Christiaan Huygens stated what is now known as the second of Newton's laws of motion in a quadratic form.Ernst Mach, The Science of Mechanics (1919), e.g. p. 143, p. 172 and p. 187 . In 1659 he derived the now standard formula for the centripetal force, exerted by an object describing a circular motion, for instance on the string to which it is attached.Westfall, Richard S. (1971). The Construction of Modern Science: Mechanisms and Mechanics, p. 130Gindikin, Semyon Grigorevich (1988). Tales of Physicists and Mathematicians, p. 86–87Jammer, Max (1997). Concepts of Mass in Classical and Modern Physics, p. 62–63Jammer, Max (1999). Concepts of Force: A Study in the Foundations of Dynamics, p. 109–10Graneau, Peter; Graneau Neal (2006). In the Grip of the Distant Universe: The Science of Inertia, p. 111–12Ginzburg, Vladimir B.; Ginzburg, Tatyana V. (2007). Prime Elements of Ordinary Matter, Dark Matter & Dark Energy: Beyond Standard Model & String Theory, p. 82–83 In modern notation:
