DIVISION INTO ANY NUMBER
OF
EQUAL PARTS A line may be divided into more than two
equal
parts by trial and error with the dividers. Geometric
construction for dividing a line into any number
of equal parts is shown in figure 46. To divide
AB into 10 equal parts, draw a ray line CB from
B at a convenient acute angle to AB. Set a compass
to spread less than onetenth of the length
of CB, and lay off this interval 10 times from
B on CB. Draw a line from the 10th interval
Figure 46.Dividing a line into any number of equal parts.
Figure 47.Using a scale to lay off equal intervals on a random
line.
to A, and project the other points of intersection from
CB to AB by lines parallel to the first one. The
projected points of intersection divide AB into
10 equal parts.
Figure 47 shows how you can use a scale to lay
off equal intervals on the ray line.
DIVISION INTO
PROPORTIONAL
PARTS
Figure 48 show’s a method of dividing
a
line into given proportional parts. The problem
here is to divide the line AB into parts
that are proportional as 2:3:4. Lay off
ray line CB from B at a convenient acute
angle to AB. Set a compass to a convenient
spread, and lay off this interval from
B on CB the number of times that is
equal to the sum of the figures in the proportion
(2 + 3 + 4 = 9). Draw a line from the
point of intersection of the last interval to
A, and use a straightedge and triangle to project
the second and fifth intercepts on CB to
AB by lines parallel to the first one. The projected
intercepts divide AB into segments that
are proportional as 2:3:4.
Here again, you could use a scale to lay off nine
equal intervals on CB.
