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.

176

DESCRIPTIVE GEOMETRY

of the surface, and will cut from S a straight line whose vertical
projection is p'-m', parallel to S-s'. By this plane W two more
points, Q and R, are located.
CASE 2. To draw a rectilinear tangent to the curve.
By analyses previously given, a rectilinear tangent to the curve,
cut from any surface by a plane, may be drawn whenever a plane
can be drawn tangent to the surface at the point of tangency.
CASE 3. To find the true size of the intersection.
Analysis and Construction. See Fig. 158. Revolve the plane
S, the plane of the curve, about S-s, into H. Any point of the
curve, as 0, will fall at oH, and other points may be found in the
same way.*
NOTE. In the following six problems apply the principles suggested by the
analysis in Problem 268, Case 1.
398. Problem 269. Find the intersection of a cylinder of revolution
by an oblique plane.
399. Problem 270. Find the intersection of a cone of revolution
by an oblique plane.
400. Problem 271. Find the intersection of a sphere by a plane
oblique to G-L.
401. Problem 272. Find the intersection of an ellipsoid of revolution by an oblique plane.
402. Problem 273. Find the intersection of a paraboloid of revolution by an oblique plane.
403. Problem 274. Find the intersection of a hyperboloid of revolution by an oblique plane.
* In this revolution the radii have all been shortened by a constant quantity in
order to reduce the space occupied by the drawing.