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.

44

DESCRIPTIVE GEOMETRY

Construction. See Fig. 54. The projections of the point M are
m,, m'. The projections of the line, when the line is parallel to V
and makes an angle of 30 degrees with H, are m,-n,, and m'-n",
where m,-n,, is parallel to G-L and where mr-n" is 5 units long
_____ m, and makes an angle of 30 degrees
', / with G-L.
ta /, When the line is revolved to its
' a / " final position, no will move in an arc
i':,, of a circle to n, and n" will move in!-________ a straight line parallel to G-L, to
I' a ~. n'. The required projections are then
I. -m,-n, and m'-n'.
The line just located is in the
third quadrant and runs from the
given point downward to the left
Fro. 54
FIG. 54 and toward V.
Consider other positions which the line may occupy and yet
satisfy the requirements of the problem.
111. Problem 49. Construct Problem 48 when M=- 2, - 5, 1.
112. Problem 50. Construct Problem 48 when 1M= 2, 5, 1.
113. Problem 51. Construct Problem 48 when M= 2, 2, - 6.
114. Problem 52. Draw the two projections
of a straight line 4 units long, passing through
the point M = 1, - 1, - 3, making an angle of \
45 degrees with V, and in such a position \
that its vertical projection makes an angle of m,
60 degrees with G-L. a:. -L
Analysis. First draw the projections of the I
line when it passes through the given point,
is parallel to H, and makes the required
angle with V. Then revolve the line about -mU
an axis through the given point perpendicu- FIG. 55
lar to V, until the vertical 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.
Construction. See Fig. 55. The projections of the given point
Ml are i,, m'. The projections of the line, when the line is parallel