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.

SINGLE CURVE1) SURFACES

99

It must be remembered that in assuming the circular base and
the vertex, both at random, we have represented a cone at random
and not one of definite dimension
and position.
CASE 4. To represent the cone //
when the plane of its base is oblique to
H but perpendicular to V. See Fig.
107. The circle whose center is a, G --- ' l
represents the horizontal projection b'
of the base, and the straight line
f'-g' included between the two ver- f
tical lines f,-f' and g,-g', each drawn e
tangent to the circle whose center is
a,, represents the vertical projection d 9g
of the base. B represents the vertex
FIG. 107
and A-B represents the axis.
The horizontal projections of the extreme elements B-D and
B-E may now be determined as in the previous case.
The lines b'-f' and b'-g' represent the vertical projections of the
highest and the lowest elements, and therefore the extreme elements,
as seen from the observer's standpoint while projecting on V.
241. To assume a Rectilinear Element of the Cone. Let the cone
be represented with a circular base on H, as shown in Fig. 108.
Assume any point, as D, on
the circumference of the base.
Connect D and B by a straight
\ b,< I\ line. B-D, horizontally projected in b,-d, and vertically
^^ / ~ projected in b-d', is the required
____:d a':ea Le element.,,// /- 242. To assume a Point upon
the Surface of the Cone. Let the
cone be represented as in Fig.
Uby~~ ~108. Assume the horizontal
FIG. 108s
projection o, of the point at random. Draw b,-o,-d,-e, to represent the horizontal projection of
the element containing the point O. This element pierces H either