I'm trying to understand Lagrange's theorem which I found in Harold Edward's book ''Galois Theory''. I was trying to find this theory in internet but all Lagrange's theorems which I found are not exactly this one. Do you know where can I read about that? Or find proof or example for particular polynomial?
Theorem:
If $t$ and $y$ are any two polynomials in he roots $x'$,$x''$,$x'''$,$\dots$ of $x^\mu+mx^{\mu-1}+nx^{\mu-2}+px^{\mu-3}+\dots=0$ and if these functions are such that every permutation of the roots $x'$,$x''$,$x'''$,$\dots$ which changes $y$ also changes $t$, one can, generally speaking, express $y$ rationally in terms of $t$ and $m$,$n$,$p$,$\dots$,so that when one knows a value of $t$ one will also know immediately the corresponding value of $y$; we say generally speaking because if the known value of $t$ is a double or triple or higher root of the equation for $t$ then the corresponding value of $y$ will depend on an equation of degree $2$ or $3$ or higher with coefficients that are rational in t and $m$,$n$,$p$,$\dots$