The law of continuity is a heuristic principle introduced by Gottfried Leibniz based on earlier work by Nicholas of Cusa and Johannes Kepler.
[1] Kepler used the law of continuity to calculate the area of the circle by representing it as an infinite-sided polygon with infinitesimal sides, and adding the areas of infinitely many triangles with infinitesimal bases.
The transfer principle provides a mathematical implementation of the law of continuity in the context of the hyperreal numbers.
[2][3] Leibniz expressed the law in the following terms in 1701: In a 1702 letter to French mathematician Pierre Varignon subtitled “Justification of the Infinitesimal Calculus by that of Ordinary Algebra," Leibniz adequately summed up the true meaning of his law, stating that "the rules of the finite are found to succeed in the infinite.
"[5] The law of continuity became important to Leibniz's justification and conceptualization of the infinitesimal calculus.