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VP, then the elevation of that line will be a point in the VP, where the foot of the projector drawn through the original line touches the VP. These two cases embrace the principles involved in finding by projection the " elevation of an object when its plan is given," or pro- jection from the lower to the upper plane. Having previously worked out the problems of finding the " elevations " of any of the four plane geometrical figures from their "plans," we proceed now to show how the elevations of solid objects, whose sides or faces are plane figures, are obtained when their plans are given. As previously advised in the case of the cube, prism, etc., no difficulty will be met with in obtaining these projections, if the relations of the several sides of the original objects to each other are previously understood. Our first problem in this part of the subject is Problem 37. Given the plan of a rectangular slab of solid ma- terial, with its vertical sides inclined to the VP, to find its elevation. Let the rectangle ABCD, Fig. 126, Sheet 7, be the plan of the slab in the position stated in the problem. Thus shown, all its sides and ends are rectangular plane surfaces, the upper and under ones being assumed to be parallel to the HP. The parts of it that will be seen, looking in the direction of the arrow x, will be the end AB and the side BC. The points A, B and C are the upper ends of the corner edges, or lines, which have a length equal to the thickness of the slab ; therefore to find its elevation, through points ABC, draw projectors Aa, B6, Cc perpendicular to the IL into the upper plane or VP. If the 71