JVlifcettanea Curio fa. 103 



terfe&ions is requird to the Conftru&ion, 

 therefore either but one, or the three re- 

 maining Roots, do denote one or three ^ as 

 in the cafe of Contad whence its plain, 

 that there are found two equal Roots, and 

 that the Problem from whence the Equation 

 refults, is really Plain. 



Therefore all Cubick^ Equations however af- 

 fected, are explicable by one, or by three 

 Roots, which are always fojfible^ that is, if 

 we admit Negative Roots fox true ones. So 

 Biquadraticks whofe laft Term r is affected 

 with the Sign — <, are explicable by two or 

 four j but if it be -y r in the Equation, and 



It be fo great that -h ar (See Fig.. 10.) 



be lefs than that the Circle defcrib'd with 

 that Radius and on the Center (7, can touch 

 the Para bole in any point •, the given Equa- 

 tion is altogether impoflible, nor is it expli- 

 cable by any Affirmative or Negative Root ; 

 but more of this in the following Pages. 



Now lince there is fo great a difference be- 

 tween the Cafes of Cubick and Biquadratick 

 Equations, that they cannot be comprehend- 

 ed together, we will firft of all handle the 

 Cubicks, and then the others. The Gubicks 

 are conftrufted by an infinite Number of 

 Circles in a given Parabola ; but the Biqua- 

 draticks by one alone (at leafl by thefe 

 Methods) and that becaufe, putting a>--e (or 

 any Indeterminate) equal to nothing, the 

 Gubick Equation is reduced to a Biqudratick 

 having the fame Roots with the Cubick, and 

 befides that, another Root equal to e ; whence 

 it comes to pafs that the Cubick Equation 

 H 4 may 



