It is often claimed that the Greeks had a single, straightforward conception of number, based on units that are counted. This conception views numbers as collections of units, a perspective clearly expressed in the second definition of Euclid’s Elements, Book VII. However, we argue that there are a few traces in the Elements of a different conception of number, which we may call ‘divisive’. This conception is grounded in division and multiplication, rather than in the addition of units, and it a…
Read moreIt is often claimed that the Greeks had a single, straightforward conception of number, based on units that are counted. This conception views numbers as collections of units, a perspective clearly expressed in the second definition of Euclid’s Elements, Book VII. However, we argue that there are a few traces in the Elements of a different conception of number, which we may call ‘divisive’. This conception is grounded in division and multiplication, rather than in the addition of units, and it appears to have deep roots in Plato’s Dialogues. It is probably within the framework of this divisive understanding that we can fully grasp the use of the adjective πρῶτοι to describe prime numbers.
