[I]t may not be amiss to set down here two Approximations I have formerly hit upon. The one is a Series of Terms for expressing the Root of any Quadr… - Brook Taylor

A general Series for expressing the Root of any Quadratick Equation.
Any Quadratick Equation being reduc’d to this Form <math>xx - mqx + my = 0</math>, the Root <math>x</math> will be exprest by this Series of Terms. <math> x = \frac {y}{q} + A \times \frac{1}{\frac{mq^2}{y} -2} + B \times \frac {1}{a^2 - 2} + C \times \frac {1}{b^2 - 2} +D \times \frac {1}{c^2 - 2}</math> etc. Which must be thus interpreted.
1. ...A, B, C, etc. stand for the whole terms with their Signs, preceding those wherein they are found, as <math>B = A \times \frac {1}{\frac{mq^2}{y} - 2}</math>
2. ...<math>a, b, c,</math> etc. ...are equal to the whole Divisors of the Fraction in the Terms immediately preceding; thus <math>b = a^2 - 2</math>.

It is generally thought very ridiculous to pretend to write an Heroic Poem, or a fine Discourse upon any Subject, without understanding the Propriety of the Language wrote in; and to me it seems no less ridiculous for one to pretend to make a good Picture without understanding Perspective...

I would recommend it to the Masters of the Art Painting... to establish a better Method for the Education of their Scholars, and to begin their Instructions with the Technical Parts of Painting, before they let them loose to follow the Inventions of their own uncultivated Imaginations.