Please tell me how it supports Vattel for this matter? They appear to have different opinions.
To deny and ridicule the importance of Vattel and his work with respect to defining the meaning of the natural born citizen clause also constitutes a denial and ridicule of the works and histories used to compile his work.
Vattel was an important writer on the law of nations. However, not all nations agreed with every aspect of what he wrote. There were several things in his book you probably wouldn't agree with, such as rulers having the right to give over their subjects as hostages. If you want to consider that denial and ridicule, enjoy.
Likewise, those who wrongly try to argue that the British common law contradicts Vattel fail to understand the very British common law they are citing or its own origins.
Ok, please show how we are misunderstanding English Common Law, that you claim actually agrees with Vattel. And while you're at it, show how Madison's quote doesn't say what it appears to say.
A starting point is to secure an acknowledgment that the common law in the British colonies in America and the Republic of the United States of America was never synonymous with British common law. American common law was derived in part from British common law, but American common law underwent a major divergence from British common law even while British common law underwent its own substantial changes and developments. If we cannot agree on this historical fact, there can be no common basis of agreement on all of the matters dependent upon this historical observation.