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I guess Thomas Jefferson didn't know what the intent of the Founders had been when he decided to enter into undeclared wars with France, and with the Barbary pirates.
Thomas Jefferson didn't want to go to war without a Declaration of War. He asked for one, but Alexander Hamilton, a believer in a strong central government, argued that a Declaration of War wasn't necessary, and persuaded Congress to insist that Jefferson go to war anyway, on the grounds that as we were attacked, a declaration of war was unnecessary.
Jefferson complied, either for political considerations or because he didn't want to waste time fighting over procedure. That was a mistake on his part, I believe. He should have let Congress take the heat, and insisted on a Declaration of War before acting.
President Bush, on the other hand (along with the other presidents of the modern period), have looked upon congressional authorizations as bank checks, to be cashed or not, depending on when and whether they felt like it. This is what makes it a perversion of what the Founders explicitly intended. As you correctly pointed out earlier, it unconstitutionally delegates to the President the decision of war and peace.
As for the thing about Hamilton, that was in reference to an incident that occurred prior to the congressional resolution, when American naval vessels captured a Barbary vessel, then released it on Jefferson's orders, citing the lack of official hostilities. Hamilton castigated him for that, saying that the immediate situation called for keeping the vessel in captivity.