$60$ is the mean proportional of $36$ and $P$. Find the value of $P$.

If $60$ is the mean proportional of $36$ and $P$, then by definition:
$$\frac{36}{60}=\frac{60}{P}$$
Squaring the mean proportion gives:
$$60^2=36\times P$$
$$3600=36\times P$$
Solving for $P$:
$$P=\frac{3600}{36}=100$$
Therefore, the value of $P$ is $100$.