Continue to step off in this manner until you have
divided the circle into six equal parts. If the points of
intersection between the arcs and the circumference
are connected as shown in figure 2-13, the lines will
intersect at the center of the circle, forming angles of
Figure 2-12.Two methods used to divide a line into equal
point A, draw a straight line tangent to the arc that is
below point B. Do the same from point B. With the
dividers set at any given distance, start at point A and
step off the required number of spaces along line AD
using tick marks-in this case, six. Number the tick
marks as shown. Do the same from point B along line
BC. With the straightedge, draw lines from point 6 to
point A, 5 to 1, 4 to 2, 3 to 3, 2 to 4, 1 to 5, and B to
6. You have now divided line AB into six equal parts.
When the method shown in view B of figure 2-12
is used to divide a line into a given number of equal
parts, you will need a scale. In using this method, draw
a line at right angles to one end of the base line. Place
the scale at such an angle that the number of spaces
required will divide evenly into the space covered by
the scale. In the illustration (view B, fig. 2-12) the base
line is 2 1/2 inches and is to be divided into six spaces.
Place the scale so that the 3 inches will cover
2 1/2 inches on the base line. Since 3 inches divided
by 6 spaces = 1/2 inch, draw lines from the 1/2-inch
spaces on the scale perpendicular to the base line.
Incidentally, you may even use a full 6 inches in the
scale by increasing its angle of slope from the baseline
and dropping perpendiculars from the full-inch
graduation to the base line.
To divide or step off the circumference of a circle
into six equal parts, just set the dividers for the radius
of the circle and select a point of the circumference for
a beginning point. In figure 2-13, point A is selected
for a beginning point. With A as a center, swing an arc
through the circumference of the circle, like the one
shown at B in the illustration. Use B, then, as a point,
and swing an arc through the circumference at C.
If you need an angle of 30 degrees, all you have
to do is to bisect one of these 60-degree angles by the
method described earlier in this chapter. Bisect the
30-degree angle and you have a 15-degree angle. You
can construct a 45-degree angle in the same manner
by bisecting a 90-degree angle. In all probability, you
will have a protractor to lay out these and other angles.
But just in case you do not have a steel square or
protractor, it is a good idea to know how to construct
angles of various sizes and to erect perpendiculars.
Many times when laying out or working with
circles or arcs, it is necessary to determine the
circumference of a circle or arc. For the applicable
mathematical formula, refer to appendix II of this text.
Another method of determining circumference is
by use of the circumference rule. The upper edge of
the circumference rule is graduated in inches in the
same manner as a regular layout scale, but the lower
edge is graduated, as shown in figure 2-14. The lower
edge gives you the approximate circumference of any
circle within the range of the rule. You will notice in
figure 2-14 that the reading on the lower edge directly
below the 3-inch mark is a little over 9 3/8 inches. This
Figure 2-13.Dividing a circle into six equal parts
Figure 2-14.Circumference rule.