My records of Vattel writtings show his arguments were ‘The natives, or natural-born citizens, are those born in the country, of parents who are citizens’. We must have different versions of what Vattel defined as ‘natural born’. Along with other readings about this Constitutional requirement I will consider my take on Vattel as being more rigidly accurate and appropriate.
Do you need me to find for you the section where he says that those born of soldiers serving their nation overseas are deemed to be born in country for such purposes?
What do I get when I find it for you? Will you admit you were wrong?
As to defining what is “natural born” - Vattel in 212 is more accurately translated as “indigenous or natives”. There is nothing in the original French that could be accurately translated to “natural born” which was the common term in English law for one born a citizen.
His comment, from his own Swiss point of view, was that the natives, or indigenes (we would say the "indigenous people" of a country) were those born in the country of parents who were citizens.
His book was never the source of our phrase natural born citizen (which came from natural born subject), and no one ever translated his "natives or indigenes" to mean "natural born ciitizens" until 10 years after our Constitution was written.
When they did, it wasn't even an American translator who used that phrase. It was some guy over in England.
Vattel has nothing at all to do with "natural born citizen" in our Constitution. And yes, if Ted Cruz was born an American citizen, he's eligible to be elected President.