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.

SUPPLEMENTARY PLANES OF PROJECTION

29

perpendicular to U-u, and at a distance from U-u, equal to the
distance of M from H. For the same
reason NU will fall at nuH, and the line
muH-nuH will represent in revolved\ B
position the supplementary projection
of the line M-N. \.mu,
Fig. 41 shows how the projections
of Fig. 40 will appear after the planes nu
H, V, and U have taken their position \
of coincidence. \.'\
Fig. 42 represents a supplementary \ -L
plane of projection assumed parallel to
the vertical projecting plane of a line
M-N. This plane is perpendicular to
V and its vertical trace is U-u'. The
supplementary projection of M is MU, m
the supplementary projection of N is
NVU, and the supplementary projection FIG. 41
of the line is MU-NU.
It will be observed that the supplementary projection of any
point, as M, upon this
U\, ~.. \plane is at the same,:"I. \ \s distance from V as the
point itself.
It will also be ob-. - / served that the lines
\UI ^ ^* —E::^MU-mu' and m'-mu' are
' \ / n''nuV both perpendicular to
U-uZ at the same point.
Now if the supple/ mu \ \ mentary plane U be re-..... \ volved about its vertical
/' \ \ trace as an axis until it
/ \ muV coincides with F, MU
will fall at muV upon
FIG' 42
a straight line drawn
through m' perpendicular to U-u' and at a distance from U-u'

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