[Uncle Chip]

And yet we find Vattel's definition behind the wording of the Naturalization Act of 1790 right after the Constitution was written:

"And the children of citizens of the United States that may be born beyond sea, or out of the limits of the United States, shall be considered as natural born citizens: Provided, That the right of citizenship shall not descend to persons whose fathers have never been resident in the United States:"

Note that children of citizens were to be "natural born citizens", according to them, no matter where they were born. And the father not the mother was the determining factor of that citizenship.

[The Pack Knight]

"And the children of citizens of the United States that may be born beyond sea, or out of the limits of the United States, shall be considered as natural born citizens: Provided, That the right of citizenship shall not descend to persons whose fathers have never been resident in the United States:"

Yes, the Naturalization Act of 1790 does not allow children of non-citizens born outside the United States to be natural born citizens. It makes no provision for the citizenship of persons born within the United States whether to citizen parents or not.

It seems to me that the implication of this act is that those born in the United States are inherently natural born citizens, while children born to citizen parents outside the United States are natural born citizens only by Act of Congress and subject to the conditions of this statute.