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A new METHOD of refohing CUBIC EQjJATIONS. 

 By THOMAS MEREDITH, A. B. Trinity College, Dublin. 



X HE roots of a cubic equation of this form, x^ + ^c. x- +3f'.* Read June 

 + c' — a — o which differs from a power only in its laft term, ""''797' 

 can be found, by tranfpofing, </, and extrading the cubic root on 

 each fide, provided, a, is not an impoffiblq binomial. 



Problem. To reduce any cubic equation to this form, 

 x' + 3 c. jv' + 3 <r'. X + c' — a — o, that is, to reduce it to an equa- 

 tion, in which, the fquare of the co-efficient of the fecond term is 

 triple the co-efficient of the third. * 



If the roots of a cubic equation, jc' + px' + qx + r — o, are en- 

 creafed or diminiihed by any quantity, /"and 3$', will be en- 

 creafed or diminifhed by an equal quantity, if multiplied, will 

 be multiplied by an equal quantity, therefore their equality or 

 inequality, not affeded by thofe transformations. 



Af = 



