Isometric Cube

I enclose this cube within a circle, as in Fig. 143. To form this cube the circle (A) is drawn and bisected with a vertical line (B). This forms the starting point for stepping off the six points (C) in the circle, using the dividers without resetting, after you have made the circle. Then connect each of the points (C) by straight lines (D). These lines are called chords. From the center draw two lines (E) at an angle and one line (F) vertically. These are the radial lines. You will see from the foregoing that the chords (D) form the outline of the cube - or the lines farthest from the eye, and the radial lines (E, F) are the nearest to the eye. In this position we are looking at the block at a true diagonal - that is, from a corner at one side to the extreme corner on the opposite side.

Let us contrast this, and particularly Fig. 142, with the cube which is placed higher up, viewed from the same standpoint.

Flattened Perspective

Fig. 144 shows the new perspective, in which the three vertical lines (A, A, A) are of equal length, and the six angularly disposed lines (B, C) are of equal length, but shorter than the lines A. The only change which has been made is to shorten the distance across the corner from D to D, but the vertical lines (A) are the same in length as the corresponding lines in Fig. 143. Notwithstanding this change the cubes in both figures appear to be of the same size, as, in fact, they really are.

In forming a perspective, therefore, it would be a good idea for the boy to have a cube of wood always at hand, which, if laid down on a horizontal support, alongside, or within range of the object to be drawn, will serve as a guide to the perspective.

Technical Designations

As all geometrical lines have designations, I have incorporated such figures as will be most serviceable to the boy, each figure being accompanied by its proper definition.

Fig. 146.	Fig. 147.

Before passing to that subject I can better show some of the simple forms by means of suitable diagrams.

Referring to Fig. 145, let us direct our attention to the body (G), formed by the line (D) across the circle. This body is called a segment. A chord (D) and a curve comprise a segment.

Sector And Segment

Now examine the shape of the body formed by two of the radial lines (E, E) and that part of the circle which extends from one radial line to the other. The body thus formed is a sector, and it is made by two radiating lines and a curved line. Learn to distinguish readily, in your mind, the difference between the two figures.