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To put on the paper the new elevation, No. 3, in the required posi- tion, draw in the axial line at the required angle, and to it transfer the points in the same line, No. 1 ; through these draw ordinates as shown, and on them set off in points a, 1, 2, 3, 4, the corresponding lengths of the same lines in No. 1, and draw in the curve. To obtain its plan in this position, let fall projectors from the several points in it in the elevation, and through the corresponding points in the plan, No. 2, draw projectors parallel to the IL, cutting those let fall from No. 3 ; a line drawn through the points of intersection of these projectors will give a 1 BC, No. 4, the plan of the line required. In the foregoing, Nos. 1 to 4, the axial line about which the com- bined line has been supposed to rotate has in each case been assumed to be parallel to the VP. Let it now be supposed, while still inclined to the HP at the same angle as before, to be also inclined to the VP at an angle say, of 45, and let an elevation of the combined line in this position be required. To obtain this, we must first show in on the paper, the plan of the combined line in its new position with respect to the VP or IL, before we can proceed with its elevation. This means that the last- obtained plan of the combined line must be moved from its present position viz., that of having the assumed axial line c' C parallel to the VP to one in which that line will make an angle of 45 with the VP or IL ; and is tantamount to swinging the line on its end C, as a pivot, through an arc of 45 in such a way that each point in it while being swung is kept at the same height in its plane of rotation above the HP. This new position of the last-found plan of the line is therefore correctly shown, by drawing a line the assumed axial one at an angle