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will be the lines of penetration sought. 63. To find the same lines by the use of intersecting planes, it will be seen at once that if a plane be caused to pass through the axes of both prisms parallel to the VP, it would intersect the prisms in the points 1, 2, 3, 4, No. 2 ; and if a second plane, parallel to the first and tangent to the edge ab of the prism B, be passed through A, it would intersect the edge ab, No. 1, in the points 5 and 6, as the section of A made by this plane would be the parallelogram cdef shown in faint lines in No. 2, the points of intersection of the edge ab by it being 5 and 6, which, joined to 1 and 3 and 2 and 4, give the same lines of penetration as by the first method. It will be seen, on studying this figure, that the resultant lines of penetration are nothing more nor less than the intersections of pairs of planes at an angle, and it is in the judicious application of such section planes that the whole art of finding the lines of penetration of solids consists. It will, however, be evident that in the problem just solved, and that which follows it, their use in practice would be dispensed with, as the lines sought can be found at once by simple projection from the plans of the objects ; but, as it is advisable MECHANICAL AND ENGINEERING DRAWING 147 that at this stage the student should understand the application and use of such planes, they have been introduced thus early. For our next problem, the same solids are taken as in the last, but instead of both axes being parallel to the VP, that of the prism B is inclined at an angle to it. This position is shown in plan in No. 3, Fig. 171 a transfer of No. 1 at an angle to the VP or IL and it is required to find the elevation of the prisms, and their lines of penetra- tion when so posed.