To help visualization of the rotation of a line about a horizontal axis, take a pair of dividers (Fig. 32a), open them slightly, hold one leg horizontally and spin it between your fingers. This leg represents the rotation axis and retains this orientation throughout. The other leg represents the line which rotates; note how it changes orientation during rotation. It sweeps out a cone in space. This cone has a horizontal axis which corresponds to the rotation axis.

Cones project to give small circles (Fig. 32b). Therefore, a given line rotating about a fixed axis moves to take up different positions on the same small circle (Fig. 32c). The rotation axis R occupies the centre of the small circle defined by the line which rotates.

To rotate a line L about a horizontal axis, R

1. 1 Plot lines L and R on a stereogram (Fig. 32c). (The method for plotting lines is explained on pp. 22–5.) R is horizontal and therefore plots as a point on the primitive circle.

2. 2 Rotate the net beneath the stereogram until the point at the centre of all the net's small circles is positioned beneath R on the stereogram (Fig. 32d).

3. 3 The small circle on which L lies describes its path during rotation. For example, in Figure 32d, L lies on the α = 30° small circle.

4. 4 The new orientation of L (labelled new in Fig. 32d) is found by moving it around the small circle by an amount governed by the required angle of rotation (50° in Fig. 32d) in a direction governed by the required sense of rotation.