 In trying to understand what Aristotle tells us about formal numbers, it is necessary to bear in mind the fundamental distinction he draws between formal numbers and mathematical numbers: both are, according to Aristotle, composed of units, but formal numbers are composed of very strange units, such that those in one formal number cannot be combined with those in any other. The units of which mathematical numbers are composed can be added and subtracted freely. (See here Metaphysics XIII 6. 1080a15–b4.) And furthermore there is only one formal number for each of the numbers 2, 3, 4, etc., where there are indefinitely many instances of each among the mathematical numbers. (See here Metaphysics I 6. 987b14–18.) The mathematical numbers are the ones mathematicians work with, e.g. in performing arithmetical operations, and that is presumably why they are called ‘mathematical’. There is a corresponding division between types of geometrical figures, but we hear too little about this; most of what follows will be concerned with numbers.