66 FIRST PRINCIPLES OF front and back faces of the cube the thickness of its sides, and through 5' 5" draw lines parallel to those sides ; through points 3, 4 in Fig. 108 draw projectors to cut the parallels drawn through 5' 5" in points 3' 3", 4' 4" ; the surface included between the inner and bound- ing lines of the figure is that exposed by the cutting plane AC in passing through the cube, and is indicated by cross or section-lining. As the removal of the part of the cube to the left of the cutting plane AC exposes its interior, the angle formed within it at point 5, by the meeting of the sides AD, DC, will be seen as a line between points 5" 5" in Fig. 110. With the drawing in of this line as shown, the required sectional elevation is complete. Again Problem 35. Let the cube Fig. 108 be cut "by a plane 8P, and let it be required to give a side elevation of it, when the part cut off to the left is removed. Proceed as in Fig. 103, Sheet 3, to obtain by projection the top and bottom edges, and the front and back faces of the cube, and letter them as before. Through points S P in the section plane Fig. 108, draw projectors parallel to the IL, cutting the line f g (Fig. Ill) in points sp, and through these points parallel to ff' draw the lines s's", pp. Then to show the thickness exposed by the cutting plane in passing through the sides AB, BC of the cube, through points 1, 2 (Fig. 108), and parallel to the IL, draw in Fig. Ill the lines IT', 2 '2". Parallel to, and at a distance from the front and back faces fg, f'g', equal to the thickness t of the cube, draw the lines 1', 2' ; 1", 2" : cross-line the surface between the inner and bounding lines of the section as shown, and as in the case of the section obtained in