Question 2: The ancient period introduced some of the ideas of ________ calculus, but does not seem to have developed these ideas in a rigorous or systematic way.

Question 3: In the 19th century, calculus was put on a much more rigorous footing by mathematicians such as ________, Riemann, and Weierstrass (see (ε, δ)-definition of limit).

Question 4: In the modern period, independent discoveries relating to calculus were being made in early 17th century Japan, by mathematicians such as ________, who expanded upon the method of exhaustion.

Question 5: This realization, made by both Newton and Leibniz, who based their results on earlier work by ________, was key to the massive proliferation of analytic results after their work became known.

Question 6: His contribution was to provide a clear set of rules for manipulating infinitesimal quantities, allowing the computation of second and higher derivatives, and providing the product rule and ________, in their differential and integral forms.