“So my great-grandfather couldn’t become a citizen unless his father came over and became a citizen, and my great-great-grandfather couldn’t become a citizen unless his father came over and became a citizen, and my great-great-grandfather needed his father to come over and become a citizen before he could become a citizen?”
I’ve heard birthers seem to imply that, but very few and possibly by mistake. Most of the two-citizen-parents faction of the birthers make it all about the parents’ citizenship on the child’s date of birth. On that they actually disagree with their favorite source, Emerich de Vattel. Vattel wrote in French, and thus never dealt with what our term “natural born citizen” means, and what he did write is not what this birther faction claims.
“Les Naturels ou indigènes font ceux qui font nés dans le pays de Parens Citoyens.”
The obvious translation of Naturels is “naturals”, so I looked is up in /Black’s Law Dictionary/, Ninth Edition. The most applicable of the given meaning is the native people. This is not just ‘native’ as in born here, as I am, but native as “Native-Americans” refers to American Indians. “Indigènes” obviously corresponds to “indigenous”, which again refers to more than one or two generations.
“Parens” seems to translate to “parents”, but that might not be correct. I don’t speak French. I’ve heard from a French-speaker that in this context “Parens” can means blood relatives, and not just mother and father.
Vattel did not present “Naturels ou indigènes” as a special class under the law, precisely distinguishing by the dates their parents became citizens. Rather, they are the indigenous natives. They were born here; their parents were born here; their parents parents were born here; and so on for longer than we can trace. Vattel’s concept of a nation’s “Naturels ou indigènes” does not map well to a nation formed from settlers who rebelled against their homeland.
The founders spoke and read French. The Editions of Vattel given to them by Charles Dumas were all in French.Benjamin Franklin used the French Version of Vattel as a code book to communicate with agents in Europe. 
The Founders did not need the term translated. They translated it themselves into the phrase "Natural Born Citizen." Learn what you are talking about.