Viète (1540-1603) worked on what is known as Horner's method for the
approximation of polynomial roots, and also he discovered another substitution
to solve cubics of the form 
. Horner's method for approximating
roots is similar in concept to the Newton-Raphson method. Take for example a
quadratic equation 
. Substitute 
where 
is known
to be a good approximation of x. If 
is small, i.e. if 
is
small, then 
will be very small, and may be cancelled. So we get
. Proceeding inductively we can approximate
any root to any degree of accuracy. Notice that 
is the derivative of
. The new substitution for solving the cubic involved
, which brought to solving 
, a quadratic in
.