[Illustration: Fig. 7. Use of Steel Square to Find Miter and Side of Octagon.]
In Fig. 7 the same process is shown applied to the octagon. The degree line in all the polygons is found by dividing 360 by the number of sides in the figure:
This gives the degree line for the octagon. Complete the process as was described for the other polygons.
By using the following figures for the various polygons, the miter lines may be found; but in these figures no account is taken of the relative size of sides to the foot as in the figures preceding:
Triangle 7 in. and 4 in. Pentagon 11 " " 8 " Hexagon 4 " " 7 " Heptagon 12½ " " 6 " Octagon 17 " " 7 " Nonagon 22½ " " 9 " Decagon 9½ " " 3 "
The miter is to be drawn along the line of the first column, as shown for the triangle in Fig. 8, and for the hexagon in Fig. 9.
In Fig. 10 is shown a diagram for finding degrees on the square. For example, if a pitch of 35 degrees is required, use 8-13/32 on tongue and 12 on blade; if 45 degrees, use 12 on tongue and 12 on blade; etc.
[Illustration: 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.
[Illustration: 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.