By the way, other words and phrases that never appeared in Vattel:
Vattel didn't write about Presidents, he wrote about Sovereigns, meaning Kings. He lived in pre-revolution France, when all the French leaders were named King Louis, and pre-revolution Switzerland, where the rule of law went from God to Pope and then down. His writings reflect that.
Vattel is not a founding father, his writings in no way resemble the US constitution.