The essentials of descriptive geometry . Fig. 53. intersection may be found by passing an auxiUary plane Uthrough S and T parallel to H. B and N when joined give theplan view bn and the elevation bn of the required intersectionof the planes S and T. 55. Special Cases, i. Find the intersection of two planeswhen one pair of traces are parallel. 2. Find the intersection of two planes which are parallel tothe G. L. 56. Proposition 9. Given a plan and elevation of a line tofind where it pierces a given plane. PROBLEMS ON POINTS, LINES, AND PLANES 65 Discussion. If any plane be passed through the gi
The essentials of descriptive geometry . Fig. 53. intersection may be found by passing an auxiUary plane Uthrough S and T parallel to H. B and N when joined give theplan view bn and the elevation bn of the required intersectionof the planes S and T. 55. Special Cases, i. Find the intersection of two planeswhen one pair of traces are parallel. 2. Find the intersection of two planes which are parallel tothe G. L. 56. Proposition 9. Given a plan and elevation of a line tofind where it pierces a given plane. PROBLEMS ON POINTS, LINES, AND PLANES 65 Discussion. If any plane be passed through the given hne itwill contain all points of that hne. It will, therefore, containthe required point. Since the required point lies in the givenplane and in the auxiliary plane it will lie on their line of inter-section. If then the line of intersection be found and the point. Fig. 54. common to it and the given line be located it will be the requiredpiercing point. Construction. In Fig. 54 is shown the plan and elevation ofa timber whose center line is OP. The problem is to find thepoint where this Hne OP pierces the plane tTt. Pass the auxil- 66 ESSENTIALS OF DESCRIPTIVE GEOMETRY iary plane R through OP. Since the required piercing point liesin the plane R and in the given plane T it will lie on their inter-section MN. (See Proposition 8.) The required point lies onMN and OP; therefore, it will be at the intersection of these twolines or at Q. q then is the plan and q is the elevation of therequired point. It should be noted that any auxiliary plane through OP willserve, but, for convenience in drawing, one which is perpendicularto H or V should be used. The points where the edges of thetimber pierce T may be found in a similar manner and whenjoined give the plan and elevation of the section cut from thetimber by plane T. 57. Special Cases. Find where a l
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