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

43

106. Problem 44. Draw the two projections of a straight line passing through the point l = - 4, - 4, 2, running parallel to V, and
making an angle of 60 degrees with H.
107. Problem 45. Draw the two projections of a straight line
passing through the point M=- 4, 3, -1, running parallel to H,
and making an angle of 45 degrees with V.
108. Problem 46. Given the straight line [M= - 4, 5, 1; N= 4,
2, 6]; required to find the true distance between M and N, and to
determine the angle which the line makes with H.
Analysis. Revolve the line about an axis through M perpendicular to H until the line is parallel to V. The vertical projection of
any portion of the line in this new position will be equal in length
to the assumed portion of the line itself, and the angle which this
vertical projection of the line in this new position makes with G-L
will indicate the angle which the line itself in true position makes
with H.
109. Problem 47. Given the straight line [Ai=- 4, 5, 1; N= 4,
2, 6]; required to find the true distance between the points M and N,
and to determine the angle which the line makes with V.
Analysis. Revolve the line about an axis through M perpendicular to V until the line is parallel to H. The horizontal
projection of any portion of the line in this new position will
be equal in length to the assumed portion of the line itself, and
the angle which this horizontal projection makes with G-L will
indicate the angle which the line itself in true position makes
with V.
110. Problem 48. Draw the two projections of a straight line 5
units long, passing through the point M = 2, - 4, - 1, making an
angle of 30 degrees with H, and in such a position that its horizontal
projection makes an angle of 45 degrees with G-L.
Analysis. First draw the projections of the line when it passes
through the given point, is parallel to V, and makes the required angle with H. Then revolve the line about an axis
through the given point perpendicular to H until the horizontal
projection of the line makes the required angle with G-L. The
two projections of the line in this last position will be the required
projections,