Fig. 8. Use of Square to Find Miter of Equilateral Triangle.
In [Fig. 11] is shown the relative length of run for a rafter and a hip, the rafter being 12 inches and the hip 17 inches. The reason, as shown in this diagram, why 17 is taken for the run of the hip, instead of 12 as for the common rafter, is that the seats of the common rafter and hip do not run parallel with each other, but diverge in roofs of equal pitch at an angle of 45 degrees; therefore, 17 inches taken on the run of the hip is equal to only 12 inches when taken on that of the common rafter, as shown by the dotted line from heel to heel of the two squares in [Fig. 11].
Fig. 9. Use of Square to Find Miter of Hexagon.
In [Fig. 12] is shown how other figures on the square may be found for corners that deviate from the 45 degrees. It is shown that for a pentagon, which makes a 36-degree angle with the plate, the figure to be used on the square for run is 14⅞ inches; for a hexagon, which makes a 30-degree angle with the plate, the figure will be 13⅞ inches; and for an octagon, which makes an angle of 22½ degrees with the plate, the figure to use on the square for run of hip to correspond to the run of the common rafters, will be 13 inches. It will be observed that the height in each case is 9 inches.
Fig. 10. Diagram for Finding Pitches of Various Degrees
by Means of the Steel Square.
[Fig. 13] illustrates a method of finding the relative height of a hip or valley per foot run to that of the common rafter. The square is shown placed with 12 on blade and 9 on tongue for the common rafter; and shows that for the hip the rise is only 67⁄16 inches.