Using the Twitter REST API to Get Bounding Box Tweets

I am trying to use the Twitter API to get bounding box tweets. Currently I've only managed to do this with the streaming API, but tweets are pretty slow, so I'm looking to use past tweets.

I can't seem to find a way to do this using the REST API. This seems to resolve "locations", but how can I do this when my request might fall across multiple locations, or only partial locations?

Ideally, I would like to be able to collect tweets in the same area using the REST API as I used with the Streaming API.