1. The third proportional to two numbers $a$ and $b$ is a number $x$ such that $\frac{a}{b} = \frac{b}{x}$. 2. This means $x$ satisfies the equation $a \times x = b \times b$. 3. Rearranging, we get $x = \frac{b^2}{a}$. 4. So, the third proportional to numbers $a$ and $b$ is $x = \frac{b^2}{a}$.