“In the Pythagorean doctrine, number comprises within itself two species⁠—odd and even; it is therefore the unity of these two contraries; it is the odd and the even. Now the Pythagoreans said also that one, or the unit, is the odd and the even; and thus we arrive at this result, that one, or the unit, is the essence of number, or number absolutely. As such, it is also the ground of all numbers, and is therefore named the first one, of whose origin nothing further can be said. In this respect the Pythagorean theory of numbers is merely an expression for ‘all is from the original one,’⁠—from one being, to which they also gave the name of God; for in the words of Philolaus, ‘God embraces and actuates all, and is but one.’⁠ ⁠…

“But in the essence of number, or in the first original one, all other numbers, and consequently the elements of numbers, and the elements of the whole world, and all nature, are contained. The elements of number are the even and the odd; on this account the first one is the even-odd, which the Pythagoreans, in their occasionally strained mode of symbolizing, attempted to prove thus; that one being added to the even makes odd, and to the odd, even.”