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.

98

9DESCRIPTIVE GEOMET RY

CASE 2. To represent a circular cone whose axis is perpendicular
to V and whose base is a right section. See Fig. 105.
CASE 3. To represent the cone when its base is on H and its axis
is oblique to H and V. See Fig. 106.
Let the circle whose center is a, represent the base on H, let B
represent the vertex, and let A-B represent the axis.
Through the point b, and tangent to the
circle whose center is a, draw b,-d, and b,-e,.
These lines represent the horizontal projections of the extreme or limiting elements
as seen from the observer's standpoint while
G.... _ L projecting on H, since no elements can occupy! i^ ~ positions at greater distance from the horizontal projecting plane of A-B. The vertical
projections of D and E are d' and et respectively, and the lines b'-d' and b'-e' are the
vertical projections of these elements.
FIG. 105 Tangent to the circular base and perpendicular to G-L draw f,-f' and g,-g. Connectf and b', also connect
gF and b', by straight lines. These lines represent the vertical projections of the extreme or limiting elements as seen from the
observer's standpoint while I
projecting on V, since no elements can occupy positions at
greater distance from the ver- a g
tical projecting plane of A-B.
The lines f,-b, and g,-b, repre-!
sent the horizontal projections G L
of these elements.
The outline b,-d,-g,-e,-b,
represents the horizontal projection of the cone, and the FIG. 106
outline b'-f-g'-bf represents the vertical projection of the cone.
It will be evident that if the dimensions or position of the cone
be changed, the projections of the cone will also be changed. It
will also be evident that a cone of definite dimension and position will have definite projections fully determining the cone.