BS show me where English common law uses the term natural born citizen.
How about the Congressional record, citing Black's Law Dictionary:
Black's Law Dictionary defines "native" as "a natural-born subject or citizen by birth; one who owes his domicile or citizenship to the fact of his birth within the country referred to". Black defines "natural born" as "In English law one born within the dominion of the King".
Or even the birther site Federalist Blog:
Under the old English common law doctrine of natural-born subject, birth itself was an act of naturalization that required no prior consent or demanded allegiance to the nation in advance...
Because Britain considered all who were born within the dominions of the crown to be its natural-born subjects
Or how about in United Stats v. Wong Kim Ark where the United States Supreme Court ruled:
It thus clearly appears that by the law of England for the last three centuries, beginning before the settlement of this country, and continuing to the present day, aliens, while residing in the dominions possessed by the crown of England, were within the allegiance, the obedience, the faith or loyalty, the protection, the power, and the jurisdiction of the English sovereign; and therefore every child born in England of alien parents was a natural-born subject
It seems that English common law considers a natural-born subject (citizen) to be granted by the place of birth. Black's Law Dictionary states as much, the Congressional record states as much, the US Supreme Court states as much, and birther sites state as much. This should not be in doubt.
Vattel also discusses the role of a sovereign; where is the US sovereign? And in the section in Vattel on citizens and natives it explicitly states that it is the opinion of Vattel himself - not that of natural or other laws - that a man's natural born citizenship flows from his parents. Vattel is quite clear on that; the other "laws" in that section refer to the behavior of other nations (and interestingly, often that of England!), but in terms of the Vattel definition of natural born citizen, is comes from Vattel himself, alone.
So here's a question for you: what legal tradition - other than the de-facto pronouncement of a single man, with no references or tradition to buttress himself - considers the citizenship of a child's parents in terms of natural born status?