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" "[T]he Method which ought to be follow'd in instructing a Scholar in the Executive Part of Painting; ...first have him learn the most common Effections of Practical Geometry, and the first Elements of Plain Geometry, and common Arithmetic.
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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The Greatest Masters have been the most guilty... The great Occasion of this Fault, is certainly the wrong Method that generally is used in the Education of Persons to this Art: For the Young People are generally put immediately to Drawing, and when they have acquired a Facility in that, they are put to Colouring. And these things they learn by rote, and by Practice only; but are not at all instructed in any Rules of Art. By which means when they come to make any Designs of their own, tho' they... don't know how to govern their Inventions with Judgment, and become guilty of so many gross Mistakes, which prevent themselves, as well as others, from finding that Satisfaction, they otherwise would do in their Performances.
<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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There may be regular Methods also invented for teaching the Doctrine of Light and Shadow; and other Particulars relating to the Practical Part of Painting, may be improved and digested into proper Methods... But I only hint at these... recommending them to the Masters of the Art to reflect and improve upon.