His BC, actually both long and short forms, has been posted here many times, it says he was born in Colon, Panama, which is neither on a US base, nor in the Canal Zone. But since he was born of two US Parents, he's natural born by all but the definition(s) that requires the birth be on US soil.
But that doesn't conform with the Common law definition in use at the time the Constitution was written. It also does not conform with the general practice of most nations *other than England* at the time, which went strictly by the parent's citizenship, regardless of birth location, and in "split" cases, by the father's citizenship. The English were more "liberal" and also made anyone born "in the realm" a natural born subject, with a few exceptions such as the children of ambassadors or of an occupying military force. That's per "Blackstone's Commentaries on the Laws of England". (Blackstone makes note of the difference between English and French practice in this regard).
This is the UB4 position. Both parents citizenship is a requirement, place of birth is incidental. It is no the same as the theory based on the 18th century book cited above.
Which is it?