07 Dec




















formed by the meeting of those sides. Now the points a and b, in the line fg in No. 3, are evidently the plans of the lines required. There- fore, through them draw projectors into the VP, and they will cross the front face of the pyramid between the points 5, 6, and 7, 8 in its top and bottom edges, and will give the lines of penetration sought. These being put in, in full, and joined up to / and /', and a' respectively, will complete the solution of the problem. As shown in a previous problem, the lines of penetration just found can also be determined by assuming a section plane to pass vertically through the prism on the line of the front face of the pyramid giving the rectangular section a bed, No. 4 shown in faint lines, intersect- ing the triangular section first found in the points 5, 6, 7, 8 ; and thereby giving the lines of penetration sought. The second case of the penetration of a prism by a pyramid is that in which the prism is in the same position with respect to the VP as before ; but the pyramid penetrates it in such a way that an axial plane passing through both, divides each solid into two equal ones having triangular bases. Problem 72 (Fig. 174). A square prism, in the same position as in the last problem, is penetrated by a square pyramid having its sides equally inclined to both planes of projection ; required their plan and elevation and lines of penetration. With one exception, the plan of the solids in the positions given in the problem will be similar to that given in No. 3 (Fig. 174). The exception is caused by the altered position of the pyramid. The triangle efg in No. 3 represented & flat surface perpendicular to the VP one of the faces of the pyramid whereas in No. 5, the pyramid having

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