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.

28

DESCRIPTIVE GEOMETRY

As profile planes are parallel the distance mpV-npv in Fig. 39
must be equal to the distance M-N.
55. Other Supplementary Planes of Projection. Supplementary
planes of projection may be assumed in any position whatever.
Fig. 40, which is a pictorial drawing, represents a, S^mpv \, supplementary plane of
projection U, assumed par| ^ \\ allel to the horizontal proQ _G__.__ \- -_ _! L jecting plane of the line
\ P \ | 7i-N2V.
nr-................. According to Section 5
the supplementary projecm,-... _mp, tion of M in this case is
I, IMU and the supplementary projection of N is
FIG. 89
NU. Therefore the supplementary projection of M-N is MU-NU.
It will be observed that because the supplementary plane of
projection is perpendicular to H, the supplementary projection of
any point, as M, will fall at.u.mu
the same distance from the \\ - /
horizontal trace U-ut of
the supplementary plane \
as the point M is from H, \ <
or, what is the same thing,.-____
as far as the vertical pro- MU /'
jection m' is from G-L. U, —
It will also be observed \
that the lines MU-mu
and m,-mu, are both per-,,
pendicular to U-u, at the
same point. /
Now if the supplementary plane U be revolved FIG. 40
about its horizontal trace as an axis until it coincides with H,
MU will fall at mu, upon a straight line drawn through m,