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

FIG. 26.

Let ABCD be the given dimensions of plan for a roof, the height RT also being given; draw the diagonal AR, meeting the top or ridge Rs on plan; from R, at right angles with AR and equal to the required height, draw the line RT, then TA, equal the length of the struts or corners of the roof; from A, with the distance AT", describe an arc Tl, continue the diagonal AR until it cuts the are T1, through which, and parallel with the ridge Rs, 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 Ao, 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.