Question

Given the large number of tangent and area problems solved by the mid-seventeenth century, what was still needed before one could say that calculus had arisen?

Answer 1

By the middle of the seventeenth century, many of the elementary techniques and facts of calculus were known including methods for finding the tangents to simple curves and formulas for areas bounded by the areas. What was lacking until late seventeenth century was realisation that these two kinds of problems are related to each other. It needed only someone to give systematic methods of computing tangents and inverting that process to find the areas. This is the work actually done by newton and Leibiniz.