2. The flat pencil formed by all the lines through a point in a plane. Its base is the point in the plane.
3. The axial pencil formed by all planes through a line which is called its base or axis.
II. Of two dimensions.
1. The field of points and lines—that is, a plane with all its points and all its lines.
2. The pencil of lines and planes—that is, a point in space with all lines and all planes through it.
III. Of three dimensions.
The space of points—that is, all points in space.
The space of planes—that is, all planes in space.
IV. Of four dimensions.
The space of lines, or all lines in space.