Cornplanter left his mark. So did Big Sky, Handsome Lake and Soonohquaukau. Accompanied by 1,600 members of their tribes, the leaders of the Six Nations had assembled near Lake Canandaigua in upstate New York in 1794 to negotiate a treaty with the United States government. When the document was complete, each scratched a skewed X, certified with a red-wax seal. Below came the signature of George Washington.

The agreement set boundaries for Indian lands in New York, established annual payments to the tribes, and arranged for “free passage through their lands, and the free use of the harbors and rivers adjoining and within” for the citizens of the young United States. That treaty is on display at an important new exhibition at the National Museum of the American Indian here, on the occasion of the museum’s 10th anniversary: “Nation to Nation: Treaties Between the United States and American Indian Nations.”

Because of preservation concerns, the treaty on display — chosen from a selection of eight from the National Archives — will rotate every six months. But it doesn’t much matter which is shown, for by the time we come upon it, we have already learned that such formal agreements were rife with misunderstanding. Two different worldviews were colliding — “two ways of being,” the exhibition calls them. A reproduction of a 1734 painting shows the British trustees of colonial Georgia, wearing long coats, breeches and wigs, receiving a bare-chested, feathered delegation of Creek Indians. How much mutual understanding could there have been?