It is difficult to say who it is who first recognized the advantage of always equating to zero in the study of the general equation. It may very like… - 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).

Of the contemporaries of Newton one of the most prominent was John Wallis. ...Wallis was a voluminous writer, and not only are his writings erudite, but they show a genius in mathematics... He was one of the first to recognize the significance of the generalization of exponents to include negative and fractional as well as positive and integral numbers. He recognized also the importance of Cavalieri's method of indivisibles, and employed it in the quadrature of such curves as y=xⁿ, y=x^1/n, and y=x⁰ + x¹ + x² +... He failed in his attempts at the approximate quadrature of the circle by means of series because he was not in possession of the general form of the binomial theorem. He reached the result, however, by another method. He also obtained the equivalent of <math>ds = \!dx \sqrt{1+(\frac{dy}{dx})^2}</math> for the length of an element of a curve, thus connecting the problem of rectification with that of quadrature.

With the coming of the Jesuits in the 16th century, and the consequent introduction of Western science, China lost interest in her native algebra...