This is incorrect. Much of the Constitution is based on English Common Law, and the common law definition is quite different. You may be very sure that the Founders were conversant with English Common Law. So much so, that the Naturalization Act of 1790 said
And the children of citizens of the United States that may be born beyond Sea, or out of the limits of the United States, shall be considered as natural born Citizens: Provided, that the right of citizenship shall not descend to persons whose fathers have never been resident in the United States [emphasis added]Thus many of the Founders voted on this act, which said those born out of the limits would be considered as natural born. While the 1790 version would have excluded Ted Cruz because his father had not been resident in the US (to my knowledge), but it has been amended many times and the act in effect at the time of his birth had only a residency requirement for his mother, which she fulfilled.
"This is incorrect. Much of the Constitution is based on English Common Law, and the common law definition is quite different."
There is no definition in English Common Law for natural born Citizen, as the British were all subjects of the king.
"The citizenship of no man could be previous to the declaration of independence, and, as a natural right, belongs to none but those who have been born of citizens since the 4th of July, 1776."....David Ramsay, 1789.
A Dissertation on Manner of Acquiring Character & Privileges of Citizen of U.S.-by David Ramsay-1789