David Ramsay, eminent historian of the Revolution explained 'natural born' this way:
In his 1789 article, Ramsay first explained who the original citizens were and then defined the natural born citizens as the children born in the country to citizen parents. He said concerning the children born after the declaration of independence, [c]itizenship is the inheritance of the children of those who have taken part in the late revolution; but this is confined exclusively to the children of those who were themselves citizens . Id. at 6.
He added that citizenship by inheritance belongs to none but the children of those Americans, who, having survived the declaration of independence, acquired that adventitious character in their own right, and transmitted it to their offspring . Id. at 7. He continued that citizenship as a natural right, belongs to none but those who have been born of citizens since the 4th of July, 1776 . Id. at 6.
The above two paragraphs and more are in an Essay on Ramsay