On Nicomachus's Introduction to Arithmetic

Again, from another principle of quantity, according to the first division, one part is even and the other is odd. The even is that which is capable of being divided into equal parts, both greatest and least: greatest in magnitude and in its relation to the whole, because it is divided into halves; and least in quantity, because it is divided into two (for there is nothing in nature smaller than two, since there is no number inside the dyad; for this is the first system of units, which is the definition of number in general). The odd is that which, when divided into the smallest parts, produces parts unequal to one another. For it is not divisible into two equal parts; for this would be destructive of the naturally indivisible monad, which is useful for the entire technology and such physiologies. Since the even number, when divided in any way—whether into equal or unequal parts—is always resolved into homogeneous things; for they are either both even or both odd. But the odd is resolved into the other two lengths of number. The followers of the school called the heteromēkēs oblong number "even" by accident, based on the meaning, as it possesses only one of the lengths of the number in its divisions. Contrasted to this, they called the odd number amphimēkēs both-sided/having both lengths, because it provides both of these together. They could also be recognized through one another in the natural exposition of number: the even is that which differs from the odd by a unit in either direction, and the odd is that which differs from the even by the same. Each genus is formed specifically and accidentally: the even is even specifically by the dyad, and accidentally by the monad...