Things that are self-evident do not require a definition - otherwise, we'd have ended up with a 100-page monstrosity like the EU "Constitution." The basic fact is that anything that relies on "natural law" relies on the "Law of Nations."
You should particularly pay attention to John Jay's letter to Washington suggesting the restriction to Natural Born Citizens as a way to bar someone with divided loyalties from becoming Commander-in-Chief.
The definition is also implicit in the exception made for "a Citizen of the United States, at the time of the Adoption of this Constitution." Everyone alive at the time had parents who were not citizens at the time of their birth, even though they had been born in one of the colonies that became states. It was felt that, having participated in the Revolution that brought us independence, they could be trusted not to betray us.
Finally, whether or not the Founders defined the term explicitly, the US Supreme Court definitely did in Minor vs. Happersett - which remains binding precedent to this day. To quote from that decision, “The Constitution does not in words say who shall be natural-born citizens. Resort must be had elsewhere to ascertain that. At common law, with the nomenclature of which the framers of the Constitution were familiar, it was never doubted that all children born in a country of parents who were its citizens became themselves, upon their birth, citizens also. These were natives or natural-born citizens, as distinguished from aliens or foreigners. Some authorities go further and include as citizens children born within the jurisdiction without reference to the citizenship of their parents. As to this class there have been doubts, but never as to the first."
Note that they say that there are doubts as to whether "children born within the jurisdiction without reference to the citizenship of their parents" are even citizens at all - not whether they qualify as NBC. Since the case they were considering involved a woman who was a NBC (born in the US of parents who were both citizens), they had no need to resolve the doubts as to the status of second group of potential, plain (i.e. not natural born) citizens
Yeah, yeah, yeah, shouda, coulda, wouda. PROOF man!
Things that were “self evident” as you put it came from English common law, not Vattel. Vattel’s book was originally published in 1758. How many colonists knew his work to make it “common” knowledge? Are you for real?
Are you seriously posing that Vattel was “self evident” during the revolution? That’s 18 years for pete’s sake yet all colonists took this guy’s theories to heart. THIS IS INSANITY!!!!!!!
As for the other dicta you cite; that and $5 will get you a cup of coffee at Starbucks.