Mifcellanea Curio fa. 1 1 7 



For another Example, Jet us enquire out 

 the Roots of the Equation x3 — 1 5*2 — 229* 



—525 m 0. Here V i bb -V \pi=zS/ 101 j — 



V and the Radius of the Circle = V405 f • 



roifVWf 

 the Tabular Sine of an Arch, whole Log- 

 9.9736426, and the Arch it felf 70 0 . 14'. 22"- 

 The third part of it, is 23 0 . 24. 47 'i, and 

 of the Complement, is 36 0 . 35'. i2"i, whofe 

 Log. Sines are 9.599183, and 9-7752-757 to 



which adding the Log. ¥405^, we have the 

 Log. 0.903089=8, and Log. 1.079181 = 12, 

 the Sum of which is equal to 20. Hence we 

 conclude that 20 ~Y j b or 25, is equal to 

 the Affirmative Root, and 8 and 12 — j b 7 

 that is 8 and 7 equal to the Negative Roots. 

 But if the Equation had been x3 ~b 1 5-v 2 

 2,29*— 525=0, then 8 & 7 bad been the Affir- 

 mative Roots, and 25 the Negative. As for 

 the other Cubicks which are explicable by 

 one only Root, they are to be refolv'd by 

 Cardan's Rules, after the fecond Term is 

 taken away } neither do I fee how the bufi- 

 nefs can be done with lcfs Calculation. 



But if this Root be defir'd to be expreffed 

 in the Terms of the Quantities b 7 p, ^, I 

 fay that in the firft Formula it is, f b *\- or ~* 

 the Sum or Difference of the Cubick Roots 



of ^ \qq — fo 8 ; 2 bi-Y\ 7 bl q^ibfffij fz 



± %/j>\ \\ q — ibp (viz... if \ r hi +• i q be 

 I 3 greater 



