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.

52

DESCRIPTIVE GEOMETRY

133. Problem 71. Given the straight line [M= 0, - 6, - 2;
N = 0, - 2, - 6]; required to find the points in which 1-N~ intersects H and V.
134. Problem 72. To find the distance between two given points
in space.
This distance will be measured on the straight line joining the
given points.
Analysis 1. If the straight line connecting the two points be
revolved about its horizontal projection as an axis into H, the line
will be seen in its true length (see Sections 26 and 87).
Analysis 2. If the straight line connecting the two points be
revolved about its vertical projection as an axis into V, the line
will be seen in its true length.
Analysis 3. If the straight line connecting the two points be
revolved about the horizontal projecting line of one of its points
as an axis until the line is parallel to V, the vertical projection of
the line in this revolved position will be equal in length to the
line itself (see Sections 26 and 104).
Analysis 4. If the straight line connecting the two points be
revolved about the vertical projecting line of one of its points as
an axis until the line is parallel to H, the._ _,'/~ horizontal projection of the line in this,, / revolved position will be equal in length, Ns / to the line itself.
a In,__ Construction 1. See Fig. 61. Let M,M, L and N represent the two given points.
\,Then m,-n, will represent the horizontal
'v ~ projection and mr-n' will represent the
vertical projection of the straight line
connecting these points. Following AnFIG. 61 alysis 1, revolve M-N about m,-n, as an
axis into H (see Section 87). M falls at mH and N falls at n~,
and mn-nH is the distance sought.
Construction 2. See Fig. 62. Let M and N represent the given
points. Following Analysis 4, revolve M-N about the vertical
projecting line of M until M-N is parallel to H (see Section 105).
M will remain stationary, but N will move, its vertical projection