English: Newton's derivation of the area law from the laws of motion: as an object orbits the Sun it sweeps out equal areas in equal intervals of time.

An object (not shown) is in orbit around the Sun (Point S ). The effect of the Sun's gravitational attraction is represented as a sequence of impulses, always directed towards point S . In the limit of infinitely many small impulses the representation approaches infinitely close to smooth gravitational attraction.

When the object is at point B it receives an impulse towards point S . Without that impulse the object would proceed to point c . The actual displacement BC follows from the rules for velocity composition; the displacement BC is the vector sum of the displacements BV and Bc . The triangles SBc and SBC have the same base and the same height, hence they have the same surface area.

At point C the object receives another impulse towards point S . Without that impulse the object would have proceeded to point d in an equal interval of time. The impulse towards point S makes the object proceed to point D .

The triangles SBc , SBC , SCd , SCD , SDe , SDE all have the same surface area.

In the limit of the time intervals going to infinitisimally small the sequence of lines connecting the points B , C , D , E , etc approaches infinitely close to the actual smooth trajectory.