Das velocidades às fluxões

Abstract

Newton's De methodis (written in 1671) results from a revision of an uncompleted treatise that he had written in October-November 1666 (The October 1666 tract on fluxions, as Whiteside called it). In 1666, Newton already had the main results that he would expound 5 years later in the text that is unanimously considered the best presentation of his theory of fluxions. However, the term "fluxion" itself did not appear however in The October 1666 tract on fluxions, where the question addressed had to do with motions or velocities. From the strict point of view of mathematical formalism, the shift from (punctual) velocities to fluxions is not especially relevant: the mathematical methods of the De methodis are essentially the same as those of The October 1666 tract on fluxions. Still, this terminological change is, I think, the symptom of a different way to understand these methods and the objects they apply to. This is quite explicitly said by Newton in a crucial passage at the beginning of the De methodis, where he claims that the term "time" in his treatise does not refer to the time formaliter spectatum, but to "another quantity" for the "fluxion of which the time is expressed and measured". In this paper, I discuss this passage and try to clarify the essential differences between the 1666 notion of velocity and the new notion of fluxion introduced in 1671. This also enables me to discuss the role of Newton in the origin of 18th century analysis.