The Naturalization Act of 1790 has since been amended many times by Congress. Transport yourself to the 21st Century. This is the current law:
"A child born abroad to one U.S. citizen parent and one alien parent acquires U.S. citizenship at birth under Section 301(g) of the INA provided the U.S. citizen parent was physically present in the United States or one of its outlying possessions for the time period required by the law applicable at the time of the child's birth. (For birth on or after November 14, 1986, a period of five years physical presence, two after the age of fourteen, is required. For birth between December 24, 1952 and November 13, 1986, a period of ten years, five after the age of fourteen, is required for physical presence in the United States or one of its outlying possessions to transmit U.S. citizenship to the child.) The U.S. citizen parent must be the genetic or the gestational parent and the legal parent of the child under local law at the time and place of the child's birth to transmit U.S. citizenship.
They will question whether citizenship is the same as natural born citizen. I think there is a difference when it comes to the eligibility matter. You legal word smiths can take that matter up and help me understand it all.