[Read before the Canadian Institute, March 3rd, 1883]. 
RESOLUTION 
OF 
SOLVABLE EQUATIONS OF THE FIFTH DEGREE, 
BY GEORGE PAXTON YOUNG, 
Toronto, Canada. 
CONTENTS. 
1. Sketch of the method employed. General statement of the 
criterion of solvability of an equation of the fifth degree. §2-5. 
2. Case in which uw wy = ug ug. The roots determinable in terins 
ot the coefficients p; , po, etc., even while particular numerical values 
have not been assigned to the coefficients. Three verifying instances ; 
one, in which the auxiliary biquadratic is irreducible ; a second, in 
which there is a quadratic sub-auxiliary ; a third, in which the roots of 
the auxiliary biquadratic are all rational. §6-10. 
3. Deduction, in the case in which w v4 = wz uz, of the equation 
p’ = 0; where p’ is a rational function of the coefficients p1 , pz , etc. 
Verifying instances. §11-13. 
4, The trinomial quintic 2 + pya + ps =0. Form which the 
criterion of solvability here takes. Example. §14-16. 
5. When any relation is assumed between the six unknown quantities, 
the roots of the quintic can be found in terms of p,, pz, ete. §17. 
. 6. The general case. §18. 
$1. By means of the laws established in the paper entitled ‘“ Prin- 
ciples of the Solution of Equations of the Higher Degrees,” which is 
concluded in the present issne of the Journal of Mathematics, a 
criterion of the solvability of equations of the fifth degree may be 
found, and the roots of solvable quintics obtained in terms of given 
numerical coefficients. In certain classes of cases, the roots can be 
determined in terms of coefficients to which particular numerical 
values have not been assigned, but which are only assumed to be so: 
related as to make the equations solvable. 
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