Yes, and our nation was also a colony of England before the war of Independence. So the basis of most American law was English law. So the definitions used by the best legal minds of the day have direct bearing on the what the words meant to the founders. I had assumed that this was fairly clear, but apparently not. So, yes Americans took over the concept of "natural born citizen" from English (and more generally European law). And yes, of course they did not apply it to citizenship in England under a King (subject) but to citizenship in the new Republic, under the Constitution. Not everything was invented brand new on July 4, 1776.
Now I move on to the comments you have posted from Professor Solumn.
If the American conception of “natural born citizen” were equivalent to the English notion of a “natural born subject,” then it could be argued that only persons born on American soil to American parents would have qualified.
I'm at a loss to where he gets this, given that the British position, as explained by Blackstone in the excerpt I posted says exactly the opposite of that. Blackstone goes on at great length about the fact that the child of two natual born parents living abroad was concerned natural born.
So his thesis is clearly contradicted by the plain text, above.
I don't believe that your assorted quotes from John Jay and other early Supreme court cases are in context or particualarly relevant. I note in particular the lack of capitalization in the quote discussing the law of nature and the law of nations. I would not therefore assume that the author is discussing a particular book, as you seem to be asserting.
I would be interested, of course, is seeing the primary source documents quoted at length (without too much intersperced commentary) as I have done with Blackstone's commentaries.
Have you seen this very long thread about Vattel?
http://www.freerepublic.com/focus/f-news/2499410/posts
Or this one:
http://www.freerepublic.com/focus/f-bloggers/2500780/posts
Very good threads with source documentation about what is a natural born citizen.
Go do your own research.