  How were surfaces evaluated before the invention of the sexagesimal place
value notation in Mesopotamia? This chapter examines a group of five tablets
containing tables for surfaces of squares and rectangles dated to the Early
Dynastic period (ca. 2600-2350 BCE) and unearthed in southern Mesopotamia. In
order to capture the methods used by ancient scribes to quantify surfaces,
special attention is paid to the layout and organization of the tables, as well
as to the way in which measurement values are written down. It is argued that
these methods vary according to the dimensions of the squares or rectangles
concerned: the quantification of small surfaces does not use the same
mathematical tools as the quantification of large parcels of land. The chapter
shows a reciprocal influence between the metrological systems adopted by the
ancient scribes and the methods of calculation of surface they implemented.
Some methods may reflect ancient land-surveying practices, and others may
testify the emergence of new mathematical concepts applied to all kinds of
surfaces, large or small. Ultimately, several different conceptualizations of
the notion of surface emerge from the examination of these tables.
