60 degree angles have a special place in drawing nineteenth century fortifications; 60 degree was considered the minimum measure for any salient angle: angles that were any more acute were too easily destroyed by the erosive effects of weather, too easily battered by enfilading artillery fire, and limited the interior space available to the defenders beyond reasonable expectation. This construction provides a method to quickly and easily draw these minimum angles and, in studying fortification traces, to test the application of rule to individual fortifications.

Given a circle (O) construct a 60 degree angle inside the circle with its vertex on the circumference.

Draw a diameter (AB) through the center of the circle (O).

Using Point B as center describe an arc of a circle whose radius is equal to the radius of the circle, being careful to cut the circumference of the circle at two points (C and D).

Produce two right lines from Point A, the vertex of the 60 degree angle, to Points C and D.

Angle CAD measures 60 degrees.

~ An Instructive Animation Wherein the Foregoing Construction is Visually Explained ~