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.

30

DESCRIPTIVE GEOMETRY

equal to the distance of M from V. For the same reason NU
will fall at nu", and the line mu'-nu" will represent in revolved
position the supplementary projection of the line M-VN.
Fig. 43 shows how the projections of Fig. 42 will appear after
the planes H, V, and U have taken their position of coincidence.
56. Revolution of the Supplementary Planes. After projection
has been made upon a supplementary plane of projection the plane
is revolved about either its horizontal trace or its vertical trace
until coincident with the corresponding plane of projection.
The revolution is always made in
such a way that that portion of the
/\ { supplementary plane above H or in
front of V, according as the axis is
U L in H or in V, shall move toward the
principal projections already made
"-. /upon H or V, and that that portion
/ / nux of the supplementary plane of projection below H or back of V shall
pm^~ ailmove in the opposite direction or
/ mu' away from the principal projections
on H or V.
G vmu~r Illustration of this practice may
IG. 43be seen in Fig. 36, where the supplementary projection of M-N upon
P back of V is revolved to the right, or away from the projection
m'-n'; also in Fig. 38, where that portion of the supplementary
plane P in front of V is revolved toward the left and that portion
back of V is revolved toward the right, the former toward and the
'latter away from the projection m'-n'; again in Fig. 40, where that
portion of the supplementary plane U below H is revolved toward
the right, or away from the projection m,-n,.
In case the supplementary plane is on the left of the magnitude, that portion of the supplementary plane above H or in front
of V, according as the axis of revolution is in H or in V, is revolved,
according to the rule, toward the right, or in a direction opposite to
that assumed by supplementaryplanes on the right of the magnitude.