l o i MifceEanea Cur i of % , 



in which they either of them (by a like Fata 

 tho' in a different way) committed a Para* 

 . logifm, perhaps the only one in ail their 

 Geometrical Writings ; as fhall be afterwards 

 prov'd. Wherefore being fenfible, as well of 

 the Difficulty, as the Excellency of the Sub- 

 ject, I refolv'd to apply to it ftrenuoufly, 

 that I might not be thought unable to per- 

 form my Promifes, and that fo noble part of 

 Geometry, and fo little cultivated, might 

 not lie any longer wrapt up in Darknefs, but 

 be render'd plain and intelligible by thefe 

 few Lucubrations of mine. But firft the 

 Ileader muft take notice, that w=hile he fets 

 to the Reading of this, he ought to have 

 the foremention'd DilTertation (No. 188J at 

 hand by him, and to underftand the Con- 

 ft ructions there delivered very well j becaufe 

 thofe things that follow do chiefly depend 

 upon them, neither are they to be here re- 

 peated again.' 



It is plain from Cartefim, and what was 

 there faid, that both in Cubick and Biqua- 

 dratic^ Equations, the Roots may be expoun- 

 ded by Perpendiculars let fall, upon the Axis 

 or given Diameter of the given Parabola, 

 from the Interfe&ions of that Curve with a 

 Circle. And whereas when a Circle inter- 

 feds a Parabola, it muft neceflarily do fo* 

 ' either in four or in two points *, it's manifeft, 

 that in Biquadraticks there muft always be, 

 either two or four true Roots, Affirmative or 

 Negative as alfo if the Circle happens to 

 touch it, in which cafe the equality of two 

 Roots of the fame Sign, is concluded* But 

 m Vukick, Equations, becaufe one of the In- 

 terferons 



