In 1858 Charles Hermite and simultaneously Leopold Kronecker published “On the Solution of the General Equation of the Fifth Degree”. Using the elliptic function and methods available to the mid- 19^{th} century mathematician, the approach to solving fifth degree polynomials was finally solved after centuries of unsuccessful attempts. Having discussed symmetry of odd order equations to solve sequence number in the last Chapter, I find a similar symmetry required to solution of the quintic. A three-step process reflecting a workable methodology of the 1800s is demonstrated with a particular general example.

Solving the Quintic using Methods Available in the 19th Century