The origin of limit
The germination of limit thought can be traced back to ancient Greece and China during the Warring States Period, but the concept of limit first appeared in arithmetica infinitorum by Wallis, and Newton explicitly used the word limit in Mathematical Principles of Natural Philosophy.
But as late as the second half of18th century, D'Alembert and others realized that calculus would be perfect if it was based on the concept of limit. Cauchy first gave a descriptive definition of limit, and then Verdot Strass gave a strict definition of limit (ε-δ and ε-N definitions).