Vandermonde proposed in 1770 that the key to solving a general polynomial
equation
was represented by the roots of the equation
. Gauss has the undoubted credit for having laid the first stone in
the path that Galois successively followed. He showed that the roots of the
polynomial equation 
where p is prime are rational functions of the
roots of a sequence of equations 
where the
coefficients of 
are rational expressions of the roots of 
and
the degrees of the polynomials in the sequence are the all the prime numbers
in the factorization of p-1.