The Sahagún account, compiled from Aztecs’ recollections of their lost city, has proved strikingly accurate. Of the 78 structures he described, archaeologists have found vestiges of more than half.

During the most recent excavation, underneath a small plaza wedged between the Templo Mayor and the cathedral, Mr. Barrera had been looking for the round ceremonial platform because it had been described in the Sahagún record.

Much of what the friar and other witnesses chronicled now lies as deep as 25 feet underground. To get there, Mr. Barrera’s team must first navigate the electricity lines and water mains that are the guts of the modern city and then travel down through a colonial layer, which yields its own set of artifacts.

“It is like a book that we are trying to read from the surface to the deepest point,” he said.

But despite the guidance from historical records, Mexico City’s archaeologists cannot dig anywhere they please.

Part of the sacred precinct is now a raucous medley of the mundane. The street vendors hawking pirated Chinese-made toys and English-language lesson CDs from crumbling facades are merely the loudest. To excavate under the area’s hotels, diners, cheap clothing stands and used bookstores would entail fraught negotiation.

Along the quieter blocks of the precinct, handsome colonial structures are now museums and government buildings, themselves historical landmarks.

Archaeologists believe that the Calmécac, a school for Aztec nobles, extends under the courtyards of Mexico’s Education Ministry building. For now, the only part of the Calmécac that has been excavated are several walls and sculptures on display under a building housing the Spanish cultural center, discovered when it was remodeled.