Mathematics for Carpenters and Builders - Carpenter's and Builder's Math, Plans, and Specifications - page 158

In Figure 5-35, bisect the inclination of the given lines AB and CD
by the line NO . From a point P in this line, draw the perpendicular
PB to the line AB , and on P , describe the circle BD , touching the
lines and the centerline at E . From E , draw EF perpendicular to the
center line intersecting AB at F , and from F , describe an arc EG
intersecting AB at G . Draw GH parallel to BP , thus producing H ,
the center of the next circle, to be described with the radius HE , and
so on for the next circle IN .

B F G

A

O

E

P

H

I

N

D

C

Figure 5-35 To describe a series of circles tangent to two in-
clined lines and tangent to each other.

Problem 15
To construct an equilateral triangle on a given base.
In Figure 5-36, with A and B as centers and a radius equal to
AB , describe arcs l and f . At their intersection C , draw lines CA
and CB , which are the sides of the required triangle. If the sides are
to be unequal, the process is the same, taking as the radii the lengths
of the two sides to be drawn.

Figure 5-36 To construct an
equilateral triangle on a given
base.

I

C

f

A B