bisected a line, erected a perpendicular from a given
point on a line, and drew parallel lines by geometric
construction. Use those geometrical principles to do a
lot of layout problems rapidly and accurately.
You should also know how to BISECT AN
ANGLE. Angle ABC (fig. 12-19) is given. With B as a
center, draw an arc cutting the sides of the angle at D
and E. With D and E as centers, and with a radius greater
than half of arc DE, draw arcs intersecting at F. A line
drawn from B through the point F bisects the angle
DIVIDE A LINE INTO ANY GIVEN NUMBER
OF EQUAL PARTS. You need only a straightedge and
a compass. Figure 12-20 illustrates the dividing of a line
into 10 equal parts. To divide line AB into 10 equal
parts, draw random line CB from B at a convenient
acute angle to AB. Set a compass to a spread less than
one-tenth of the length of CB, and lay off this spread 10
times from B on CB. Project the intermediate points of
intersection on CB to AB by lines parallel to the line
between the 10th point of intersection and A. The
projected points of intersection divide AB into 10 equal
DIVIDE OR STEP OFF THE CIRCUMFERENCE
OF A CIRCLE into six approximately equal parts. Set
the dividers for the radius of the circle and select a point
Figure 12-l8.--Laying out a drip pan with dividers.
a point, swing a wide arc like the one shown in the
second step in figure 12-18.
Step 3. Extend the end and side lines as shown in
the last step in figure 12-18, andcomplete the stretchout
by connecting the arcs with a scriber and straightedge.
Step 4. Now lay out tabs like those shown in figure
12-11. Their size is determined by the diameter of the
rivet, which in turn is determined by the thickness of the
sheet. All that remains to be done now is to transfer the
pattern to the sheet, cut the metal, and form it.
You have seen how a pan can be laid out without a
steel square by the use of geometric construction. You
Figure 12-20.--Dividing a line into any number of equal parts.