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144 FIRST PRINCIPLES OF concerned ; for if through two such intersecting solids a section plane is passed, the points where that plane cuts the surfaces of both solids will be at once shown. If, then, the two solids be imagined to be cut 8iiiin.Uaneov.sly by a number of planes, and the points of intersection of their surfaces by those planes be noted, a line drawn through those points will be the " line of penetration '' of one solid by the other. As the plane solids usually met with in machine details are prisms and pyramids, with their frustums, the problems in this connection will deal first with prisms penetrated by prisms. The first is Problem 66 (Fig. 170). Given the plan Xo. l y of two square pivsms A and B, of equal length, one penetrating the other at right angles ; to find their elevation and lines of penetration. As shown in the plan, A is the penetrated, and B the penetrating prism : the former having two of its sides parallel to the TP, while all four sides of the latter are perpendicular to it. The lines of intersection of the two, therefore, will only be seen on the front side of A, or that nearest to the eye in elevation. As that side is parallel to the TP, and the prism B penetrates it at right angles, the lines of penetration will coincide with those forming the front end of that prism. Therefore, find by projection the elevation of the prisms, in the positions shown in plan, and the lines ah, be, cd, da, in No. 2 will although representing the front end of prism B- be the lines of penetration sought. In this problem, as the four sides of the penetrating prism B are planes of intersection with the two sides or the one nearest to, and that .farthest from the TP of the penetrated one A, the use of any section planes in finding the lines of penetration is unnecessary.