Continue to step off in this manner until you havedivided the circle into six equal parts. If the points ofintersection between the arcs and the circumferenceare connected as shown in figure 2-13, the lines willintersect at the center of the circle, forming angles of60 degrees.Figure 2-12.—Two methods used to divide a line into equalparts.point A, draw a straight line tangent to the arc that isbelow point B. Do the same from point B. With thedividers set at any given distance, start at point A andstep off the required number of spaces along line ADusing tick marks-in this case, six. Number the tickmarks as shown. Do the same from point B along lineBC. With the straightedge, draw lines from point 6 topoint A, 5 to 1, 4 to 2, 3 to 3, 2 to 4, 1 to 5, and B to6. You have now divided line AB into six equal parts.When the method shown in view B of figure 2-12is used to divide a line into a given number of equalparts, you will need a scale. In using this method, drawa line at right angles to one end of the base line. Placethe scale at such an angle that the number of spacesrequired will divide evenly into the space covered bythe scale. In the illustration (view B, fig. 2-12) the baseline is 2 1/2 inches and is to be divided into six spaces.Place the scale so that the 3 inches will cover2 1/2 inches on the base line. Since 3 inches dividedby 6 spaces = 1/2 inch, draw lines from the 1/2-inchspaces on the scale perpendicular to the base line.Incidentally, you may even use a full 6 inches in thescale by increasing its angle of slope from the baselineand dropping perpendiculars from the full-inchgraduation to the base line.To divide or step off the circumference of a circleinto six equal parts, just set the dividers for the radiusof the circle and select a point of the circumference fora beginning point. In figure 2-13, point A is selectedfor a beginning point. With A as a center, swing an arcthrough the circumference of the circle, like the oneshown 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 haveto do is to bisect one of these 60-degree angles by themethod described earlier in this chapter. Bisect the30-degree angle and you have a 15-degree angle. Youcan construct a 45-degree angle in the same mannerby bisecting a 90-degree angle. In all probability, youwill have a protractor to lay out these and other angles.But just in case you do not have a steel square orprotractor, it is a good idea to know how to constructangles of various sizes and to erect perpendiculars.Many times when laying out or working withcircles or arcs, it is necessary to determine thecircumference of a circle or arc. For the applicablemathematical formula, refer to appendix II of this text.Circumference RuleAnother method of determining circumference isby use of the circumference rule. The upper edge ofthe circumference rule is graduated in inches in thesame manner as a regular layout scale, but the loweredge is graduated, as shown in figure 2-14. The loweredge gives you the approximate circumference of anycircle within the range of the rule. You will notice infigure 2-14 that the reading on the lower edge directlybelow the 3-inch mark is a little over 9 3/8 inches. ThisFigure 2-13.—Dividing a circle into six equal partsFigure 2-14.—Circumference rule.2-5

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