The classical central-force problem was solved geometrically by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica, in which Newton introduced his laws of motion. Newton used an equivalent of leapfrog integration to convert the continuous motion to a discrete one, so that geometrical methods may be applied. In this approach, the position of the particle is considered only at evenly spaced time points. For illustration, the particle in Figure 10 is located at point A at time t = 0, at point B at time t = Δ t, at point C at time t = 2Δ t, and so on for all times t = n Δ t, where n is an integer. The velocity is assumed to be constant between these time points. Thus, the vector r AB = r B − r A equals Δ t times the velocity vector v AB (red line), whereas r BC = r C − r B equals v BC Δ t (blue line). Since the velocity is constant between points, the force is assumed to act instantaneously at each new position; for example, the force acting on the particle at point B instantly changes the velocity from v AB to v BC. The difference vector Δ r = r BC − r AB equals Δ v Δ t (green line), where Δ v = v BC − v AB is the change in velocity resulting from the force at point B. Since the acceleration a is parallel to Δ v and since F = m a, the force F must be parallel to Δ v and Δ r. If F is a central force, it must be parallel to the vector r B from the center O to the point B (dashed green line); in that case, Δ r is also parallel to r B.