Interesting. I know that one of the general methods for solving
cubics also involves a linear tranformation, and perhaps the one for
quartics also.
One wonders how these things were discovered.
But Descartes couldn't have followed it completely, at least in the sense
of a sequence of linear transformations, because that would
mean that all zeros of polynomials are algebraic, which Abel and Galois
showed isn't so.
Phil Mahler
Mddlesex CC
Bedford, MA