Hence, Barry Obama, were he born in Hawaii to Barack Sr, would have been, as Vattell says, "NATURALIZED AT BIRTH" under US statute at the time. Barry is a therefore a naturalized citizen at best given his claimed father and not a natural born citizen.
In ENGLIGH Common Law, regardless of what other countries might have done, someone born in the country is "natural born". Vattel never said that was not the case in England, and he isn' a valid cite for proving the practice in England.