Territorial Expansion of the United States: 1783-1853 In the Treaty of Paris, which formally ended the Revolutionary War in 1783, England recognized American territorial claims that included most of the land south of the Great Lakes and east of the Mississippi River.The precise borders of modern Maine and the lines between Lake Superior and the headwaters of the Mississippi remained vague, but no European settlements had yet been established along those borders.Spain retained its claims to land bordering the Gulf of Mexico.