3. A diagonal drawn from the center point on the lower horizontal edge of

the square through the center point on the far edge will intersect the

extension of the top edge as shown in Figure 2-14. A vertical dropped from

this intersection will add the equivalent of a half to that side. As you

can see, this process can be continued as many times as necessary, and the

sections so established can be divided in turn.

4. Now suppose you are asked to draw in perspective a bookcase 36 inches

high, 24 inches wide, and 12 inches deep.

Since the 36 inches can be

divided into 18 inches or 9 inches but not into 24 or 12, it will be better

to make the basic cube 24 inches, which can easily be divided into 12 inches

and to which 12 inches can be added. In Figure 2-15, these dimensions have

been established. Note that the same method used for multiplying areas in a

horizontal direction, shown in Figure 2-14, may be applied to multiplying

them in a vertical direction.

Figure 2-15. Finding the outside dimensions

of a bookcase in perspective.

5. Suppose that the bookcase is constructed of boards which are 1 inch

thick. The top shelf is 8 inches high; that is, the upper front edge is 9

inches from the top of the bookcase, and the lower shelves are 12 inches

high, that is, 13 inches including the width of one shelf, with the lowest 1

inch shelf resting on the floor. Notice that 9 inches is one-fourth of the

total height of the bookcase, which should make it easy to find this

dimension. A diagonal may be used to create a 36-inch square, as shown in

Figure 2-6, and diagonals may be used to locate the top shelf, as shown in

Figure 2-16.

Figure 2-16.

Locating the shelves of the bookcase