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I said, therefore, that Eustrophus solved the difficulty most excellently with his number. For since, I continued, every number may be classified as even or odd, and unity, by virtue of its potentiality, is common to both, for the reason that its addition makes the odd number even and the even number odd, Cf. 429 a, infra. and since twTo makes the first of the even numbers and three the first of the odd, and five is produced by the union of these numbers, very naturally five has come to be honoured as being the first number created out of the first numbers; and it has received the name of marriage Cf.Moralia, 263 f, 1012 e, 1018 c, and Clement of Alexandria, Stromateis, v. chap. xiv. 93. 4 (p. 702 Potter). because of the resemblance of the even number to the female and of the odd number to the male. Cf.Moralia, 288 c-e. For in the division of numbers into two equal factors, the even number separates completely and leaves a certain receptive opening and, as it were, a space within itself; but in the odd, when it undergoes this process, there is always left over from the division a generative middle part. Wherefore it is more generative than the other, and in combination it is always dominant and is never dominated. Cf. Plutarch, Life and Poetry of Homer, 145 (Bernardakis, vol. vii. p. 416). For in no combination of these two numbers (even and odd) is there produced from the two an even number, but in all combinations an odd. Moreover, each when applied to itself and made composite with itself shows the difference. For no even number united with even gives an odd number, nor does it ever show any departure from its own distinctive nature, being impotent through its weakness to produce the other number, and having no power of accomplishment; but odd numbers combined with odd produce a numerous progeny of even numbers because of their omnipresent generative function. It would not be timely at this moment to enumerate the other potent properties and divergences of numbers; let it suffice to say that the Pythagoreans called Five a Marriage on the ground that it was produced by the association of the first male number and the first female number.
