PERSPECTIVE. k 383 



to it. Lay off, at pleasure, CD for the distance of 

 the picture, if C be the centre of the picture. 

 Draw a line from D, touching the end B of the line 

 to be divided: draw DBE, cutting the ground- 

 line in . Then AE represents the actual dimen- 

 sions of the line AB, which is seen in perspective. 

 (Here it may be observed, that this gives a rule 

 also for finding the real length of any line which 

 tends to a vanishing-point.) Divide AE into the 

 same number of equal parts into which you pro- 

 posed to divide the given line AB; as Al, 12, 23, 

 &c. Then from these different divisions draw lines 

 to D, cutting the line AB in a, b, c, d, &c, which 

 will represent the required number of equal parts, 

 but diminishing in size as they are farther removed 

 from the eye. If it be wished to divide the line 

 AB into any number of unequal parts, or to lay off 

 doors, windows, &c. upon it, the line AE, found as 

 before, must be divided in the required proportion ; 

 and lines drawn from those to D will give the re- 

 quired divisions on AB, from which perpendiculars 

 may be drawn for the doors, windows, &c. 



To draw a circle in perspective. 



The perspective representation of every circle is 

 a regular ellipsis, when the eye is without the 

 circle, which may be demonstrated, by considering 

 that the rays from the circumference of the circle 

 to the eye, form an oblique cone. But it is well 

 known to those who are acquainted with conic sec- 

 tions, that every section of a cone, whether right 

 or oblique is a true ellipsis, except in one case only, 

 which is, when the section is taken sub-contrary to 

 its base, a situation which happens so rarely in 

 drawings, that it may be disregarded altogether, 

 and the section of a cone, or the perspective of a 

 circle, in all cases considered as a perfect ellipsis. 



