numerical one, it should be, and it is, construed to the mind as one one. One one, then, is the first arithmetical number, and, if so, we must be able to show that its elements are the μονὰς and the δυὰς for these are, according to Pythagoreans, the elements of all number without exception; and this can be shown without much difficulty. One one: which word, in that expression, stands for the monad, the point of agreement in all numbers? The first one does so. We say one one, one five, one ten, one hundred. All these numbers agree in being one—i.e., once what they are. Then, again, which word, in the expression one one, stands for the duad—the diversity, the point in which one one differs from all other numbers? The second one does so. One one, one five, one hundred. The second word in each of these expressions expresses the difference of each of these numbers. One one is different from one five in its second term, but not in its first. From these remarks it appears, I think, that even number one is no exception to the Pythagorean law, which declares that the elements of all number are the monad and the duad, and that these are not themselves numbers. Thus, by considering numbers, we obtain light as to the constitution of the universe. Everything in the universe has some point in which it resembles everything else, and it has some point or points in which it differs from everything else; just as every number has some point in which it resembles all other numbers, and some in which it differs from all other numbers.
