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plane OP in the diagram, all its vertical edges will be perpendicular to OP, and its horizontal ones parallel to it. Then as to its projections No. 3 and No. 4, although the cube itself in its new position No. 2 is inclined to the VP and HP, this has not in any way altered the relative position of the bounding edges of its faces in the projections, as the lines 1, 1' ; 2, 2'; 3, 3' ; 4, 4', are still parallel to each other, as well as those representing the top and bottom edges of the cube. To assist the student to a more complete realization of the position of the " planes of projection " with respect to the original object, in Fig. 163 let a line be drawn perpendicular to the IL through point 3' of the cube in No. 2. This line would then represent an end elevation of the YP, with the corner 3' of the cube touching it. If, then, the inclined plane OP, with the cube upon it, together with this vertical plane, be imagined to swing round on the HP through 90, the view of the cube shown at No. 3 would be identical with its appearance on the inclined plane when viewed at right angles to the YP. 57. With the foregoing explanation of the reasoning applied in finding the projection of the cube in its uncut state when inclined to the VP and HP at a given angle, there should now be no difficulty in obtaining its sectional projections required by the problem, as these are nothing more than similar views to those already found, with the MECHANICAL AND ENGINEERING DRAWING 129 130 FIRST PRINCIPLES OF exception that a portion of the solid is assumed to be removed, exposing the cut surface. The fact of the cube being in the same position as before, reduces