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.

204

DESCRIPTIVE GEOMETRY

isometric projections of a number of the points of the curve and
by tracing the required curve through these projections.
If the curve is of single curvature; locate, by reference to two
rectangular axes, a sufficient number of points on the curve to
determine the curve accurately. Find the isometric projections of
the rectangular axes and then by use of the known coordinate
distances determine the isometric projections of the points which
locate the curve.
If the curve is of double curvature, locate, by reference to three
rectangular coordinate planes, a sufficient number of points on the
X~~,lX,/'1 b"X curve to determine it.
'^^^^' J ^(, Find the isometric pro^^ Ad ^ ~jections of the coordinate
~a"l ~ ~ axes and then by use of
\ y the known coordinates,
FIG 182 ref erred to these axes,
determine the isometric
projections of the points which locate the curve.
445. Problem 309. To make an isometric drawing of a circle.
See Figs. 182 and 183. Fig. 183 represents the circle referred
to the four sides of a circumscribing square A-B-C-D, any two
of whose adjacent sides may be taken as rectangular axes of reference. The coordinates of a number of points, E, L, F, M, G, N,
K, P, on the circumference, including the points of tangency, are
here determined.
Fig. 182 shows the isometric projection of the circle in three
positions. First, when the isometric projections of the axes A-B and
A-D coincide with the isometric axes o'-x' and o'-z' respectively.
Second, when the isometric projections of the axes D-C and D-A