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.

198

DESCRIPTIVE GEOMETRY

By Section 434 find m' and n', the isometric projections of the
two given points. The line m1'-n' is the required projection.
436. Problem 301. To find the isometric projection of a square
card when the coordinates of its four vertices with reference to two
^^ '! ~ rectangular axes are known.
~>/^ q ) \ N. x'/ In Fig. 171 let o'-x' and o'-z'
represent the isometric projec-.s.._. / tions of the two axes to which
>'^ >~ the card is referred.
By Section 433 find the isometric projections of the four
yle ~ vertices Mi, iV, P, and Q.
The polygon m'-n'-p'-q' is the
FIG. 171 projection sought.
The projection may be made with reference to the axes o'-x
and o'-y', or with reference to the axes o'-y' and o'-z'.
437. Problem 302. To find the isometric projection of a triangular
card when the coordinates of its three vertices with reference to three
rectangular coordinate planes are known.
In Fig. 172 let o'-x', o'-y', and o'-z' represent the isometric
projections of the axes to whose planes the card is referred.
By Section 434 find the iso-r zr
metric projections of the three I',
vertices il, N, and P. The tri-
angle m'-n'-p' is the projection I |
sought. l I
438. Problem 303. To make an I -
isometric projection of a cube.
See Fig. 173. Let o'-x', o'-y',
and o'-z' represent the isometric
axes. Place the cube so that one
of its vertices shall coincide with
the origin of coordinates, 0, and so that its three adjacent edges
shall coincide with the three coordinate axes O-X, O-Y, and 0-Z.
The isometric projections of these three edges will fall on the
isometric axes, and the isometric projections of the remaining
edges will be parallel to these three axes.