Mifcellanea Curio fa. 123 



crcife and Pleafure, of fending out thefe 

 things by themfelves. As for the Limita- 

 tion of the leaft Term r 0 it cannot be found 

 with the fame eafmefs, and that becaufe, to 

 let fall a Perpendicular upon the Curve of 

 a Parabola, is a fetid Probleme^ and which 

 cannot be refolv'd without the lblution of a 

 Cubick Equation. Therefore firft of all let 

 the fecond Term be wanting, or if there, 

 let it be taken away, fo that the Equation 

 may have this Form &4. *. pz, 2 - r'.w^ 

 And if it be — r, it is always explicable by 

 two or four Roots ; but that there may be 

 four, the Center of the Circle ought to be 

 pofited within the foremention'd Paraboloids, 

 or that it may be — p, and qq may be lefij 

 than 2 - 7 or the Cube of f p. Then let the 

 Roots of this Equation y3. *. | py. if — *, 

 be gotten, the Quantities p and q having the 

 fame Sines as in the Biquadratick. And 

 thefe Roots are found expeditioufly enough 

 by the help of the Table of Sines. But 

 having found thofe three y (which are ordi- 

 nately applied, to the Axis of the Parabola, 

 from the points, where the Perpendiculars 

 to the Curve of it do fall, irte. YZ in Fig. 3.) 

 than pyy — 3_y4 of the lejfer y will denote the 

 greatest Quantity of r\ if it be— r, than 

 which if r be lefs, the Equation will have 

 four Roots, otherwife but two. But if it 

 be rig* r, it ought to be lefs than iy^~pyy 

 of the middle y, for if it be greater, it can 

 have but two Roots ; at leaft, if r be lefs 

 than 3^4 — pyy of the greatefi y. But if 

 it be greater than this, the Equation, 

 is not explicable by any true Root at all, 



Thefe 



