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.

CHAPTER VI

PROBLEMS RELATING TO THE POINT, LINE, AND PLANE
86. Introductory Statements. As a rule the solution of a problem will be divided into two parts: (1) the analysis, or general
theory of solution, in which a clear and logical statement of the
method of procedure without reference to any diagram will be
made; and (2) the construction, or actual graphic work necessary
in the solution, in which the suggestions of the analysis will be
followed in order.
The graphic construction of every problem in descriptive
geometry should be checked.
A check in drafting is an application of some graphic process
by which the accuracy of construction may be tested. No one can
be absolutely sure of the accuracy of his results until they have
been carefully tested.
The nature of the check for any particular problem may be
determined by a study of the various conditions which must be
satisfied by the processes of construction.
A problem may be said to be checked when the same result has
been obtained by two distinct processes of solution.
87. Problem 25. Given a straight line in H and a point in space;
required to revolve the point about the line as an axis into H.
Principle. Revolution in descriptive geometry is always made
about a rectilinear axis occupying a definite position.
Principle. A point is being revolved about an axis when it
moves in a plane perpendicular to the axis and retains a constant
distance from the axis. A point situated in the axis will not move
during revolution.
Principle. When a plane is revolved about an axis the relative
position of magnitudes in the plane is not changed.
Analysis. In Fig. 44, which is a pictorial drawing, let M-N
represent the line in H and let O represent the point in space.
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