Machinery's Handbook, 31st Edition
66 PROPOSITIONS OF GEOMETRY The geometric constructions below are produced with a compass, protractor, and straight edge. The compass point marks the “centers” in the constructions that follow. The techniques described also apply for electronic drafting programs. As the section pro- gresses, some constructions rely on previous ones. Table 2a. Geometric Constructions
C
To bisect a line segment (divide it into two equal parts): With the ends A and B as centers and a radius greater than one-half the line segment, use the compass to draw circular arcs. Through intersections C and D , use the straight edge draw line CD . This line bisects AB and is also perpendicular to AB .
A
B
D
To draw a perpendicular to a line from a point A on that line: With A as the center and with any radius, use the compass to draw circular arcs intersecting the given line at B and C . Then, with B and C as centers and a radius longer than AB , draw circular arcs intersecting at D . With the straight edge, draw line DA . This line is perpendicular to BC .
D
B
C
A
To draw a perpendicular line from a point A to C at the end of line AB : Draw line AB , and then with any point D not on AB as center, use the compass to draw a circle intersecting AB at E . Draw a line through E and D intersecting the circle at C ; then join AC . This line is the required perpendicular. To draw a perpendicular to a line AB from a point C at a distance from it: With C as center, use the compass to draw an arc intersecting the given line at E and F . With E and F as centers, draw circular arcs with a radius longer than one-half the distance between E and F . These arcs intersect at D . Line CD , drawn with the straight edge, is the required perpendicular. To divide a line segment AB into a number of equal parts: Assume line segment AB is to be divided into five smaller segments of equal measure. Draw line AC at an acute angle with AB . Mark off on AC five parts of equal measure, any convenient length. With the straight edge, draw the segment B -5 and then draw lines parallel to B -5 through the other division points on AC . The points where these lines intersect AB are the required division points.
C
D
A
E B
C
A
B
E
F
D
C
5
4
3
2
1
A
B
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