VOL. XXIX. ] PHILOSOPHICAL TRANSACTIONS. I73 



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 its full 

 extent. The whole book consists of 5 sections. 



The first section contains an explanation of the fundamental principle of this 

 art, with the definitions of the terms, and 4 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 ought 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 specta- 

 tor'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 size, 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 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 plane passing through 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. 1.) Having found the representation of one point 

 in any line, by any method whatever, he finds the representation of the whole 

 line by its vanishing point, which he shows an easy way to find, in Prop. 6, 

 8, 12, which are in the 2d section. And by this means 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 shows how the compleat representations of any proposed 

 figures may be found, having given the representation only of some principal 

 parts of them. 



The 2d section contains several propositions to that purpose, showing 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 3d section shows how to find the representation of the shadows of all 

 objects. 



