The meaning of the term linear perspective is a line view; the previous examples have been composed of surfaces placed fronting the eye; perspective is the science which treats of the changes of form produced by viewing them in various oblique positions.
The slightest alteration of position will change the appearance of an object; this can be easily shown—for illustration take a coin, the actual shape of which is a perfect round; or, strictly speaking, a circle. If we take the coin between the thumb and the first finger, holding it in an upright position, and exactly facing the eyes, as in [Fig. 296], it appears of its true form, viz., a circle. If we alter its position, balancing it upon the thumb, in a level position, with its edge directly opposite the eye, as in [Fig. 297], its appearance is changed, and what we know to be really a circle, appears to us as a straight line.
Fig. 296.—Fig. 297.—Fig. 298.
Now, still balancing the coin upon the thumb, but changing its position with regard to the eye, by holding it a little lower than in the last position, that is slightly beneath the level of the eye, as in [fig. 298], we see both the edge and the surface, the coin now appearing neither a circle nor a straight line, but a curved figure of an elliptical form. Thus the same coin held in three different positions has assumed three different shapes.
Let us take two coins of the same size, holding (in the position shown at [fig. 296]) one in each hand. Now, closing one eye, (which will make the experiment more clear), hold one coin out at arm’s length, and the other at about the distance of a foot from the eye. On comparing them, we find that the coin which is further from the eye appears less than the nearer one. We know that the coins are really equal in size, yet one appears smaller than the other.
We thus see that when we change the position of an object, we have as a consequence a change of appearance; also that the change of appearance may affect both the shape and the size of the object.
These diversities of appearance may be remarked in everything around us. We can observe them in the street by looking at a building from different points of view, or by comparing the apparent sizes of the street lamps; in the railway station, by watching the arriving or departing train; and at sea, by noticing the vessels as they approach, or as they retire, ultimately vanishing from our sight in that line where the sea and sky appear to meet.
All these interesting variations of appearance are in strict accordance with the laws of GEOMETRY and OPTICS. The former subject has been enlarged upon beginning with [page 81] of this work, where a line, a point, an angle, etc., are defined; other terms are explained at [page 41] and the following pages; to these we add a few definitions essential to the subject.
A PLANE is a surface which is perfectly even and flat; to use a familiar illustration, a plane is like the surface of a sheet of plate glass; recollect particularly, that a surface which is at all curved, is not a plane.