Stair-Building and the Steel Square / A Manual of Practical Instruction in the Art of Stair-Building and Hand-Railing, and the Manifold Uses of the Steel Square

by Fred. T. Hodgson; Morris Williams

To Find the Miter and Length of Side for any Polygon, with the Steel Square.

In [Fig. 5] is shown a pentagon figure. The miters of the pentagon stand at 72 degrees with each other, and are found by dividing 360 by 5, the number of sides in the pentagon. But the angle when applied to the square to obtain the miter, is only one-half of 72, or 36 degrees, and intersects the blade at ²³⁄₃₂, as shown in [Fig. 5].

Fig. 5. Use of Steel Square to Find Miter and Side of Pentagon.

By squaring up from 6 on the tongue, intersecting the degree line at a, the center a is determined either for the inscribed or the circumscribed diameter, the radii being a b and a c, respectively.

The length of the sides will be 8²³⁄₃₂ inches to the foot.