Vieta: 1QC - 15QQ + 85C - 225Q + 274N, aequator 120. Modern form:<math>x^6 - 15x^4 + 85x^3 - 225x^2 + 274x = 120</math> - David Eugene Smith

Vieta was the first algebraist after Ferrari to make any noteworthy advance in the solution of the biquadratic. He began with the type <math>x^4 + 2gx^2 + bx = c,</math> wrote it as <math>x^4 + 2gx^2 = c - bx,</math> added <math>gx^2 + \frac{1}{4}y^2 + yx^2 + gy</math> to both sides, and then made the right side a square after the manner of Ferrari. This method... requires the solution of a cubic resolvent.
Descartes (1637) next took up the question and succeeded in effecting a simple solution... a method considerably improved (1649) by his commentator Van Schooten. The method was brought to its final form by Simpson (1745).

When we speak of the early history of algebra it is necessary to consider... the meaning of the term. If... we mean the science that allows us to solve the equation <math>ax^2 + bx + c = 0</math>, expressed in these symbols, then the history begins in the 17th century; if we remove the restriction as to these particular signs, and allow for other and less convenient symbols, we might properly begin the history in the 3rd century; if we allow for the solution of the above equation by geometric methods, without algebraic symbols of any kind, we might say that algebra begins with the or a little earlier; and if we say that we should class as algebra any problem that we should now solve with algebra (even though it was as first solved by mere guessing or by some cumbersome arithmetic process), the science was known about 1800 B.C., and probably still earlier.<

Among his <nowiki>[</nowiki>John Wallis'<nowiki>]</nowiki> interesting discoveries was the relation <math>\frac{4}{\pi} = \frac32\cdot\frac34\cdot\frac54\cdot\frac56\cdot\frac76\cdot\frac78\cdots</math>
one of the early values of π involving infinite products.