If as Comrade Obama Jr claims his dad was Barak Hussein Obama Sr, of Kenya,
than it's not possible for Junior to be a Natural Born Citizen of the U.S.
At the time of the drafting and ratification of the United States constitution,
the definition of natural born citizen, combined both the principles of jus soli and jus sanguinis.
The citizens are the members of the civil society; bound to this society by certain duties, and subject to its authority, they equally participate in its advantages. 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 therefore 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.
Emmerich De Vattel, (1714-1767,) Law of Nations, 1758, § 212, "Of the citizens and naturals."
There seems to be an error in your post in that the text you post of Vattle was not translated to English until 1797 and not 1758.
Absolutely true. Regardless of the fact he may have been born in Hawaii, California, New York, or any other state. His father was a foreign student, a Kenyan, and at the time, a British subject. BHO Sr. returned to Kenya after completing his studies in the U.S.. BO Jr. does not qualify to be POTUS period.