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Ellicott, a prominent professional surveyor, hired Benjamin Banneker, an astronomer and mathematician from Maryland, to make the astronomical observations and calculations necessary to establish the south corner of the square at Jones Point in Alexandria. According to legend, "Banneker fixed the position of the first stone by lying on his back to find the exact starting point for the survey ... and plotting six stars as they crossed his spot at a particular time of night." From there, Ellicott's team embarked on a forty-mile journey, surveying ten-mile lines first along the southwest line, then along The northwest line, next along the northeast line, and finally along the southeast line. The team completed this rough survey in April 1791.

On April 15, 1791, the Alexandria Masonic Lodge placed a small stone at the south corner at Jones Point in ceremonies attended by Ellicott, federal district commissioners Daniel Carroll and David Stuart, and other dignitaries. George Washington did not attend the ceremony, although he did visit the site the prior month. Newpapers around the country announced the story of the beginning of the new federal city. (In 1794, the ceremonial stone at Jones Point was replaced by a large stone, still in place today, with the inscription "The beginning of the Territory of Columbia" on one side.