Before there was a District...................
Ignoring the Native Americans who'd lived, loved, farmed, ranched, and died on the land for the past 4,000 years, on June 20, 1632, Charles I, King of England, made a land grant in North America to Cecilius Calvert, 2nd Baron Baltimore which became the Province of Maryland (later the state of Maryland). This grant set the boundary of Maryland at the low-water mark of the southern bank of the Potomac River.
To induce Englishmen to settle in the new province, Lord Baltimore established the "headright system", which granted an individual 50 acres of land for each person they brought into the colony (whether settler, indentured servant, or slave).
Maryland grew swiftly. In 1662, Baltimore granted the first "land patents" (legal title) in what would later become the District of Columbia to George Thompson and Thomas Gerrard. Thompson received what is now Blue Plains, on the north bank of the confluence of the Potomac River and Oxon Run. Gerrard received what is now St Elizabeths. Both men later received tracts on the southern bank of the Anacostia River, in what is now the Capitol Hill neighborhood, and along the bank of the Potomac River. Thompson and Gerrard's descendents would later sell some of their land to people like Thomas Notley, George Gordon, George Beall, and Daniel Carroll.
By 1749, the population in the area had built up enough that the town of Alexandria, Virginia, was formally organized. Two years later, the town of Georgetown was established just upstream, atop the heights overlooking the Potomac on the Maryland side. Since the Potomac River rises and falls significantly each day with the tides (up to the point where it reaches the Great Falls of the Potomac, just north of Georgetown), fully laden ocean-going ships could navigate all the way to Georgetown and Alexandria.
East of the Anacostia River, there were extensive land patents, too, (although I don't have nearly as cool or complete a map).
By 1791, nearly all of the District of Columbia was farmland. (Swamp my ahistorical ass!!) A great many tracts were maintained as forest for use as lumber and fuel sources, but most of the land west of the Anacostia had been cleared.
A a small monument to these "original patentees" sits on the east side of The Ellipse in D.C.