On Nicomachus's Introduction to Arithmetic

The monad is the minimum of quantity, or the first and common part of quantity, or the principle of quantity. According to Thymaridas, it is a limiting quantity, since the beginning and end of each thing is called a limit, and there are things of which the center is also a limit, as is the case, naturally, with a circle and a sphere. The moderns define it as that by which each of the things that exist is called one. This definition lacked the provision that it should also be systematic. The Chrysippeans say confusedly, "A monad is a single multitude"; for this alone is contrasted with multitude. Some of the Pythagoreans said, "A monad is the boundary between number and its parts"; for from it, as from a seed and an eternal root, the logoi proportions increase conversely toward both sides, being diminished in grandeur while being divided toward infinity, and being magnified while increasing toward infinity. Others defined the monad as the "form of forms," as it contains in potentiality all the logoi proportions in number. For indeed, it is polygonal in a plane from a triangle to infinity, and appearing in all solid forms, both spherical and conical, restorative, lateral, diametrical, and, most commonly, heteromēkēs oblong/unequal-sided, whenever it provides the notion of a greater dynamis potentiality having arisen from itself, and proportional, and relative according to the ten relations, and in other ways, as many as will be demonstrated. The monad is so called because its own logos proportion/rational principle persists throughout. And all other things are likewise made rational by it.