Is Newton’s second law really Newton’s?

Abstract

When we call the equation f = ma “Newton’s second law,” how much historical truth lies behind us? Many textbooks on introductory physics and classical mechanics claim that the Principia’s second law becomes f = ma, once Newton’s vocabulary has been translated into more familiar terms. But there is nothing in the Principia’s second law about acceleration and nothing about a rate of change. If the Principia’s second law does not assert f = ma, what does it assert, and is there some other axiom or some proposition in the Principia that does assert f = ma? Is there any historical truth behind us when we call f = ma “Newton’s second law”? This article answers these questions.

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