Isaac Newton (1642–1727), physicist, mathematician, alchemist (tried to ”create” gold), was born in Woolsthorpe, England. Professor of mathematics at Cambridge, ”Master of the Mint” in London, a position he held for the rest of his life. His infinitesimal calculus was called the theory of fluxions. It was conceived in the plague years of 1665–1666, when the university was shut down, but the theory did not appear in print until 1704, as an addendum to a book about optics. His best-known work, Philosophiae Naturalis Principia Mathematica (”The Mathematical Principles of Natural Philosophy”), usually referred to as Principia, appeared in 1687. It addressed the motion of bodies and the structure of the universe.

Principia 1687.

Newton's theory of fluxions

Newton regarded curves as paths of a moving point. This motion is dependent on time. Newton called a quantity that varies when moving (for example x) a fluent. He called the velocity at which the fluent was moving the fluxion. This is marked with a dot, as . In the infinitely brief time o, the point thus moves ẋo. We can get an idea of how Newton conceived of his calculations in his Method of Fluxions, which was first published nine years after his death. Pay particular attention to paragraphs 13–18 in the copy below.

Last modified: 2023-01-18