Brook Taylor

[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 …

z and x being two flowing Quantities (whose Relation... may be exprest by any Equation...) by [the aforesaid] Corollary, while z by flowing uniformly becomes z+v, x will becomex + \frac {\dot{x}}{1 \cdot \dot{z}}v + \frac {\ddot{x}}{1 …

The Book it self is so short, that I need not detain the Reader any longer in the Preface...

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... …

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

[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 …

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.

[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.

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 …

are not at all instructed in any Rules of Art. By which means when they come to make any Designs

The Greatest Masters have been the most guilty... The great Occasion of this Fault

It is generally thought very ridiculous to pretend to write an Heroic Poem, or a fine Discourse upon any Subject, without understanding the Propriety of the Language wrote in; and to me it seems no less ridiculous for one to pretend to …

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...

of the Nature of these Principles.

by the extensive Notions it will give

they will find the vast Benefit

This will take up a little more Time at first; but

to draw new ones of their own, in all the Variety of Circumstances

not to be contented with the Schemes they find here; but

I have endeavour'd to make every thing so plain, that a very little Skill in Geometry may be sufficient to enable one to read this Book by himself.

The true and best way of learning any Art, is not to see a great many Examples done by another Person, but to possess ones self first of the Principles of it, and then to make them familiar, by exercising ones self in the Practice. For it …

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 …

And I was forced to invent new Terms of Art

I found it absolutely necessary to consider this Subject entirely anew, as if it had never been treated of before