1 2o Idifcellanea Curio fa. 



Roots, the determination of which depends 

 partly on the Coefficients^ partly on the Sine 

 and Magnitude of the abfolute Number 

 give'n. A general Conftru&ion for all thefe 

 (and that eafy J conceive enough) I have de- 

 livered at N° 1 88, .which I fuppofe the Rea- 

 dear to be acquainted with j but yet the 

 Figure relating to that Matter, I think 

 proper to bring hither, (Fig. 2.)- In the Con- 

 fcrudion of -the Equation £4 — bzA r Y pz.2 — qt 

 ir r = 0, let B D — 4 h, A B == f 6 bb, B K = i 

 or \ the Parameter, K C = 2 A B = $ K E 



^ ri % and EG = f, £ 3 -~\b r Y \q. 

 Which done, a Circle oh the Center G with 



the Radius VgD 2 — r, will interfedl the Pa- 

 rabola, either in none, or 2 or 4 Points, 

 from whence Perpendiculars let fall on DH, 

 will give all the Roots zi. But that there 

 may be 4, 'tis evident that the Center of the 

 Circle ought to be found fomewhere within 

 a fpace from any Point of which, three Per- 

 pendiculars may be let fall upon the Curve 

 of the Parabola; and alio that the Radius 

 is lefs than the greateft of thofe Perpendi- 

 culars, and greater than the middle one. 

 But that if the Center be pouted without 

 this fpace, fo that there can be but one 

 Perpendicular let fall upon the Parabola, ancf 

 the Radius greater than it, or if it be lefs 

 than the middle one of the 3 Perpendiculars, 

 but greater than the leait of them - 7 then 

 there can be but two Roots only, But there 



Is no Root at all, when the Radius Vg D^—r 



