(3) And out of the triad one stands apart; and in the heptad there are two triads, and one standing apart. The dodecad symbolizes war, the triad of amity, the triad of enmity, three which are life-giving, three which are death-dealing, and God, the faithful king, rules over all from the throne of his sanctity. One above three, three above seven, and seven above twelve, and all are linked together, and one with another.

(21) And as marriage generates from male and female, so six is generated from the odd number three, which is called the masculine number, and the even number two, which is considered the feminine. For twice three are six.

(12) Hermes: This dwelling-place through which we have just passed circle of the twelve types-of-life, this being composed of elements, twelve in number, but of one nature, an omniform idea. For man's delusion there are disunions in them, son, while in their action they are one. Not only can we never part Rashness from Wrath; they cannot even be distinguished. According to right reason (logos), then, they naturally withdraw once and for all, in as much as they are chased out by no less than ten powers, that is, the Ten. For, son, the Ten is that which giveth birth to souls. And Life and Light are unified there, where the One hath being from the Spirit. According then to reason (logos) the One contains the Ten, the Ten the One.

(20) For the motion of the sun from solstice to solstice is completed in six months - in the course of which, at one time the leaves fall, and at another plants bud and seeds come to maturity. And they say that the embryo is perfected exactly in the sixth month, that is, in one hundred and eighty days in addition to the two and a half, as Polybus the physician relates in his book On the Eighth Month, and Aristotle the philosopher in his book On Nature. Hence the Pythagoreans, as I think, reckon six the perfect number, from the creation of the world, according to the prophet, and call it Meseuthys and Marriage, from its being the middle of the even numbers, that is, of ten and two. For it is manifestly at an equal distance from both.

(9) Again the Barbarian philosophy knows the world of thought and the world of sense - the former archetypal, and the latter the image of that which is called the model; and assigns the former to the Monad, as being perceived by the mind, and the world of sense to the number six. For six is called by the Pythagoreans marriage, as being the genital number; and he places in the Monad the invisible heaven and the holy earth, and intellectual light. For "in the beginning," it is said, "God made the heaven and the earth; and the earth was invisible." And it is added, "And God said, Let there be light; and there was light." And in the material cosmogony He creates a solid heaven (and what is solid is capable of being perceived by sense), and a visible earth, and a light that is seen. Does not Plato hence appear to have left the ideas of living creatures in the intellectual world, and to make intellectual objects into sensible species according to their genera? Rightly then Moses says, that the body which Plato calls "the earthly tabernacle" was formed of the ground, but that the rational soul was breathed by God into man's face. For there, they say, the ruling faculty is situated; interpreting the access by the senses into the first man as the addition of the soul.

(2) All things accord in number:

which he very frequently uttered to all his disciples. Or again, Friendship is equality; equality is friendship . Or in the word cosmos , i. e. the world ; or by Jupiter, in the word philosophy , or in the so much celebrated word tetractys . All these and many other inventions of the like kind, were devised by Pythagoras for the benefit and amendment of his associates; and they were considered by those that understood them to be so venerable, and so much the progeny of divine inspiration, that the following was adopted as an oath by those that dwelt together in the common auditory:

(26) Wherefore also man is said to have been made on the sixth day, who became faithful to Him who is the sign (tp epishmw), so as straightway to receive the rest of the Lord's inheritance. Some such thing also is indicated by the sixth hour in the scheme of salvation, in which man was perfected. Further, of the eight, the intermediates are seven; and of the seven, the intervals are shown to be six. For that is another ground, in which seven glorifies eight, and "the heavens declare to the heavens the glory of God."

(16) But here we may be questioned about these numbers which we describe as the primal and authentic:

"Where do you place these numbers, in what genus among Beings? To everyone they seem to come under Quantity and you have certainly brought Quantity in, where you say that discrete Quantity equally with the continuous holds place among Beings; but you go on to say that there are the numbers belonging to the Firsts and then talk of other numbers quite distinct, those of reckoning; tell us how you arrange all this, for there is difficulty here. And then, the unity in sense-things- is that a quantity or is quantity here just so many units brought together, the unity being the starting-point of quantity but not quantity itself? And, if the starting-point, is it a kindred thing or of another genus? All this you owe it to us to make clear."

Be it so; we begin by pointing out a distinction:

You take one thing with another- for we must first deal with objects of sense- a dog and a man, or two men; or you take a group and affirm ten, a decad of men: in this case the number affirmed is not a Reality, even as Reality goes in the sphere of sense, but is purely Quantity: similarly when you resolve into units, breaking up the decad, those units are your principle of Quantity since the single individual is not a unity absolute.

But the case is different when you consider one man in himself and affirm a certain number, duality, for example, in that he is at once living and reasoning.

By this analysis and totalling, you get quantity; but there are two objects under consideration and each of these is one; each of the unities contributes to the complete being and the oneness is inherent in each; this is another kind of number; number essential; even the duality so formed is no posterior; it does not signify a quantity apart from the thing but the quantity in the essence which holds the thing together. The number here is no mere result of your detailing; the things exist of themselves and are not brought together by your reckoning, but what has it to do with essential reality that you count one man in with another? There is here no resultant unity such as that of a choir- the decad is real only to you who count the ten; in the ten of your reckoning there cannot be a decad without a unitary basis; it is you that make the ten by your counting, by fixing that tenness down to quantity; in choir and army there is something more than that, something not of your placing.

But how do you come to have a number to place?

The Number inherent apart from any enumeration has its own manner of being, but the other, that resulting upon the appearance of an external to be appraised by the Number within yourself, is either an Act of these inherent numbers or an Act in accordance with them; in counting we produce number and so bring quantity into being just as in walking we bring a certain movement into being.

But what of that "Number within us having its own manner of being"?

It is the Number of our essence. "Our essence" we read "partakes of Number and harmony and, also, is Number and harmony." "Neither body nor magnitude," someone says: soul, then, is Number since it is essence. The number belonging to body is an essence of the order of body; the number belonging to soul constitutes the essences of souls.

In the Intellectuals, all, if the Absolute Living-Form, there is a multiple- a triad, let us say- that Triad of the Living-Form is of the nature of essence: and the Triad prior to any living thing, Triad in the realm of Being, is a principle of essence.

When you enumerate two things- say, animal and beauty- each of these remains one thing; the number is your production; it lay within yourself; it is you that elaborate quantity, here the dyad. But when you declare virtue to be a Tetrad, you are affirming a Tetrad which does actually exist; the parts, so to speak, make one thing; you are taking as the object of your act a Unity- Tetrad to which you accommodate the Tetrad within yourself.