In Fig. 484. let C B D E be the elevation of the required shape. Produce the sides C B and E D until they intersect at A. Then A will be the apex of the cone of which C B D E is a frustum. Draw the axis A G, which produce below the figure, and from a center lying in it draw a half plan of the article, as shown by F G H.
Fig. 484. - The Envelope of the Frustum of a Right Come Whose Upper Plane is
Oblique to its Axis.
Divide this plan into any number of equal parts, and from the points carry lines parallel to the axis until they cut the base line, and from there extend them in the direction of the apex until they cut the upper plane B D. Place the T-square at right angles to the axis, and, bringing it against the several points in the line B D, cut the side A E, as shown. From A as center, with A E as radius, describe the arc C1 E1, on which lay off a stretchout of either a half or the whole of the plan, as may be desired, in this case a half, as shown. From the extremities of this stretchout, C1 and E1, draw lines to the center, as C1 A and E1 A. Through the several points in the stretchout draw similar lines to the center A, as shown. With the point of the compasses set at A, bring the pencil to the point D in the side A E, and with that radius describe an arc, which produce until it cuts the corresponding line in the stretchout, as shown at D1. In like manner, bringing the pencil against the several points between D and E in the elevation, describe arcs cutting the corresponding measuring lines of the stretchout. Then aline traced through these intersections will form the upper line of the pattern, the pattern of the entire half being contained in C1 B1 D1 E1.