them, and they bring forward as proof that each one of these is number, and the result then is that at this place there is already a multitude of compounded quantities because those states of number have each their place—is this number in heaven the same which it is necessary to assume that each of these things is, or is it something different? Plato says it is different; still, he thinks that both these things and the causes of them are numbers; but the one class are ideal causes, and the others are sense causes. ii. 1; 996 a 4. And the most difficult and perplexing question of all is whether unity and being are not, as Plato and the Pythagoreans say, something different from things but their very essence, or whether the underlying substance is something different, friendship, as Empedokles says, or as another says, fire, or water, or air. ii. 4; 1001 a 9. Plato and the Pythagoreans assert that neither being nor yet unity is something different from things, but that it is the very nature of them, as though essence itself consisted in unity and existence. 1036 b 17. So it turns out that many things of which the forms appear different have one form, as the Pythagoreans discovered; and one can say that there is one form for everything, and the others are not forms; and thus all things will be one. ix. 2; 1053 b 11. Whether the one itself is a sort of essence, as first the Pythagoreans and later Plato affirmed.... xi. 7; 1072 b 31. And they are wrong who assume, as do the Pythagoreans and Speusippos, that the most beautiful and the best is not in the first principle, because the first principles of plants and animals are indeed causes; for that which is beautiful and perfect is in what comes from these first principles. xii. 4; 1078 b 21. The Pythagoreans (before Demokritos) only defined a few things, the concepts of which they reduced to numbers, as for instance opportunity or justice or marriage.... xii. 6; 1080 b 16. The Pythagoreans say that there is but one number, the mathematical, but things of sense are not separated from this, for they are composed of it; indeed, they construct the whole heaven out of numbers, but not out of unit numbers, for they assume that the unities have quantity; but how the first unity was so constituted as to have quantity, they seem at a loss to say. b 31. All, as many as regard the one as the element and first principle of things, except the Pythagoreans, assert that numbers are based on the unit; but the Pythagoreans assert, as has been remarked, that numbers have quantity.