Mifcellanea Curio fa. 9 1 



Conftru&ion. Or elfe taking a for Unity, 

 thofe Equations are reduced to thefe Forms, 

 pfe. Cub. *p z,. q i=:0,and Biquadr. ^ 4 *.p£.z,; 

 qz.. r. gsi 0. Now the Parabola FAG, Fig, 9 be- 

 ing given, whofe Axis is A,CDKL, and Para- 

 meter^ a or 1 j let AC be taken 1=3 \ a, and 

 be fet off always from the Vertex A, towards 

 the inner parts of the Figure. Then take CD 

 I />, in that Line AC, continued towards C, if 

 it be — f in the Equation, or towards the 

 contrary Point, if it be Farther,from the 

 point D for from the point C, if the quantity 

 p be not in the Equation) Let DE (ere&ed 

 perpendicular to the Axis) be made s=s lq 

 which is to be fet to the right hand if it be 

 but to the other fide of the Axis if it be 

 -Yq. And then a Circle defcribed on the 

 Center E, which the Radius AE(if the Equa- 

 tion be but a Cubical one) 'will interfeft the 

 Parabola in as many Points (m. F, G, G,) as 

 the Equation has True Roots, of which the 

 Affirmative ones, as GK, fhall on the right 

 fide of the Axis, and the Negative ones as 

 FL, on the Left. But if the Equation be a 

 Biquadratical one, then the Radius of the Cir- 

 cle AE, by adding (if it be — r) or Subtract- 

 ing (if it be -Yr) from the Square of it, the 

 JlecVangle a x r, or the content under the Pa- 

 rameter, and the given Quantity r; which is. 

 very eafily done Geometrically. And the In- 

 terferons of this Circle with the Parabola, 

 will give (letting fall Perpendiculars from 

 thence to the Axis) all the true Roots of 

 the Biquadratical Equation; the Affirma^ 

 five ones being on the Sight fide of the Axis, 

 and the Negative ones, on the Left. The de- 



demon- 



