The
Law of Continuity is a heuristic principle introduced by
Gottfried Leibniz based on earlier work by
Nicholas of Cusa and
Johannes Kepler. It is the principle that "whatever succeeds for the finite, also succeeds for the infinite". Kepler used it to calculate the area of the circle by representing the latter as an infinite-sided polygon with infinitesimal sides, and adding the areas of infinitely-many triangles with infinitesimal bases. Leibniz used the principle to extend concepts such as arithmetic operations, from ordinary numbers to
infinitesimals, laying the groundwork for
infinitesimal calculus. A mathematical implementation of the law of continuity is provided by the
transfer principle in the context of the
hyperreal numbers.