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THE INTERSECTIONS OF PLANE SOLIDS (continued). 66. BEFORE passing directly to the finding of the lines of penetration of one pyramid by another, the solution of such a problem will come much easier to the student if some preliminary practice is had with the case of a pyramid penetrating a prism. As such a combination is often used in practice, in giving form to simple ventilators, cowls, etc., we give as problems in this connection those in which the two solids are combined for such purposes. The first combination, shown in plan and elevation in No. 1 and No. 2 (Fig. 174), is the simplest possible, it being that of a square prism, with its axis vertical and sides parallel and perpendicular to the VP, penetrated by a square pyramid, the axis of which is parallel to both the VP and HP, and in the same piane as that of the prism. From the relative position of the two solids, as shown in the figure, it is evident that neither in plan nor elevation will any lines of penetra- tion be visible in this case, as the two faces a and b of the prism, which are penetrated by all four faces of the pyramid, are in plan and elevation through being perpendicular to both planes of projection each represented by one straight line only, with which the actual lines of penetration coincide, and therefore cannot be seen. Had the faces of the prism, however, been in the least inclined to the VP still remain- ing perpendicular to the HP, then one line of penetration only would have come into view, dependent upon the inclination of the axis of the pyramid to the VP. For all purposes where combinations of solids are used to give form to mechanical details, it is usual in practice to so combine them that their intersections shall be symmetrical. That is to say, that when the