<math>z</math> and <math>x</math> being two flowing Quantities (whose Relation... may be exprest by any Equation...) by [the aforesaid] Corollary, wh… - Brook Taylor
" "<math>z</math> and <math>x</math> being two flowing Quantities (whose Relation... may be exprest by any Equation...) by [the aforesaid] Corollary, while <math>z</math> by flowing uniformly becomes <math>z+v</math>, <math>x</math> will become<math>x + \frac {\dot{x}}{1 \cdot \dot{z}}v + \frac {\ddot{x}}{1 \cdot 2 \cdot \dot{z}^2}v^2 +</math>... etc. or
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About Brook Taylor
Brook Taylor (18 August 1685 – 29 December 1731) was an English mathematician and secretary of the Royal Society of London, most famous for Taylor's theorem and the Taylor series.
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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>.
I make no difference between the Plane of the , and any other Plane whatsoever; for since Planes, as Planes, are alike in Geometry, it is most proper to consider them as so, and to explain their Properties in general, leaving the Artist himself to apply them in particular Cases, as Occasion requires.
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