What is "law of continuity"

Continuity \Con`ti*nu"i*ty\, n.; pl. Continuities. [L. continuitas: cf. F. continuit['e]. See Continuous.] the state of being continuous; uninterrupted connection or succession; close union of parts; cohesion; as, the continuity of fibers.
--Grew.

The sight would be tired, if it were attracted by a continuity of glittering objects.
--Dryden.

Law of continuity (Math. & Physics), the principle that nothing passes from one state to another without passing through all the intermediate states.

Solution of continuity. (Math.) See under Solution. [1913 Webster] ||

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.