And we can also go to Blackstone's Commentaries, also well known to the Founding Fathers, and find an entirely different definition of natural-born citizen.
Blackstone's view doesn't help you either, as he passes citizenship via the father, if not requiring both parents to be citizens. However, it makes no difference, as the founding fathers specifically repudiated English law on this point. From the same link:
"The Naturalization Act of 1795, which was also signed by George Washington, recognized Blackstone's commentaries on English Common Law, making children born overseas in the lands under British rule, British Subjects. Even if their parents were American. This act removed the words natural born from children born overseas of American parents, so that no other potentate could lay claim to this person, and thus establish "a presence of influence" in the Executive Branch. It was the intent of our Founding Fathers to “naturalize at birth†these children, but not give them the status "natural born citizens." Also in this act of 1795, we see the importance of complete allegiance to the United States for all people naturalized, as this is the first appearance of the oath of allegiance "to renounce forever all allegiance and fidelity to any foreign prince, potentate, state, or sovereignty whereof such alien may at that time be a citizen or subject." This oath is still in effect today."