This section is from the book "Hicks' Builders' Guide", by I. P. Hicks. Also available from Amazon: Hicks' Builders' Guide.

Fig. 85. - Finding the Plumb Cut of the Valley Rafters. an Octagon Roof.

Fig. 86. - Finding the Lengths and Bevels of Hips and Jacks on

Let us now consider the problem of finding the lengths and bevels of octagon hips and jacks by the easy system. Referring to Fig. 86, let A B C D E and F represent the wall plate line, F G being the run of common rafter, G H the rise and F H the length of common rafter. Next swing the common rafter round to a perpendicular position, as F I. Set off half the side of the octagon A J and square up the length of the common rafter J K. Draw K I for the ridge line and K A for the hip. Space and draw the jacks perpendicularly from A J to the hip as shown. The bevel at R is the bevel across the back and the plumb cut is the same as that of the common rafter shown at H. The length and bevels will be the same on each side of the octagon, hence further explanation of Fig. 86 is unnecessary.

The cuts of jacks in an octagon, hexagon or a polygon of any description may be found in the following manner. Referring to Fig. 87, let A B represent the length of the side, and from the center set off the length of the common rafter C D. Draw A D and B D for the length and position of hips Space the jacks on the line A B and draw perpendicular to the hips as shown, which will give their lengths. A bevel set in the angle at E will give the bevel across the back, the down bevel being the same as that of the common rafter. Fig. 87 refers only to the length and bevel of the jacks, but the length and cuts of all the rafters in any regular polygon may be found in the following manner : Referring now to Fig. 88 let A B C D and E represent four sides of an octagon. Set off the center of one side as B F, and square into the center G F,which is the run of the common rafter.

Square up the rise G H and draw F H for the length of the common rafter. The bevel at H is the top bevel, and at F the bottom bevel. G E being the run of the hip, square up the rise G I and draw E I for length of hip rafter. The bevel at I is the top bevel, and at E the bottom bevel. From the center of C D set off the length of common rafter J K, which should be the same length as F H. Draw K C and K D for the position of the hip rafters for finding the length and bevel of the jacks. Space the jacks on the line C D and draw perpendicular to the hips as shown, which will give the lengths. The bevel shown at L is the bevel across the back, the down bevel being the same as that of the common rafter.

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