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as the vertical pyramid has been moved round on its axis until the axial plane of both solids makes the required angle with the VP. The elevation and lines of penetration have then been found by direct projection from the plan No. 3 and elevation No. 2. The case in which two equal square pyramids penetrate each other in such a way that both have one of their greatest plane sections in one and the same plane, their axes being at right angles, is shown in Nos. 5 and 6 (Fig. 176). 69. Now, the greatest plane section of a square pyramid is evidently one obtained by cutting it through from apex to base in such a way as to divide its base diagonally into two equal triangles. Then, if two such pyramids as A and B (Fig. 176), equal in size, and at right angles to each other, be cut simultaneously by a plane passing through their axes and cutting their bases diagonally, their elevation, assuming them to be entire, and both axes parallel to the VP, will be as shown in No. 5, but without the lines of penetration 1, 2, 3 ; 4, 5, 6. To find these lines, first draw in the plan (No. 6) of the pyramids as if entire. Assume a vertical plane, tangent to the front edge x b of pyramid B, to cut through A to its base. It would intersect that base in its two front edges at points f^g, and its front slant edge in point i. Obtain by projection the elevation of the triangular section/, i, g thus produced 160 FIRST PRINCIPLES OF MECHANICAL AND ENGINEERING DRAWING 161' shown in faint lines in No. 5 and it will be found to cut the front edge x b of the prism B in points 2, 5 ; join these by straight lines to points 1, 3 and 4, 6 previously found and they will be the required