And, yes, common law principles can be properly considered in interpreting provisions of the Constitution. If a particular term in the Constitution has been unambiguously and precisely defined by courts in developing the common law, then it might be reasonable to assume that those who used that same term in the Constitution intended that same meaning when they used that word in the Constitution. But, in interpreting the Constitution, a judge who cares about "original intent" would be searching for the intent of the framers and not for the prior intent of some judge making common law. The fact that the framers used the same word or term that had previously been used by some judge creating our common law does not necessarily mean that the framers intended that same meaning.
“The fact that the framers used the same word or term that had previously been used by some judge creating our common law does not necessarily mean that the framers intended that same meaning.”
In the absence of any contrary reasonable interpretation, it would.
Natural born citizen/subject HAD a well known meaning at the time the US Constitution was written and ratified. That well known and accepted meaning, found in English common law, IS the meaning, unless someone can provide evidence that it was not.