x o6 Mifcellanea Curiofa. 



Center of the Circle that paifes thro' the 

 Vertex of the Parabola, and touches the fame 

 afterwards. 



This is that Curve which our Country- 

 man Mr. Neil (the firft of all Mortals) de- 

 monftrated to be equal to a given right Line, 

 and by that means obtain'd a Reputation 

 among the piincipal Geometricians. Its pro- 

 perties have been curiouily enquired into, by. 

 Dr. Wallis, (at the end of his Book of the 

 Cffoid ) and Hugenitu (Prof. 8 & 9, of his 

 Tract of the Evolution of Curve Lines) and 

 others, whofe Writings the Reader may con- 

 fult. This Curve delcrib'd on either fide of 

 the Axis of the Parabola (viz. VNL, VPX) 

 comprehends a Space, in which if the Cen- 

 ter of the Circle (which pailes thro' the Ver- 

 tex A) be placed, it will cut the Parabola in 

 three other points. But the Spaces more re- 

 mote from the Axis, do afford Centers for 

 Circles that will cut the Parabola but in one 

 point befides the Vertex. 



Thefe things well underftood, we are now 

 prepar'd to determine the Number of the 

 Roots. And firft of all, let the fecond Term 

 "be wanting, and let the Lotus Rettum 1, or 

 AV m i- In the Conftrudion VH is s=s i p, HR 

 ■ r=! \q ^ and fince if it be -V p in the Equation, 

 i p is to be fet off from V towards the upper 

 parts } the Center of the Circle is always 

 found without the Space LVX, and therefore 

 is explicable by one Root only, which is Af- 

 firmative if it be w ^, Negative if -f q \ and 

 thefe Roots may be inveftigated by Cardan's 

 Rules, f But if it be -« p, then UHt=s|p, is 

 fet off towards the lower parts*, and it is 



