The place of "clear, precise definitions" is in Analysis, which is a foundational part of Calculus and is being studied by mathematically inclined students.) This is how it has been used by mathematicians and physists even before, and certainly since, it was formulated as such by Newton and Leibniz. Calculus is supposed to be a tool chest of methods for solving certain kinds of problems. The new approach wasn't easy, though, as students who have had to learn his "epsilon-delta" approach to limits will still testify.' I believe that nothing is easy to an unprepared mind. For example, wrote about Weierstrass, 'His clear, precise definitions removed any trace of mystery or geometric intuition from calculus, putting it all on a logical foundation that depended only on algebra and arithmetic. (As an aside, Weierstrass' definition is often singled out by mathematics educators as a piece of calculus especially difficult for the beginning students. Starting with Newton and Leibniz in the 17 th century, practically all great mathematicians tried unsuccessfully to justify the employment of infinitesimals till in the 19 th century the infinitesimals were finally banished from mathematics and replaced with Weierstrass' ε-δ definition of the limit.
The early history of Calculus is the story of infinitesimals.
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