The entire passage talks about persons naturally becoming citizens when they are born in the country. How would that NOT be equated with natural born citizen?? Your argument is astounding in its ignorance. Further, to be born a native, it still says you have to be born of parents who are citizens. This equates directly with the concept of natural born citizenship. Third, the 1797 translation obviously followed the common usage at the time of natural born citizen. Why would a translator suddenly pluck this term out of thin air unless it was in common use?? This is how dictionaries decide to add words ... because the words have become established within society. Sorry, but your argument is a three-time loser.
I have also quotes at length from the Supreme Court, and then you deny the language says what it clearly says...so I conclude you cannot read English.
None of the language you claim is so clear uses BOTH terms in a way you claim it does, so it's not my English-reading skills that are suspect, but yours.
So do relevant passages of English constitutional law, which forms the basis for much of our own law.