Fluxion

A fluxion is the instantaneous rate of change, or gradient, of a fluent (a time-varying quantity, or function) at a given point.

Newton introduced the concept in 1665 and detailed them in his mathematical treatise, Method of Fluxions.

[2] Fluxions and fluents made up Newton's early calculus.

[3] Fluxions were central to the Leibniz–Newton calculus controversy, when Newton sent a letter to Gottfried Wilhelm Leibniz explaining them, but concealing his words in code due to his suspicion.

He wrote:[4] I cannot proceed with the explanations of the fluxions now, I have preferred to conceal it thus: 6accdæ13eff7i3l9n4o4qrr4s8t12vx.The gibberish string was in fact a hash code (by denoting the frequency of each letter) of the Latin phrase Data æqvatione qvotcvnqve flventes qvantitates involvente, flvxiones invenire: et vice versa, meaning: "Given an equation that consists of any number of flowing quantities, to find the fluxions: and vice versa".

⁠ as a non-zero quantity by stating that fluxions were a consequence of movement by an object.

Bishop George Berkeley, a prominent philosopher of the time, denounced Newton's fluxions in his essay The Analyst, published in 1734.

Berkeley referred to them as "ghosts of departed quantities", a statement which unnerved mathematicians of the time and led to the eventual disuse of infinitesimals in calculus.

⁠ as infinitely small, preferring to define it as approaching zero, using a similar definition to the concept of limit.

By this time, Leibniz's derivative (and his notation) had largely replaced Newton's fluxions and fluents, and remains in use today.