§10.
Rotation about a Point.
Having now investigated the general methods of representing relative motion in a plane, we must proceed to consider the more difficult problem of relative motion in space; in the first place, however, with the limitation that one point of the body which we are considering be supposed not to alter its position in space in reference to us. When a body moves in such a way that each of its points remains always at a constant distance from some one fixed point, it is said to turn about that point. In order to find the motion which thus takes place relatively to a stationary body rigidly connected with a fixed point, let us describe about 'that point A, Fig. 29, a sphere of such a size that it shall pass through
Fig. 29.
Fig. 30.
the moving body, giving us a spheric section of it, PQ. If we then know the motion of such a sectional figure upon the sphere, it is evident that we shall know the motion of the body itself. But the motion of the figure R Q is known if all the positions of two of its points, as P and Q, or of the great circles connected with them, be known. For from the position of this curved line the positions of all other points in the figure may be found by considering them as vertices of spherical triangles, of which the position of the base (PQ) and the magnitudes of all three sides
