What are the origins of "take you up on it"

A common English idiom "take you up on it" is apparently used to indicate a general willingness or predisposition to accept something that is offered or granted. For example,

If you make an offer to help a stranger in need, don't be surprised if they take you up on it!

Does anyone know the origins of this common English idiom?

I think that part of the informality comes from transforming the verb take, which here means something like accept, to the phrasal verb take up [on].

Phrasal verbs often have meanings that are different from the verb they contain and sound more informal than just the verb.

For me there is also the playful imagery of taking up meaning something like absorb. I picture an amoeba engulfing an "offer particle".