GEOMETRICAL PERSPECTIVE. 



161 



GEOMETRICAL PERSPECTIVE. I. 



INTRODUCTION DEFINITIONS PROPORTIONAL BCALK8. 



THXRE are several very important remarks to be made before 

 we enter upon the subject of Geometrical Perspective. In the 

 first place, we must say a few words respecting the instrument* 

 and materials required for this branch of drawing. 1. A 

 T square ; 2. A parallel ruler, or set square and flat ruler ; :t. A 

 drawing-board ; 4. A sector ; 5. A pair of compasses, with a 

 movable pencil-log, and pen ; 6. A ruling-pen ; 7. A protractor, 

 for iiKikinj? and measuring angles ; 8. A plane scale all fully 

 c\!'l:unod in Lessons in Geometry, III. and IV., pages 95 and 

 113, Vol. I. It will also be indispensable that the student should 

 be well acquainted with the theory and practice of Plane Geometry : 

 it is the language of the science upon which depends the prac- 

 tical working of all the problems that we shall have to propose 

 in the course of these lessons. In previous parts of the POPULAR 

 EDUCATOR will be found all that ia necessary for this purpose. 

 Trusting, therefore, that these lessons have been carefully and 

 diligently studied, we take it for granted tlu>.t it will not be 



distance* between object*, or parts of the Mine object ; Dob*a*n* 

 or depth* are expre**ed on plan*. Thu*, when a boo** i* bmtg 

 built, before the wall* are raiaed, and toe foundation* only are 

 laid, we then reoognue <A jrio* of thehooM. A map i* a plan, 

 say of a county ; we can understand by it the relative pontoon* 

 of the town* and Tillage*, their ^HtHmt from on* another. the 

 coarse* of the riven, and the direction* of the road*. If a card 

 be laid hontontally on a sheet of paper, and a pencil i* draw 

 about it close to the margin, we shall have a plan of the tcfefe 

 f the card. If the card i* placed perpmdiatUaHg to th 



sheet of paper, the plan would be only a line, 

 cular lines projected from every portion of the upright card 

 would only produce a line. This will, perhap*, mahit it evident 

 that all plans are merely the tracing* of perpendicular line* 

 from every part of the object upon a horizontal plane. 



2. The Picture Plane i* the surface of the picture upon which 

 the object is represented. In Fig. 1 it i* shown by the lo(t*n 

 / g i h ; in this case it i* shown in petition between the eye at B, 

 and the object, abed. Fig. 1 will be further explained pre- 

 sently. When practically working oat a problem, the lower 



FlO. 2. SCALE OF \ INCH TO 1 FOOT. 

 



FlO. 3. SCALE OF 1 INCH TO 38 FEBT. 



I 



J 

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necessary for us to do more than refer the pupil to any particular 

 problem in plane geometry which may be required in connection 

 with our subject as we proceed. It is our intention, as far as 

 possible, to make a practical application of all that we shall 

 advance, knowing the valuable assistance Geometrical Per- 

 spective affords to those who are engaged in any constructive 

 art, as well as to draughtsmen in general. We hope, also, to 

 create an interest in this useful science amongst those who have 

 a loving sympathy with art for its own sake, and who take a 

 pleasure in all scientific inquiries, especially those which claim 

 to have a mathematical foundation. In a pictorial sense, there 

 is no other branch of drawing more capable of satisfying the 

 mind with regard to the appearances of nature than perspective ; 

 it is an art which enables us to draw upon a plane surface things 

 far and near as they appear to the eye, the effect of which can 

 be as clearly and as truthfully presented to us by the help of geo- 

 metry ns if the objects themselves had been tvaced upon a piece 

 of glass placed between them and the eye. We will now request 

 the pupil to make himself familiar with the following terms and 

 definitions : 



1. The Plan of an object. A plan is the representation of all 

 horizontal lengths and breadths, showing only the horizontal 



37 N.E. 



line, h i, is the only line drawn to represent the picture plane, 

 because this h i ia the plan of the picture plane, the picture 

 plane being always considered in a perpendicular position. 



3. The Horizontal Line, or Line of Sight, represent* the 

 height of the eye in the picture, and is marked in Fig. 1 and 

 figures in future lessons, H L. 



4. The Point of Sight is the point opposite the eye in the 

 picture, and consequently upon the line of sight. It ia marked p a. 



5. The Station Point, marked s p, ia the place where the spec- 

 tator ia supposed to stand when viewing the object represented. 



6. The Distance Point, marked D p, represent* the <ti*tano 

 between the eye and the picture plane. Sometime* ike distance 

 point and station point represent the aame thing. It will be 

 found in the coarse of our lessons to vary according to circum- 

 stances ; in some instances it refer* to the distance of any 

 vanishing point in the picture from the eye. All theee variation* 

 will be explained in their proper place*. 



7. Vanishing Point. If a line be drawn from the eye parallel 

 to any original straight line of the object, the point marked T P. 

 where that line cuts the picture plane, marked p p, i* the vanish- 

 ing point of that original line. 



8. Visual Rays are line* proceeding from every part of the 



