**Account of books - Ⅰ. Linear perspective, or a new method of representing justly all manner of objects, &c. By Brook Taylor, L.L.D. and R.S. Secr. 8vo. London, 1715.**

The author of this book, finding the Art of Perspective to be very imperfect in the books that have hiterto been publish'd on that subject, thought it worth his while to consider the whole matter anew; and from a careful examination of the principles this art is founded upon, he has endeavoured to establish some theorems, by means of which the practice of it might be render'd more general and easy than has yet been done. In order to this, at first sight he found it necessary to make use of new terms of art; the old ones seeming not to be expressive enough of what is meant by them, and being adapted to too confined an idea of the principles of this art. In the old perspective the chiefest regard is had to the ground plane, that is, the plane of the horizon; from whence is derived the horizontal line, and by means of that line the representations of some figures are found by good simple constructions. But then the figures in all other planes are drawn by reducing them to the horizontal plane by means of perpendiculars; which is an inartificial round about way, makes a great confusion of lines, and is not capable of so much exactness. This confined way of treating this subject, proceeds from the strong possession the mind is bred up in of the notions of upwards and downwards, which makes one apt to refer all other irregular positions to those principal ones. But the minds of all artists should be drawn as much as can be from such confined ways of thinking, and they should be taught to accustom themselves, as much as may be, to consider nature in its general view, without minding those particular relations which things have with respect to themselves. For this reason our author has rejected the term of horizontal line, because it confines the mind too much to the particular consideration of the horizontal plane; but he considers all planes alike, and all figures as they are in themselves, without considering their relation to us; leaving the artist to do that, when he comes to apply the general rules of practice to any particular design.

This treatise is very short, because the author has confined himself only to give the general rules of practice, leaving the reader to himself or to a master to find out particular examples to exercise himself in. Yet he hopes he has omitted nothing that is material to the understanding of this art in the full extent of it. The whole book consists of five sections.

The first section contains an explanation of the fundamental principle of this art, with the definitions of the terms, and four theorems. The fundamental principle of this art, is, that the representation of any point is a point on the picture where it is cut by a line drawn from the original point really placed where it out to seem to be, to the pace of the spectators eye and consequently, the representation of any line is the mersection of the picture with a surface made by drawing lines from the place of the spectators eye, to the several points of the original line to be represented, really placed where it out to seem to be. For these lines which come from the several points of the original object to be placed in its proper situation, to the spectator's eye, are as so many visual rays which make the object sensible.

When a right line is continued in infinitum, the visual ray becomes at last parallel to it, and an object of any given bigness, if it goes still further and further off on that line, will at last seem to vanish, and at that time the place of its representation on the picture is the point where the ray parallel to the original line cuts the picture. For this reason our author has thought it proper to call that point of the vanishing point of such an original line and consequently of all others parallel to it (Def.5.) and for the same reason he calls that line on the picture a vanishing line (Def.6) which is produced by the intersection of the picture with a lane passing thro' the spectator's eye parallel to an original plane. There are ten definitions in all but these are the principal. And in our author's method these vanishing points and vanishing lines are of great use for the representation of any line passing through its vanishing point. (Prop.r.) Having found the representation of one point in any line, by any method whatsoever, he finds the representation of the whole line by its vanishing point, which he shews an early way to find in propp 6,8,12. which are in the second section. And by this mean he solves several problems in perspective, which it is not possible to do by the common way, at least without a great deal of difficulty, and a great confusion of lines. And by this method he shews how the compleat representations of any proposed figures may be found, having given the representation only of some principal parts of them. The second section contains several propositions to that purpose, shewing how to find the vanishing points and lines of proposed lines and planes, according to the several circumstances proposed; and by the means of them, how to find the representation of any given figure. In the end of this section there are some examples, in the description of the regular solids and some other figures.

The third section shews how to find the representation of the shadows of all objects.

The fourth section shews how to find the representations of the reflexions of figures made by polish'd planes.

The fifth section contains a few propositions relating to the inverse Method of Perspective; or the manner of examining a picture already drawn; so as to find out what point the picture is to be seen from, or having that given, to find what the figures are which are described on the picture.

Our author has observed that there may be a very good expedient made use of in painting of large rooms and churches, which is drawn from the nature of those rays which produce the vanishing points. This not being mention'd in the book itself, he thinks it not improper to take notice of it here. The expedient is this, having some way or other found the representation of one point of a line that is wanted in the picture, to find the whole line, pass a thread stretch'd through the place of the spectator's eye, in a direction parallel to the direction the original line out to be in, and the shadow of that thread cast by a candle, so as to pass through the given point on the picture will be the representation sought. The reason of this construction is, because the rays of light that pass from the candle to the threat so stretch'd make the plane which generates the representation sought. (see Prop.1.) And there may be other expedients of the like nature gather'd from the same principle.

**A pdf version of the entire text of the Philosophical Transactions of the Royal Society of London can be found here (this article begins on page 300).**