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How did Newton discover the principle of calculus
166 1 year, Newton was admitted to Cambridge University. Under the careful guidance of Professor Barrow, he studied Descartes' geometry and Varis's arithmetica infinitorum, which laid a solid mathematical foundation. Newton wrote three important papers from 1669 to 1676. In these articles, he gave a general method to find the instantaneous rate of change, and proved that the area can be obtained by the inverse process of the rate of change. In the article, Newton introduced motion into mathematics, and he regarded the curve as generated by the motion of geometric points. He called the variable "flow" and the rate of change "flow number", and defined a central range for his "flow number technology": (1) Find the instantaneous speed from the known continuous moving distance; (2) Knowing the speed of movement, find the distance at a certain moment; (3) Find the length, area, curvature and extreme value of the curve. In A.D. 1687, Newton published an epoch-making scientific masterpiece Mathematical Principles of Natural Philosophy. This immortal masterpiece closely combines the methods he created with the research of natural science, thus making calculus deeply rooted in the soil of practice. The book Principles has also become a dazzling milestone in the history of human science! In AD 1704, Newton described the basic theorem of integral calculus in his article "Theory of Quadrature of Curves" as follows: "Let the areas ABC and ABDG be generated by the uniform motion of the ordinate BC and BD on the baseline AB.