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through x parallel to AB cuts a'c No. 2, will be the required elevation of the original point x given in No. 1, for the line last drawn may be assumed to be the base of a cone of a lesser height than the given one, x being a point in its base in the same position relatively that c or c is in the base of the larger or given cone. By a converse process to that here so fully explained, the plan of a point on the surface of a cone may be found from its given elevation. We now proceed to the projection of the conic sections, and as a first problem we take Problem 52 (Fig. 152). Given the plan and elevation of a cone, to find its sectional projections when cut by a plane, at an angle of oO ivith its axis. Let No. 1 and No. 2 be the given plan and elevation of the cone, and LS, No. 2, the line of section. Draw in the axial line No. 3, and 108 FIRST PRINCIPLES OF MECHANICAL AND ENGINEERING DRAWING 109 produce it into the HP. Choose any convenient points, as, 1, ^, 5, in LS, No. 1, and through them, parallel to the IL, draw lines to cut the sides Aa, B&', of the cone. These, being parallel to its base, will each be the edge-view of a circle or base of a small cone. To find the distance through the cone at the points 2, 3, 4, in LS, No. 2 for this is what is wanted to be known let fall from them projectors into No. 1, parallel to the axial line aa ; then from a, No. 1, as centre, and with radii equal to half the length of the lines drawn through 2, 3, 4, No. 2, draw arcs, cutting the projectors let fall from these points in 2'2", 3'3", 4'4", No. 1, the length between which is the distance through the cone at their corresponding points in