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.

200

DESCRIPTIVE GEOMETRY

Knowing the relation of the horizontal dimensions of the pillar
to the horizontal dimensions of the pedestal, we can determine the
distance between the corresponding faces of the pillar and pedestal.
Make o'-e' equal to the distance between the left-hand face of the
pillar and the left-hand face of the pedestal, and through e' draw
e'-f'-k' parallel to o'-z'. Make e'-f' equal to the distance between
the right-hand face of the pillar and the right-hand face of the
pedestal, and through f' draw f'-g' parallel to o'-x'. Make f'-k'
e.r. andf-g' each equal to
<.'w rn ^"^ B~ ~ the side of the square
f | -' ----, R — 7 ----1A pillar. Through f,
{ m> ' p, < | ' k', and g' draw the
l lM I I vertical straight lines
l II I I i N IL f'-l', k'-n', and g'-'.
l{ { I _L ~/ '_O Make f'-l' equal to
fy, D M 16 athe altitude of the
[' \'^ rIG. 176
k t I \ pillar and complete
] ^\ / 1 the drawing.
\qr ~ 440. Problem 305. To make an
|6r ~ isometric projection of an hexagonal
prism.
FIG. 175 Analysis. Imagine the hexagonal
prism to be inscribed within a rectangular prism whose rectangular bases circumscribe the hexagonal bases of the given prism, and whose altitude is equal to
that of the given prism.
Draw the isometric projection of the rectangular prism and then
by reference to this prism make the isometric projection of the
hexagonal prism.
Construction. See Figs. 175 and 176. Let L-M-N-P-... -L,
Fig. 176, represent the hexagonal base of the given prism, and
let O-D-E-A, of the same figure, represent the circumscribing
rectangle of this base.
The isometric projection of the circumscribing prism is represented in Fig. 175 by o'-a'-e1-d'-b', where o'-a' and o'-dt are equal
respectively to the horizontal dimensions of this prism, and where
o'-b' is equal to the altitude of the prism.