Of CUBIC EQUATIONS. 109 



The following examples are chiefly taken from Dr Hut- 

 ton's " Tracts Mathematical and Philofophical.''^ Tra6i 5. 



II. Example i. Let the propofed equation be 

 x' — 6x' + iix — 6 z= o. 

 Here, h. ■=. — 6, B = -f-ii, C = — 6: therefore 



M = -j-2 



N =— 2 , 

 m = + 14 

 « = + 6 



So that we have here Cafe I. 



14 _7_ 



^ ~ 2/3 ~ ^3 



and r = ^ -^ 



2 — 2 



CO 



Now, tan 90° =r co, and alfo tan 270° =. c^ : And we may take 

 either of thefe angles for <p : Take <p zz 90°, then, 



z = tan I = tan 30° = + ^ 



z = tan ^^+120°) rztan 150°=— tan3o°=: — -^ 



z — tan ^^ + 240°) = tan 270* = c^ 



— + — 

 THEREFORE.ar = ^ ^ z=.~ zz z 



, I a <> 



And fo the three roots are 1,2, and 3. • 



SiNCB, 



