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A and B, No. 1, draw the lines AC, BD, No. 2, and the required elevation is obtained. Now, let the cylinder be inclined to the IIP, at an angle of 4$ its axis being still parallel to the VP and its plan when in that position be required. First draw in the elevation of the cylinder in the given position, as in No. 3. Its ends AB and CD are now inclined to the IL or HP, and will in plan become ellipses as explained in Problem 40 because they are circular, but inclined to the plane the HP -on which their projections are required. Now, in viewing the cylinder in this position from above, or in the direction of the arrow, only one of its ends, AB, will be seen, the other, CD, being by its inclination in- visible. To find its plan when so inclined, first draw in the plan of its axis a a ; on it obtain by projection the plan of the end AB, No. 3, as shown by the ellipse Al, B2 ; through points 1 and 2, in this ellipse, draw lines parallel to the IL, which will be plans of the sides of the cylinder seen from above, or along the line a'a t No. 3 ; then find by projection the plan of that part of the bottom edge of the cylinder that will be seen, and the required plan will be obtained. Again, let the cylinder, as in No. 5, have its axis inclined to the VP, at an angle of 39, but parallel to the HP, and its elevation be required. To obtain this, proceed as in the last case, by getting first the 100 FIRST PRINCIPLES OF MECHANICAL AND ENGINEEEING DRAWING 101 elevation of the axis, and then finding by projection the two ends of the cylinder upon it, and drawing in its sides as shown in No. 6.