Did Newton estimate the [gravitational constant $\mathrm{G}$](https://en.wikipedia.org/wiki/Gravitational_constant)?

In my head, he did this by comparing:

* acceleration of an object on Earth (let's say, an apple) $9.81 \,\mathrm{m\cdot s^{-2}}$, $6400 \,\mathrm{km}$ from the centre of the Earth
* acceleration of the Moon, $384,000 \,\mathrm{km}$

As explained [here](http://www.physicsclassroom.com/class/circles/Lesson-3/The-Apple,-the-Moon,-and-the-Inverse-Square-Law).

But did he actually take the next step and calculate what G must be to explain both accelerations? If so what value did he get?