To find the various Angle* and proper Dimensions of Materials whereby to construct any figure whose form is the Frustum of a proper or inverted Pyramid, as Hipped Roofs, Mill Hoppers, etc.

Fig. 26.

Let A B C D be the given dimensions of plan for a roof, the height R T also being given ; draw the diagonal A R, meeting the top or ridge R s on plan; from R, at right angles with A R and equal to the required height, draw the line R T, then T A, equal the length of the struts or corners of the roof; from A, with the distance A T, describe an arc T l, continue the diagonal A R until it cuts the arc T l, through which, and parallel with the ridge R s, draw the line m n, which determines the required breadth for each side of the roof: from A, meeting the line m n, draw the line A o, or proper angle for the end of each board by which the roof might require to be covered; and the angle at T is what the boards require to be made in the direction of their thickness, when the corners or angles require to be mitred.