> How can I ask someone in a quiet library to stop clearing their throat?

Any nice and polite approach will help talking to this person. A quick written note is the best, because of the "quiet area" where this happens. You may also talk to any staff member, and ask them if they're aware of what occurs, and if there's a nice way to take care of it.

But, before taking any action, if you can, I'd say: *please, don't do anything right now*, and think about *sucking it up / moving / {any life hack}*. Why? 

> there has been a person on the quiet floor who clears their throat about once every two minutes.

Because the frequency of the clearing makes me think of a "disorder" (close to "*Obsessive Compulsive Disorder*") that a friend of mine has, "*ahem-ing*" every 5 to 10 seconds, all day long. It just can't be swept off by asking to stop or offering any medication. Be it a medical physical condition or mental condition. (FWIW: my friend has this only OCD, and nothing's worth trying to stop him.)

So, if you ask right now, the person won't be able to stop if they have a medical condition.

Further reading about *Chronic Throat Clearing* [HERE](http://ukhealthcare.net/blog/chronic-throat-clearing/) and [HERE](https://uknow.uky.edu/uk-healthcare/chronic-throat-clearing-may-be-your-body’s-response-irritants).

My advice: read about the disorder, weight your options, ask the staff, before any other action. You may find out that not asking this person to stop could be your best option.