Figure 4-3.-Dropping a perpendicular from a given pointto a line.Figure 4-3 shows a method of dropping aperpendicular from a given point to a line, usinga compass. To drop a perpendicular from pointP to AB, set the needlepoint of the compass atP and strike an arc intersecting AB at C and D.With C and D as centers and any radius largerthan one-half of CD, strike arcs intersecting atE. A line from P through E is perpendicular toAB.Figure 4-4 shows a method of erecting aperpendicular from a given point on a line. Toerect a perpendicular from point P on AB, set acompass to any convenient radius, and, with Pas a center, strike arcs intersecting AB at C andD. With C and D as centers and any radius largerthan one-half of CD, strike arcs intersecting atE. A line from P through E is perpendicular toAB.BISECTION OF A LINEA line can be bisected by trial and error withdividers; that is, by setting the dividers to variousFigure 4-5.-Bisecting a line.spreads until you find one that correctly measuresone-half the length of the line.Geometric construction for bisecting a line isshown in figure 4-5. To bisect the line AB, usethe ends of the line, A and B, as centers; set acompass to a radius greater than one-half thelength of AB; and strike arcs intersecting at C andD. A line drawn from C through D bisects AB.DIVISION INTO ANY NUMBEROF EQUAL PARTSA line may be divided into more than twoequal parts by trial and error with the dividers.Geometric construction for dividing a line into anynumber of equal parts is shown in figure 4-6. Todivide AB into 10 equal parts, draw a ray line CBfrom B at a convenient acute angle to AB. Set acompass to spread less than one-tenth of thelength of CB, and lay off this interval 10 timesfrom B on CB. Draw a line from the 10th intervalFigure 4-4.-Erecting a perpendicular from a given point ona line.Figure 4-6.-Dividing a line into any number of equal parts.4-2
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