PROPOSITIONS OF GEOMETRY Table 2b. Geometric Constructions Machinery's Handbook, 31st Edition
67
To draw a line parallel to a given line AB , at a given distance from it: Using the compass, with any points C and D on AB as centers, draw with the compass circular arcs with the given distance as radius. Line EF , drawn with the straight edge to be tangent to (that is, touch without intersecting) the circular arcs, is the required parallel line. To bisect an angle BAC : With A as a center and any radius, use the compass to draw arc DE . With D and E as centers and a radius greater than one-half DE , use the compass to draw circular arcs intersecting at F . Line AF , drawn with the straight edge, divides the angle into two equal parts. F To draw an angle upon a line AB equal to a given angle FGH : With point G as a center and with any radius, draw arc KL . With A as a center and with the same radius, draw arc DE . Make arc DE equal in length to KL and draw AC through E . Angle BAC then is equal in length to angle FGH . To lay out a 60-degree angle: With A as a center and any radius AB , draw an arc BC . With point B as a center and AB as a radius, draw an arc intersecting at E the arc just drawn. EAB is a 60-degree angle. A 30-degree angle may be obtained either by bisecting a 60-degree angle or by drawing a line EG perpendicular to AB . Angle AEG is then 30 degrees.
E
F
A C
D B
D
B
A
F
C
E
H
C
L
E
A
B
G
K
D
C E
A
G
B
D
E
To draw a 45-degree angle: From point A on line AB , set off a distance AC . With a straight edge, draw perpendicular DC and set off a distance CE equal to AC . Draw AE . Angle EAC is a 45-degree angle.
B
A
C
C
To draw an equilateral triangle, with the length of the sides equal to AB : Draw AB with straight edge. With A and B as centers and AB as radius, use the compass to draw circular arcs intersecting at C . With the straight edge, draw AC and BC . Then ABC is an equilateral triangle.
A
B
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