If you want to bring up something that is besides the point from a little footnote making the point about "Other legal sources frequently used bear arms in nonmilitary contexts." in the District of Columbia v. Heller, I will bring up something relevant in U.S. v. Wong Kim Ark.
From Chief Justice FULLER .
"Before the Revolution, the views of the publicists had been thus put by Vattel: 'The natives, or natural-born citizens, are those born in the country, of parents who are citizens. As the society cannot exist and perpetuate itself otherwise than by the children of the citizens, those children naturally follow the condition of their fathers, and succeed to all their rights.
The society is supposed to desire this, in consequence of what it owes to its own preservation; and it is presumed, as matter of course, that each citizen, on entering into society, reserves to his children the right of becoming members of it. The country of the fathers is herefore that of the children; and these become true citizens merely by their tacit consent. We shall soon see whether, on their coming to the years of discretion, they may renounce their right, and what they owe to the society in which they were born. I say that, in order to be of the country, it is necessary that a person be born of a father who is a citizen; for, if he is born there of a foreigner, it will be only the place of his birth, and not his country.' Vatt. Law Nat. bk. 1, c. 19, 212."
These words were not lost on Justice Grey as he never considered Wong Ark a natural born citizen. And that it shows the Supreme Court of the United States believed that de Vattel's definition is the meaning and intent behind Article 2, Section 1., Clause 5, of the United States Constitution. Note the words again - " and not his country" - in the above except.
Wong Kim Ark is not or never was a natural born citizen of the United States so is NOT Barack Obama.
BTW, because you cannot find de Vattel referenced in Madison's notes taken at the 1787 Constitutional Convention, is in noway a contradiction that you say. It's because as I contend, there was no resistance to de Vattel's natural born citizenship definition. Apparently, it was accepted by all who attended since no objections were debated.