general expression for their difference. Μονὰς is the Pythagorean term for the universal; ἀόριστος δυὰς is the Pythagorean term for the particular; and neither of these is capable of being conceived without the other. The true conceivable limit, whether considered as a thought or a thing, is the result of their combination.
16. We shall perhaps get more light thrown on these terms if we consider them under a purely arithmetical point of view. It might be thought that these words, πονὰς and ἀόριστος δυὰς, simply signified one and two, or one and indeterminate two. But that is not at all the meaning which the Pythagoreans attached to them. According to the Pythagoreans, every number consisted of these two parts; the μονὰς and the δυὰς were not numbers, but were the mere elements of number. This seems a perplexing position, yet it is susceptible, I think, of explanation. For example, every number is different from every other number; 1 is different from 5, 5 is different from 10, 10 is different from 20, and from 100, and so on. But every number also agrees with every number; and in what respect is it that all numbers agree? They all agree in this respect, that every number is once, or one times that number, whatever it may be; 5 and 10 and 20, and so on, agree in being once 5, once 10, and once 20. Each of these is one times what it is, so that they all agree in containing the μονὰς, or one. If you were to say five, or
