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Hence if <math>y</math> be the Root of any Expression formed of <math>y</math> and known Quantities, and supposed equal to nothing, and <math>z</math… - Brook Taylor
" "Hence if <math>y</math> be the Root of any Expression formed of <math>y</math> and known Quantities, and supposed equal to nothing, and <math>z</math> be a part of <math>y</math>, and <math>x</math> be formed of <math>z</math> and the known Quantities, in the same manner as the Expression made equal to nothing is formed of <math>y</math>; and let <math>y</math> be equal to <math>z + v</math>; the difference <math>v</math> will be found by Extracting the Root of this expression <math>x + \frac {\dot{x}v}{1} + \frac {\ddot{x} v^2}{1 \cdot 2} + </math> ... etc. <math>= 0</math>.
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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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Additional quotes by Brook Taylor
Hence I soon found that this Method might easily and naturally be drawn from Cor 2. Prop. 7. of my Methodus Incrementorum, and that it was capable of a further degree of Generality; it being Applicable, not only to Equations of the common Form, (viz. such as consist of Terms wherein the Powers of the Root sought are positive and integral, without any Radical Sign) but also to all Expressions in general, wherein any thing is proposed as given which by any known Method might be computed; if vice versâ, the Root were consider'd as given: such as are all Radical Expressions of Binomials, Trinomials, or of any other Nomial, which may be computed by the Root given, at least by s, whatever be the Index of the Power of that Nomial; as likewise Expressions of Logarithms, of Arches by the Sines or s, of Areas of Curves by the Abscissa's or any other Fluents, or Roots of Fluxional Equations, etc.
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