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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… - 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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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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Considering how few, and how simple the Principles are, upon which the whole Art of <small>PERSPECTIVE</small> depends, and withal how useful, nay how absolutely necessary this Art is to all forts of Designing; I have often wonder'd, that it has still been left in so low a degree of Perfection, as it is found to be, in the Books that have been hitherto wrote upon it.
<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
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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