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

39

93. Problem 31. Given the straight line [M = - 6, 0, - 5; N = 6,
0, - 2] and the point 0 = 0, - 4, 6; required to revolve 0 about
M-N into V.
94. Problem 32. Given the straight line [Ml= 6, 0, 6; N= 6,
0, - 2] and the point 0 = 0, 4, - 6; required to revolve 0 about
M-N into V.
95. Problem 33. Given a straight line in space parallel to H, also
given a point in space; required to revolve the point about the line
as an axis until the plane of the point and the line is parallel to H.
Analysis and Construction. In Fig. 47 let Ml-N represent the
given line and let 0 represent the given point.
As in Problem 25, o,-a, represents the horizontal trace of the
plane containing the point and perpendicular to the axis, and
therefore the plane in which 0 moves during revolution.: ':a, i'0f o,,a:
a,,o,
_________ _ 'It — n
G-!m' o" 0 d'!n' a '
p',b" an
/'n
FIG. 47 FIG. 48
After revolution the horizontal projection of the point 0 must
fall somewhere upon o,-a, produced, and at a distance from a, equal
to the hypotenuse of a right-angled triangle whose base is equal
to o,-a, and whose altitude is equal to o'-d', since the axis is not
in H but at a distance b-d' below H.
The point o,, represents the horizontal projection of 0 in the
required revolved position, and o", at the same distance below H
as iM-N and in a straight line through o, perpendicular to G-L,
represents the vertical projection of 0 in this position.
96. Problem 34. Given a straight line in space parallel to V, also
given a point in space; required to revolve the point about the line as an
axis until the plane of the point and the line is parallel to V. See Fig. 48.