The third proportional of two numbers $9$ and $15$ is:

Let the third proportional to $9$ and $15$ be $x$.By definition of continued proportion:
$$9:15::15:x$$
$$\frac{9}{15}=\frac{15}{x}$$
Solving for $x$:
$$9\times x=15\times 15$$
$$9x=225$$
$$x=\frac{225}{9}=25$$