 Instead of taking particular infinitesimal values, one quantifies over values of real-valued variables \(\epsilon\) and \(\delta\). For example, the claim that the slope of the squaring function at \(x\) is \(2x\) is interpreted as saying that for any desired degree \(\epsilon\) of approximation, there is some finite \(\delta\) such that for any \(x'\) within \(\delta\) of \(x\), the slope of the line from \((x,x^2)\) to \((x', x'^2)\) approximates \(2x\) to within \(\epsilon\). A single infinitesimal is replaced by a relation involving two nested quantifiers. The process of elimination of infinitesimal quantities from the calculus was a central part of a larger process known as the “arithmetization of analysis”, which aimed at removing kinematical and geometrical notions from the calculus in favour of purely arithmetical notions. (These are broadly construed to include the arithmetic of real and complex numbers. For a recent account of the history of real and complex analysis in the 19th century that also pays attention to foundational issues see Gray (2015).)