JSiifcettanea Curiofa. 105 



Equation propos'd has Roots, and they will 

 be the Perpendiculars ZY, let fall from the 

 Interfections r, to the Line B K parallel tq 

 the Axis*, of which thofe that are to the 

 Right Hand of the Line BK, are the Affir- 

 mative ones, and thofe to the Left, the Nk* 

 gative. 



The convenience/ of this Conftruftion, lies 

 in this, that 'tis perform'd by a Circle paf- 

 fing thro' the Vertex, in the fame manner as 

 if the fecond Term had been wanting. And 

 therefore to determine the Number of the 

 Roots, 'tis fufficient to know the Properties 

 of the Place, or that Curve Line which di- 

 ftinguilhes the Spaces/ in which if the Cen- 

 ter of the Circle (that pafTes thro' the Ver- 

 tex of the Parabola) be placed, the Circum- 

 ference of it fhall interfe& the Parabola ei- 

 ther in one or in three other points : That is, 

 to define the Nature of that Curve, in which, 

 fell the Centers of all the Circles paffing 

 thro' the Ver.tex, and then touching the Pa* 

 rabola. Now this Locus, is that very Tara~ 

 boloid, which the celebrated Dr. Wallis calls 

 the SemicuJpical, in which the Cubes of the 

 Ordinates are as the Squares of the corre- 

 fpondent "Abfcifles. The Latus. Retlum of 

 which, is *j of the Latus Retlum of the gi- 

 ven Parabola, and its Vertex the point U 

 (Fig. 12.) the Line AU being half the Latus 

 Retlum of the fame Parabola. That is, if 

 we put unity for the Latus Retlum of the gi- 

 ven Parabola, then If of the Cube of the 

 ordinate applicate, will s=5' the Square of the 

 intercepted Diameter ; or the Cube of f 

 Vfi ~ the Square of AR, viz.. if R be the 



Center 



