Why is the venue for surgical procedures called an operating theatre?

Two questions here-- one answer is from M-W 10th-- theater...
3 a : a place rising by steps or gradations <a woody theater of stateliest view -- John Milton>
b : a room often with rising tiers of seats for assemblies (as for lectures or surgical demonstrations)
In day's past, operation where done in 3.B, the operation theater-- some teaching hospitals still have them, in addition to OR's. (NY's famous "belleview' hospital for one) but the seat are now above, and seperated by glass from the OR.

now as for why theatre and not theater....?


my other obsession