Brook Taylor Quotes

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 make a good Picture without understanding Perspective...

It seems that those, who have hitherto treated of this Subject, have been more conversant in the Practice of Designing, than in the Principles of Geometry... that might have enabled them to render the Principles of it more universal, and more convenient for Practice. In this Book I have endeavour'd to do this; and have done my utmost to render the Principles of the Art as general, and as universal as may be, and to devise such Constructions, as might be the most simple and useful in Practice.

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.

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

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 is Practice alone, that makes a Man perfect in any thing.

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.

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.

[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 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.

A new Method of computing Logarithms.
This method is founded upon...
1. That the sums of any two Numbers is the Logarithm of the Product of those two Numbers Multiplied together.
2. That the Logarithm of Unite is nothing; and consequently that the nearer any Number is to Unite, the nearer will its Logarithm be to 0.
3rdly. That the Product by Multiplication of two Numbers, whereof one is bigger, and the other less than Unite, is nearer to Unite than that of the two Numbers which is on the same side of Unite with its self; for Example the two Numbers being <math>\frac{2}{3}</math> and <math>\frac{4}{3}</math>, the Product <math>\frac{8}{9}</math> is less than Unite, but nearer to it than <math>\frac{2}{3}</math>, which is also less than Unite. Upon these Considerations, I found the present Approximation... best explain'd by an Example. ...[T]o find the Relation of the Logarithms of 2 and of 10... take two Fractions <math>\frac{128}{100}</math> and <math>\frac{8}{10}</math>, viz. <math>\frac{2^7}{10^2}</math> and <math>\frac{2^3}{10^1}</math>... one... bigger, and the other less than 1.

Dr. Halley..., has publish'd a... compendious and useful Method of extracting the Roots of affected Equations of the common Form, in Numbers. This Method proceeds by assuming the Root desired nearly true... (...by a Geometrical Construction, or by some other convenient way) and correcting the Assumption by comparing the Difference between the true Root and the assumed, by means of a new Equation whose Root is that Difference, and which he shews how to form from the Equation proposed, by Substitution of the Value of the Root sought, partly in known and partly in unknown Terms.

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.

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.

A general Series for expressing the Root of any Quadratick Equation.
Any Quadratick Equation being reduc’d to this Form <math>xx - mqx + my = 0</math>, the Root <math>x</math> will be exprest by this Series of Terms. <math> x = \frac {y}{q} + A \times \frac{1}{\frac{mq^2}{y} -2} + B \times \frac {1}{a^2 - 2} + C \times \frac {1}{b^2 - 2} +D \times \frac {1}{c^2 - 2}</math> etc. Which must be thus interpreted.
1. ...A, B, C, etc. stand for the whole terms with their Signs, preceding those wherein they are found, as <math>B = A \times \frac {1}{\frac{mq^2}{y} - 2}</math>
2. ...<math>a, b, c,</math> etc. ...are equal to the whole Divisors of the Fraction in the Terms immediately preceding; thus <math>b = a^2 - 2</math>.

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.