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.

106

DESCRIPTIVE GEOMETRY

The greater the number of auxiliary lines assumed through
the point A, the more accurately will the line L-K-G-F be
determined.
258. To assume a Point upon a Warped Surface with Two Curvilinear Directrices and a Plane Directer. See Section 255.
259. The Conoid. The conoid is a warped surface with a plane
directer and two linear directrices, one rectilinear and the other
curvilinear.
If the rectilinear directrix of a conoid is taken perpendicular to
the plane directer, the surface is called a right conoid.
260. Problem 154. Assume a rectilinear element upon the warped
surface whose rectilinear directrices are [A = - 6, 3, 1; B = 1, 6, 6]
and [C =4, - 2, 1; D = 4, - 2, 6] and whose plane directer is
S=4, 30~, 20~.
261. Problem 155. Assume a rectilinear element upon the warped
surface whose rectilinear directrices are [A = - 4, - 4, 2; B = - 4,
4, 6] and [C = 0, 1, 6; D = 6, 6, 1] and whose plane directer is
S= 6, 30~, 60~.
262. Problem 156. Assume a rectilinear element upon the warped
surface whose rectilinear directrices are [A =- 6, - 3, 4; B = 6,
- 3, 4] and [C = - 2, - 5, 6; D = 4,1, 2] and whose plane directer
is S = 0, 30~, 60~.
263. Problem 157. Given a warped surface with two curvilinear
directrices and a plane directer, the latter coincident with V; required
to draw a rectilinear element of the surface.
264. Problem 158. Given a warped surface with two curvilinear
directrices and a plane directer, the latter parallel to G-L but
oblique to H and V; required to draw a rectilinear element of the
surface.
265. Problem 159. Given a warped surface with one rectilinear
directrix and one curvilinear directrix and a plane directer; required
to draw a rectilinear element of the surface.
266. Problem 160. Solve the preceding problem when the rectilinear
directrix is perpendicular to H and the plane directer is H.
267. The Warped Surface with Three Linear Directrices. The
warped surface with three linear directrices is generated by a
straight line moving in such a way as to touch the three directrices.