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.

138

DESCRIPTIVE GEOMETRY

CASE 2. When the plane of the base of the cone is perpendicular
to V but oblique to HI.
Construction. In Fig. 133 let A-B represent the axis of the
cone and let MIf-N represent the given line.
Through the vertex of the cone draw J-B-D parallel to iM-N,
piercing H at and piercing V at et, points in the required traces.
Through F, the point in which B-D intersects the plane of the
s, base of the cone, draw G/d, l F-0 tangent to the curve
/, ~ of the base. The horizona/^,, y// '~ tal projection of this tan// (/ gent is g,-f,-o,, and the
vertical projection of this:d, i >k -'6,,, d tangent is qg-f-o'. By
G; 'e -L analysis G-F- 0 is a line
iw JYg j. a /b of the required plane,
]j..A/ a > // ' {and pierces 11 at g and
m c!, < z /,/ pierces V at k'. Through
eY&4S / g, and d, draw the required! Hi \horizontal trace S-s,.
Through k' and e' draw
the required vertical
trace S-s'.
FIG. 133 The element of tangency is the straight line drawn through the point of tangency on
the base and the vertex of the cone.
Since another straight line may be drawn through F and tangent
to the curve of the base, another plane answering the conditions
of the problem may be constructed.
Check. Note whether the element of tangency intersects H and
V in the traces now located.
326. Problem 202. Given a cone whose axis is oblique to Tf and V and
whose base is a circle on V; required to assume a straight line in a profile
plane and to draw a plane tangent to the cone and parallel to the line.
327. Problem 203. Given a cone whose axis is oblique to H and 1,
the plane of whose base is perpendicular to H but oblique to V, and
the vertical projection of whose base is a circle; required to assume