Let $V$ be a paracompact strictly $K$-analytic space $V$. Let $f\colon V\to{\mathbb{R}}$ be a continuous function on $V$. Then $f$ can be uniformly approximated by piecewise ${\mathbb{Q}}$-linear functions. In other words, for every $\varepsilon>0$ there exists a piecewise ${\mathbb{Q}}$-linear function $\varphi\colon V\to{\mathbb{R}}$ such that $\sup_{x\in V}|f(x)-\varphi(x)|\leq\varepsilon$.