Conftruction of this, weTiave 

 BC sa j UG 53 h AC « \ b\ UE 

 UH p \b* GH sa i b *h * p, or jfcjr - 



p £ 2 . Hence HO s=s b ^ 5 r« 4 % or J ~ 

 #7 fe% and HR (that is the diftance of the Cen- 

 ter of the Circle R from the Axis) is ever the 

 difference between I bp and i 7 b} -Y \ ^,which 

 Expreflions if they are equal, then the Center 

 falls in the Axis : If \ bp be greater than P 

 %i q-y then it falls to the Left Hand of the 

 Axis, if lefs, then to the Right. If therefore 

 the fquare Root of the Cube of f UH (that is 

 °f I r* I pi or putting J b z — J p ^ 

 li^ddd) be greater than HR, that is the 

 difference between 2 j ¥ "V i q and | bp ; the 

 Center R will be found within the Space 

 NPU circumfcrib'd by the Paraboloids UPX, 

 UNL, and the interminate right LineDNP; 

 and fo the Circle will cut the Parabola in 

 three points Y 7 Y, Y, pofited to the Right 



Hand 



