In Fig. 485, let G D H be the elevation of a right cone whose base is oblique to its axis, the pattern of which is required. It will be necessary first to assume any section of the cone at right angles to its axis as a base upon which to measure its circumference. This can be taken at any point above or below the oblique base according to convenience.
Therefore at right angles to the axis D O, and through the point G, draw the line G F. Extend the axis, as shown by D B, and upon it draw a plan of the cone as it would appear when cut upon the line G F. as shown by ABC. Divide the plan into any convenient number of equal parts, and from the points thus obtained drop lines on to G P. From the apex D, through the points in G F, draw lines to the base G H. From D as center, with D G as radius, describe an arc indefinitely, on which lay off a stretchout taken from the plan ABC, all as shown by I M K. From the center D, by which the arc was struck, through the points in the stretchout, draw radial lines indefinitely, as shown. Place the blade of the T-square parallel to the line G F, and, bringing it against the several points in the base line, cut the side D II, as shown, from F to H. With one point of the compasses in D, bring the other successively to the points 1, 2, 3, 4, etc., in F H, and describe arcs, which produce until they cut the corresponding lines drawn through the stretchout, as indicated by the dotted lines. Then a line, ILK, traced through these points of intersection, as shown, will complete the required pattern.
Fig. 485. - The Envelope of a Cone whose Rase is Oblique to its Axis.