By reading Aztec records from the city-state of Tepetlaoztoc, a pair of scientists recently figured out the complicated equations and fractions that officials once used to determine the size of land on which tributes were paid. Two ancient codices, written from A.D. 1540 to 1544, survive from Tepetlaoztoc. They record each household and its number of members, the amount of land owned, and soil types such as stony, sandy, or “yellow earth.”

“The ancient texts were extremely detailed and well organized, because landowners often had to pay tribute according to the value of their holdings,” said co-author Maria del Carmen Jorge y Jorge at the National Autonomous University in Mexico City, Mexico. The Aztecs recorded only the total area of each parcel and the length of the four sides of its perimeter, Jorge y Jorge explained. Officials calculated the size of each parcel using a series of five algorithms—including one also employed by the ancient Sumerians—she added.

That meant that some of the unknown symbols had to represent fractions of a rod, she said. By trial and error, she decoded the system. A hand equaled 3/5 of a rod, an arrow was 1/2 , a heart was 2/5 , an arm was 1/3 , and a bone was 1/5 .

A set of at least five formulas emerged showing how the Aztec surveyors determined the areas of irregular shapes. In some cases, the Aztecs averaged opposite sides and then multiplied. In others, they bisected the fields into triangles.