Plutarch De E apud Delphos 8

[8] 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, ¹ 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 ² because of the resemblance of the even number to the female and of the odd number to the male. ³ 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. ⁴ 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.

There is also a sense in which it has been called Nature, since by being multiplied into itself it ends in itself again. For even as Nature receives wheat in the form of seed and puts it to its use, and creates in the interim many shapes and forms through which she carries out the process of growth to its end, but, to crown all, displays wheat again, and thus presents as her result the beginning at the end of the whole, so in like manner, while the other numbers when raised to a power end in different numbers as the result of the increase, only the numbers five and six, when multiplied by themselves, repeat themselves and preserve their identity. Thus six times six is thirty-six, and five times five is twenty-five; and furthermore, the number six does this but once, and the single instance is when it is squared; but with five this result is obtained in raising it to any power, and it has a unique characteristic, when added to itself, of producing either itself or ten alternately ⁵ as the addition progresses, and of doing this to infinity, since this number takes its pattern from the primal principle which orders the whole. For as that principle by changes creates a complete universe out of itself, and then in turn out of the universe creates itself again, as Heracleitus ⁶ says, and exchanges fire for all and all for fire, as gold for goods and goods for gold, so, in like manner, the conjunction of five with itself is determined by Nature’s law to produce nothing incomplete or foreign, but it has strictly limited changes; it produces either itself or ten, that is to say, either its own characteristic or the perfect whole.

[8] I answered therefore that Eustrophus has excellently solved the difficulty by number. For (said I) since all number is distributed into even and odd, unity is in efficacy common to them both,—for that being added to an even number, it makes it odd, and to an odd, it makes it even, two constituting the beginning of the even, and three of the odd. Now the number of five, composed of these two, is deservedly honored, as being the first compound made of the first simple numbers, and is called the marriage, for the resemblance of the odd with the male, and the even with the female. For in the divisions of the numbers into equal parts, the even, being wholly separated, leaves a certain capacious beginning and space in itself; but in the odd, suffering the same thing, there always remains a middle, of generative distribution, by which it is more fruitful than the other, and being mixed is always master, never mastered. For by the mixture of both, even and odd together, there is never produced an even number but always an odd. But which is more, either of them added to and compounded with itself shows the difference; for no even joined with another even ever produced an odd, or went forth of its proper nature, being through weakness unable to generate another and imperfect. But odd numbers mixed with odd do, through their being every way fruitful, produce many even ones. Time does not now permit us to set down the other powers and differences of numbers. Therefore have the Pythagoreans, through a certain resemblance, said that five is the marriage of the first male and the first female number. This also is it for which it is called Nature, by the multiplication of itself determining again into itself. For as Nature, taking a grain of wheat for seed and diffusing it, produces many forms and species between, by which she brings her work to an end, but at last she shows again a grain of wheat, restoring the beginning in the end of all; so, while the rest of the numbers, when they are multiplied into others, terminate by the increase only those of five and six, multiplied by themselves, bring back and preserve themselves. For six times six makes thirty-six, and five times five makes twenty-five. And again, six does this once, and only after one manner, to wit, when it is squared. But this indeed befalls five both by multiplication and by composition with itself, to which being added, it alternatively makes itself and ten; and this as far as all number can extend, this number imitating the beginning or first Cause which governs the universe. For as that first Cause, preserving the world by itself, does reciprocally perfect itself by the world, as Heraclitus says of fire, and as money is changed for gold, and gold for money; so the congress of five with itself is framed by Nature to produce nothing imperfect or strange, but has limited changes; for it either generates itself or ten, that is, either what is proper to itself, or what is perfect.