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  Pure cubic equations are therefore of the form x3=r; and hence it appears that a value of the simple power of the unknown quantity may always be found without difficulty, by extracting the cube root of each side of the equation. 
  Thus the equation 23+222+p2164rz 64=0 becomes, after reduction, v3+2pv2+(p2—4r)v—q2=o; it also follows, that if the roots of the latter equation are a, b, c, the roots of the former are 4a, ;b, ;c, so that our rule may now be expressed thus: Let y4+py2+qy+r=o be any biquadratic equation wanting its second term. 
  Thus we have the biquadratic equation y4+2Py22—84 R.y+P24Q=o, one of the roots of which is y= J a+ J b+ A) c, while a, b, c are the roots of the cubic equation z3+Pz2+Qz—R=o. 
 encyclopedia.jrank.org /correction/edit?content_id=23314&locale=en (10461 words) 
