112 MiJceUanea Curio fa. 



Hitherto we have obtairfd the Number of 

 the Roots in €ubick Equations, it remains 

 that we add fbniewnat concerning the quan- 

 tity of the Roots. And here it is firft of all 

 to be noted, that every Equation having three 

 Roots, may be expeditioufly enough refolv'd 

 by the help of the Table of Sines, that is by. 

 the Trifedion of an Angle, by putting 



V %b % - f f or VV .« the Radius of the Cir- 

 cle , if it be -fc f> in the Equation , or 



Vf**+fp, if — ; and the Angle to be 

 Trife&ed, that which has its Sine (in the 

 Table of Sines) h b 3 + | bp | 7. This 



Angle being found, the Sine of its third 

 part, as alto the Sine of the third part of 

 its Complement to a Semi-circle, and their 

 Sum, will be given from the Table of Sines. 

 Now thefe Sines are to be, multiplied into 



the Radius V * b 2 -\~ f />, and thus will be ob- 

 tained the quantities j& in the Fig.) the 

 Sum or Difference of which and f b, as the 

 cafe requires, Will give the true Roots of 

 the Equation. All thefe things are deduced 

 from Cartes^ Difcoverics. But that 1 may 

 comprehend all the Cafes, with as much Bre- ' 

 vity as is poffible *, I fay, that the Center 

 in the firft Formula of Equations, falling in 

 the Space tjGP, the two Interferons r, r, 

 fall between A and and confequently ei- 

 ther of the lefTer Roots is lefs than f b; 

 but the third and greater always exceeds j b i 

 tut is exceeded by b. But if the Center 



