The figures on the reproduced Plate X in the back of this book give the outline of the work that is to be completed by the student. The dimensions given on this plate are to be used in working out the problem, but are not to appear on the finished plate. The first figure shown represents a rectangular block with a rectangular hole cut through from front to back. The other two figures represent the same block in different positions. In drawing these figures, the student must put in all construction lines in order to show how each view is obtained.
After completing the construction of the views as shown, the projection of four holes, 1/2 inch in diameter each, are to be drawn. One hole passes through the center of each end, and one hole through the center of each side. All these small holes pass completely through the large hole in the center of the block. Next, put two square projecting pieces on the front face of the block, on the center line, 1/2 inch from each end. These projecting pieces are to be 1/2 inch square and 1/4 inch deep.
The projections of the four small holes and two projecting pieces are to be drawn in all views in the conventional manner, and the necessary construction lines for this work are to be left on the plate and inked in.
At the left of this plate draw the plan, front and side views of the monument shown in elevation on reproduced Plate XI in the back of the book. The total height of the monument is 6 inches. All four sides are alike except that the width of the base is 2 inches and the depth 1 1/2 inches, and the width of the body of the monument is 1 1/2 inches and the depth 1 inch. The height of the base is 1/2 inch, of body 3 inches, and the faces just above the base have a slope of 60 degrees with the horizontal. The width of the ridge at the extreme top of the monument is 1 inch.
The figures for the right side of the plate represent a pentagonal pyramid in three positions. The first position is the pyramid with the axis vertical. The height of the pyramid is 2 1/2 inches, and the diameter of the circle circumscribed about the base 2 1/2 inches. The center of the circle is 6 inches from the left margin and 2 1/2 inches below the upper border line. Spaces between figures to be 1/2 inch.
In the second figure the pyramid has been revolved about the right-hand corner of the base as an axis, through an angle of 15 degrees. The axis of the pyramid, shown dotted, is therefore at 75 degrees. The method of obtaining 75 degrees and 15 degrees with the triangles was shown in Part I. From the way in which the pyramid has been revolved, all angles with V must remain the same as in the first position; hence the vertical projection will be the same shape and size as before. All points of the pyramid remain the same distance from V. The points on the plan are found on T-square lines through the corners of the first plan and directly above the points in elevation. In the third position the pyramid has been swung around, about a vertical line through the apex as axis, through 30 degrees. The angle with the horizontal plane remains the same; consequently the plan is the same size and shape as in the second position, but at a different angle. Heights of all points of the pyramid have not changed this time, and hence are projected across from the second elevation.