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To find it, choose a suitable number of points in the given line AB, No. 1, say at 1, 2, 3, 4 ; project these over on to ab, No. 2, and produce the projectors to meet the datum plane cb, as shown ; the exact position in plan of any of these points can now be fixed. From a, 1', 2', 3', 4', b, No. 2, let fall projectors into the lower plane, or HP, and on these, in No. 3, set off from the IL the distances that the corresponding points in AB, No. 1, are from Ap ; through the points thus found draw the line a' b', and it will be the plan of the given compound curved line sought. By letting fall similar projectors from the points in AB, No. 1, and setting off on them the distances that their corresponding points in ab, No. 2, are from the datum plane cb, a similar plan of the com- pound curved line will be obtained, as shown at a f B', No. 4, to that found in No. 3, but at right angles to it, as AB, No. 1, is at right angles to ab, No. 2. From the foregoing explanation the student should be enabled to apply the principles involved to the projection of any single curved line, whether simple or compound ; but to show the actual appearances the same curved line will assume in projection when occurring in different positions, we give one problem in this connection before pass- ing on to the projection of curve-bounded figures. By way of making the problem more interesting, and of practical application, we will take an ordinary curve such as is given to the foot of a square or six-sided column combined with a straight line, and let the problem be Problem 46. Given the elevation of a combined curved and right line parallel to tJie VP, to find its plan and elevation when it makes ang given angle with the VP or HP.