Actually the Constitution is silent on what constitutes a Natural Born Citizen. The founders clarified their intent with the firsts acts of Congress. What they actuall passed and signed into law is:
“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”
“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”
The Naturalization Act of 1790 clearly stated a child born abroad acquired U.S. citizenship by naturalization as a naturalized citizen.