Brook Taylor Quotes

[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 Quadratick Equation; and the other is a particular Method of Approximating in the invention of Logarithms, which has no occasion for any of the Transcendental Methods, and is expeditious enough for making the Tables without much trouble.

The Art Perspective is necessary to all Arts, where there is any occasion for Designing... but it is more particularly necessary to the Art Painting...

[T]he Theory I have endeavour'd to explain in the Appendix, from Sir Isaac Newton, may be of very great use to Learners.

When he is sufficiently perfect in these, I would have him learn Perspective. And when he has made some progress in this, so as to have prepared his Judgment with the right Notions of the Alterations that Figures must undergo, when they come to be drawn on a Flat, he may then be put to Drawing by View, and be exercised in this along with Perspective, till he comes to be sufficiently perfect in both.

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.

In doing this he makes use of a Table of Products (...he calls Speculum Analyticum,) by which he computes the Coefficients in the new Equation for finding the Difference mentioned. This Table, I observed, was formed in the same Manner from the Equation propos'd, as the s are, taking the Root sought for the only flowing Quantity, its Fluxion for Unity, and after every Operation dividing the Product successively by the Numbers 1, 2, 3, 4, etc.

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.

[H]e should be instructed in the Theory of the Colours; that he should learn... their particular Properties... Relations, and... Effects that are produced by their Mixture; and that he should be made well acquainted with the Nature of the several material Colours... used in Painting.

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.

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.

Nothing ought to be more familiar to a Painter than Perspective; for it is the only thing that can make the Judgment correct, and will help the Fancy to invent with ten times the ease that it could do without it.