Two very important points addressed in this article:

1. Natural-Born Citizen Definition:

Book I, Chapter 19, Section 212 of The Law of Nations reads:

Natural-born citizens, are those born in the country, of parents who are citizens. As the society cannot exist and perpetuate itself otherwise than by the children of the citizens, those children naturally follow the condition of their fathers, and succeed to all their rights. The society is supposed to desire this, in consequence of what it owes to its own preservation; and it is presumed, as matter of course, that each citizen, on entering into society, reserves to his children the right of becoming members of it. The country of the fathers is therefore that of the children; and these become true citizens merely by their tacit consent. We shall soon see, whether, on their coming to the years of discretion, they may renounce their right, and what they owe to the society in which they were born. I say, that, in order to be of the country, it is necessary that a person be born of a father who is a citizen; for if he is born there of a foreigner, it will be only the place of his birth, and not his country. [Emphasis added.]

2. How this apply to the 14th Amendment?

Senator Jacob Merritt Howard (R-Mich.) was the principal architect of the citizenship clause of the 14th Amendment.

During the debates on the proposed amendment, Senator Howard insisted that the qualifying phrase “subject to the jurisdiction thereof” be inserted into Section 1 of the 14th Amendment being considered by his colleagues. Howard explained the need for the alteration:

This amendment which I have offered is simply declaratory of what I regard as the law of the land already, that every person born within the limits of the United States, and subject to their jurisdiction, is by virtue of natural law and national law a citizen of the United States. This will not, of course, include persons born in the United States who are foreigners, aliens, [or] who belong to the families of ambassadors or foreign ministers accredited to the Government of the United States, but will include every other class of persons.