  To obviate such irksome exceptions, projective geometry added to each straight line in space an ideal point, shared by every line parallel to it. Continuity requires then that all ideal points lie on a single ideal plane, which meets each family of parallel planes along a different ideal line. Fundamentalists may shudder at this seemingly wanton multiplication of entities. However, it had been practised in arithmetic for centuries, as the initial stock of natural numbers 1, 2, 3, … , was supplemented with zero, the negative integers, the non-integral rationals, the irrationals, and the so-called imaginary numbers. 