[Non-Sequitur]

But I don't think Title 8 U.S.C. § 1401 used the term "natural-born". It certainly does not do so now.

So does that mean that "a person born in the United States, and subject to the jurisdiction thereof" (8 U.S.C. § 1401, paragraph (a)) is not a natural born citizen, either?

[El Gato]

So does that mean that "a person born in the United States, and subject to the jurisdiction thereof" (8 U.S.C. § 1401, paragraph (a)) is not a natural born citizen, either?

It doesn't make them so, nor does it make them not. It only makes them a citizen, although it's also redundant, since it's the same criteria as the 14th amendment's