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.

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DESCRIPTIVE GEOMETRY

base. Through e, draw e,-o, parallel to a-b,, and through e' draw
et-o' parallel to af-bt. E-O is the required element.
234. To assume a Point upon the Surface of the Cylinder. Let
the cylinder be represented as in Fig. 103. Assume at random the
horizontal projection o, of the
point. Draw o,-d,-e, parallel to
/^ r a,-b,, to represent the horizontal
a,< >^ B^ ~ projection of the element con~( ia, /. taining the point 0. This element pierces H either at d, or at
_eWa_':, et according as 0 is assumed on
L the upper or on the lower surface
of the cylinder. Assuming the
point on the lower surface of the
cylinder, the element in question
will be vertically projected at
FIG. 103 e'-o', and the point 0 must be
vertically projected at o' on the straight line through o, perpendicular to G-L.
235. Problem 147. Given a cylinder whose axis is oblique to H
and V and whose base is a circle in V; required to draw the two
projections of the cylinder and to assume a point upon the surface.
236. Problem 148. Given a cylinder whose right section is a circle
and whose axis is in such a position that its horizontal projection is
inclined 30 degrees to G-L and its vertical projection is inclined
60 degrees to G-L; required to draw the two projections of the
cylinder and to assume a point upon the surface.
237. Problem 149. Given a cylinder whose right section is a circle
and whose axis is parallel to G-L; required to draw the two projections of the cylinder and to assume a point upon the surface.
238. Problem 150. Given a cylinder whose base is a circle on Hand
whose axis is in a profile plane and oblique to H; required to draw the
two projections of the cylinder and to assume a point upon the surface.
239. Conical Surfaces and the Cone. The conical surface is a
single curved surface which may be generated by a moving straight
line which during the movement touches a given curved line and
constantly passes through a given fixed point (see Section 222).