|Title: ||A memoir on the quintic equation / by Prof. Cayley.|
|Personal Author: ||Cayley, Arthur, 1821-1895.|
|Date: ||[1894 or 1895]|
|Extent: ||28 leaves|
|Dimensions: ||46 cm.|
|General Note: ||See a collection of letters from Cayley to fellow mathematician Robert Harley in the collection.|
|Abstract: ||By the time of Euclid, the Greeks knew how to solve quadratic equations.
The general solution of the cubic equation was found by Tartaglia and
Cardano in the 16th century, and the general solution of the quartic
equation was found by Ferrari shortly thereafter. Attention then
turned to the quintic equation, and the attempt to solve it was one of
the central themes in the development of algebra over the next three
centuries. Finally, in 1824 Abel showed that there is no formula for the
solution of the general quintic. Nowadays, this result is best understood
in the context of Galois theory. Galois's work was done in 1832 but did
not become known until its posthumous publication by Liouville in 1846.
The quintic continued to hold great interest for mathematicians, including
Cayley and especially Harley, and many of their joint computations were
related to it. (In modern language, they investigated the resolvent and
discriminant of the general quintic.) This interest for Cayley continued
throughout his lifetime. One of his last published papers, in 1894, dealt
with the quintic:  Arthur Cayley, On the sextic resolvent equations
of Jacobi and Kronecker, J. reine angew. Math. CXIII (1894), 42-49.
Moreover, he was preparing a paper on the quintic,
which was incomplete at his death. The manuscript here consists of several drafts of this paper. (In one of these
drafts, he refers to his 1894 paper on the sextic resolvent equations
of Jacobi and Kronecker .)|
Prof. Steven H. Weintraub, Dept. of Mathematics, Lehigh University.
|Subject: ||Quintic equations.|| |