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their elevation, as if they were entire, must first be drawn. Having done this as shown in No. 1 (Fig. 177), from it find by projection their plan also as if entire as given in No. 2. The points of intersection of the upper and lower edges of the pyramid B with A are at once seen in No. 1, to be 1, 2, 3, 4. Proceed as in the previous problem to find the section of A, by a vertical plane passing through it tangent to the front edge of B, and the points in that edge cut by it ; join these up to the first found points by straight lines as before, and they will be the lines of penetration in elevation. On finding the plans of these lines as before explained and shown in No. 2, the first part of the problem is solved. For its latter part, draw in as shown in No. 3 in the figure, a repeat of No. 2, but having its axial line a b at the required angle say 30 with the VP or IL ; and from it and No. 1 find by projection the elevation of the pyramids and lines of penetration in their new position. This view, if obtained in accordance with the pro- cedure already explained in a previous problem, will give No. 4 (Fig. 177) as the result. 70. As a concluding problem in the penetration of plane-surfaced solids, we give in No. 5 and No. 6 (Fig. 177) a case in connection with pyramids which sometimes occurs in practice viz., that wherein a M 102 FIRST PRINCIPLES OF MECHANICAL AND ENGINEERING DRAWING 163 square pyramid is penetrated by a similar solid, the relative position of the two being such that an axial plane passed through both gives a similar section in each, but divides them into dissimilar solids. The