When flying a circuit, the leg after downwind and before final is called base. Where does this name come from?
Traffic pattern (circuit) phases are named so that they do not cause confusion1. I think of it as the leg which is taking me towards my landing/home base. (It is just a memory aid.)
However, the following reason is the best one which I found:
This leg represents the foundation for the final approach, that is, the base from which the final approach is initiated.
Another reason is as follows, although it is similar to a memory aid:
... base leg is called “base” because it is really the foundation of your landing (the “base” of a house is its foundation – and if it isn’t right, the whole house will never be right) – if the base leg isn’t right, your whole landing will suffer for it.
1: Although, upwind leg, crosswind leg and downwind leg relates with the wind direction too. But if wind is perpendicular to the runway, downwind leg is not actually downwind, but it is still called the downwind leg.
This is a partial answer (allowed) that I'm making a community wiki.
The usage above shows that the term base leg came after traffic pattern, which was confirmed in a Flying Magazine issue (Jun 1948, p. 64):
That linked issue shows that the base leg was also known as the crosswind leg (which today is the leg after the first turn after departure). The article also mentions circular and triangular patterns (confirmed by other issues).
Searching historic FAA regulations wasn't helpful as the FAA was formed in the late 50s. And the current regulations do not state the names of the legs, just some guidance on when to deviate from an airport's traffic pattern (14 CFR § 137.45).
- It wasn't named base leg from the start
- It was known as crosswind leg, which means the terms were standardized later
- Since triangular patterns existed, there's a chance the name base comes from the geometric shape as noted in another answer, though not necessarily of French origin.
My hypothesis at the moment is that the standardization came from military training procedures, which carried over to the civilian world. I'm having no luck finding the earliest mention of all four legs as we know them today from the late 30s.