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.

INTERSECTION OF SURFACES BY PLANES

167

will fall at b5, and other points may be found in the same way. The
curve traced through the points thus found is the curve required.
The tangent 1-L will, when revolved, take the position ra-lh
and be tangent to the revolved position of the curve.
CASE 4. To develop the surface.
Analysis. When the surface of a cylinder is rolled out upon a
plane tangent to the surface, any section of the surface made by
a plane perpendicular
S,_ W1; U t, to the elements will
'/,\ roll out into a straight
-/! J / Ad line perpendicular to. j 7 ~ the original element of
'/A -/ ' - tangency. The work
X A, Ably '< of development can
T a;' i, x \ ~therefore be much sim-T- ir,, \,S L plified by making a
I~,q ~ ',x / I! DM I
G 1
\ \\__/ _ l II I,
>R L B X EN LI
FIG. 153 FIG. 154
right section of the surface and using this line in development as
a line of reference.
Construction. Take the plane W, Fig. 153, as the plane of
development, and take the point of observation to the left of
the plane. Starting with the element of tangency K-L, in this
plane, roll the cylinder along this plane toward V, bringing the
successive elements of the surface into contact with W.
Since the plane S is perpendicular to the elements, the curve
L-B-X-E-N-L will roll out into a straight line perpendicular to
the elements.
The character of the development is shown in Fig. 154,
where K-L represents the element of tangency and where L-L',