An introduction to the modern theory of equations, by Florian Cajori.

GALOIS RESOLVENT BY ADJUNCTION 183
to G12(4). Now X does not occur in the Galois domain 2(a, a, a2.aa)
1_= D(,, y, z, w) and is, therefore, not a natural irrationality. The reduction
brought about by X can be effected by V/D, which is a number in the
Galois domain, hence is a natural irrationality. This illustrates Corollary
IV.
The relation x/D = Xn illustrates the theorem itself. We have
g(y) - (y - VD) (y + VD) = 0, or y2 = D.
Let Yi = Vv'/D, 2 = - / D), and we get h(y) (yL - V/D) (y" + VD)
-0, or y2n = D. This illustrates Corollaries II and I.
Ex. 2. If the group P of an equation is s(4), illustrate the above
theorem and corollaries by taking X== /(acC1-;wC,)~((w2+ la3)2. See
Ex. 6, ~ 113.