Elements of descriptive geometry, with applications to isometric projection and othe forms of one-plane projection; a text-book for colleges and ingineering schools by O. E. Randall.

RELATING TO POINT, LINE, AND PLANE

51

projection of the point and the point itself in which M-N intersects H.
Check. See Fig. 60. Project M-N upon the supplementary
plane U, which is assumed parallel to the horizontal projecting
plane of Ml-N.
According to Section 55 the line rnuH-nu, is the supplementary
projection of M-N. Produce muH-nuH to meet the horizontal trace
U-u, in au,, which is the supplementary projection of the point in
which M1-N intersects H. According to Section 55 the points a,
and au, should be in the same straight line perpendicular to U-u,.
CASE 2. To find the point in which the line intersects V.
Analysis. Since the point in which the line intersects V must
be both in V and in the line itself, its horizontal projection must
be both in G-L and in the horizontal projection of the line, and
therefore at their intersection. The vertical projection of the
required point must be both in a straight line perpendicular to
G-L through the horizontal projection just found, and also in the
vertical projection of the line, and therefore at their intersection.
Since the required point is in V, it must be coincident with its
vertical projection just found.
Construction. See Figs. 59 and 60. Produce the horizontal projection of the line to meet G-L at b,. At this point draw a straight
line perpendicular to G-L to meet the vertical projection of the
line at b', which is the required point.
Check. See Fig. 60. Project M-N upon the supplementary
plane W, which is assumed parallel to the vertical projecting
plane of M-N, and proceed as in Case 1.
129. Problem 67. Given the straight line [M= - 6, - 6, 2;
N = 6, 2, - 6]; required to find the points in which M-N intersects
H and V.
130. Problem 68. Given the straight line [M==- 6, - 4, 2;
N = 6, 2, 2]; required to find the point in which M-1N intersects V.
131. Problem 69. Given the straight line [M= 6, 2, - 6;
N = - 6, 2, 3]; required to find the point in which M-N intersects H.
132. Problem 70. Given the straight line [M= - 6, 6, - 6;
N= 6, - 6, 6]; required to find the points in which il-N intersects
H and V.