Now, to go into some technicalities of the matter --The above was part of a lengthier discussion concerning natural born citizenship, starting here [edit: trying to supply links to sub-threads there is way tricky; I can't get it to work as I intend. I don't know whether this will be true in five minutes, but scrolling UP from the first link I gave presents (most of) the sub-thread, whereas this link doesn't]
The US supreme Court, the Venus (1814) decision, quoting Vattel in its decision -- "The citizens are the members of the civil society; bound to this society by certain duties, and subject to its authority, they equally participate in its advantages. The natives or indigenes are those born in the country of parents who are citizens. Society not being able to subsist and to perpetuate itself but by the children of the citizens, those children naturally follow the condition of their fathers, and succeed to all their rights."
In this quote, Vattel uses "natives or indigenes" to refer to natural born citizens.
That is, in this early supreme Court decision, the Court reiterated the commonly understood meaning of the phrase 'natural born citizen' to be "those [citizens who are] born in the country of parents who are citizens" and, as under the doctrine of 'coverture', a woman's citizenship followed from her husband's, the Court also reiterated that "... those children naturally follow the condition of their fathers, and succeed to all their rights"
EDIT 2016/07/28 --
From the Wong Kim Ark, 169 US 649, 702, 703 (1898) decision --
A person born out of the jurisdiction of the United States can only become a citizen by being naturalized, either by treaty, as in the case of the annexation of foreign territory, or by authority of Congress, exercised either by declaring certain classes of persons to be citizens, as in the enactments conferring citizenship upon foreign-born children of citizens, or by enabling foreigners individually to become citizens by proceedings in the judicial tribunals, as in the ordinary provisions of the naturalization acts.Now, again, here the supreme Court is not setting a precedent, it is merely stating a fact of the matter. And that fact of the matter has not changed between 1898 and 2016 -- Ted Cruz holds US citizenship due to an Act of Congress which gave his (citizen) mother the legal right to claim US citizenship for him, via naturalization, on his behalf. Had he been born prior to 1934, she'd not have had that legal right and he'd have had to apply for naturalization himself once he attained his majority.
Ted Cruz is --
1) "A person born out of the jurisdiction of the United States"
2) the "foreign-born child[ of a US]citizen"
3) a person whose US citizenship was acquired pursuant to an "enactment[ of the Congress] conferring citizenship upon foreign-born children of citizens" ... that is, via naturalization
ERGO: Ted Cruz is a naturalized US citizen and is thereby prohibited by the US Constitution from occupying the Office of US President.
EDIT (and off-topic) --
Wow! The misplacement of "only" has a distinguished pedigree. "A person born out of the jurisdiction of the United States can only become a citizen by being naturalized" should properly be "A person born out of the jurisdiction of the United States can become a citizen only by being naturalized"