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

ABC.

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

Parts.

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

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

12-7