(15) As I said earlier, among the things that were created the monad is first, the dyad follows it, and the triad, up to the tenths. Now the tenths rule the hundredths; the hundredths rule the thousandths; the thousands rule the ten thousands. This is the pattern immortals. First Man is like this: His monad [...].

(109) The Pythagoreans revered the monad but despised the duad, because it was the symbol of polarity. By the power of the duad the deep was created in contradistinction to the heavens. The deep mirrored the heavens and became the symbol of illusion, for the below was merely a reflection of the above. The below was called maya, the illusion, the sea, the Great Void, and to symbolize it the Magi of Persia carried mirrors. From the duad arose disputes and contentions, until by bringing the monad between the duad, equilibrium was reestablished by the Savior-God, who took upon Himself the form of a number and was crucified between two thieves for the sins of men.

(73) The monad signifies (a) the all-including ONE. The Pythagoreans called the monad the "noble number, Sire of Gods and men." The monad also signifies (b) the sum of any combination of numbers considered as a whole. Thus, the universe is considered as a monad, but the individual parts of the universe (such as the planets and elements) are monads in relation to the parts of which they themselves are composed, though they, in turn, are parts of the greater monad formed of their sum. The monad may also be likened (c) to the seed of a tree which, when it has grown, has many branches (the numbers). In other words, the numbers are to the monad what the branches of the tree are to the seed of the tree. From the study of the mysterious Pythagorean monad, Leibnitz evolved his magnificent theory of the world atoms--a theory in perfect accord with the ancient teachings of the Mysteries, for Leibnitz himself was an initiate of a secret school. By some Pythagoreans the monad is also considered (d) synonymous with the one.

(101) Monad--1--is so called because it remains always in the same condition--that is, separate from multitude. Its attributes are as follows: It is called mind, because the mind is stable and has preeminence; hermaphrodism, because it is both male and female; odd and even, for being added to the even it makes odd, and to the odd, even; God, because it is the beginning and end of all, but itself has neither beginning nor end; good, for such is the nature of God; the receptacle of matter, because it produces the duad, which is essentially material.

(111) The sacredness of the triad and its symbol--the triangle--is derived from the fact that it is made up of the monad and the duad. The monad is the symbol of the Divine Father and the duad of the Great Mother. The triad being made of these two is therefore androgynous and is symbolic of the fact that God gave birth to His worlds out of Himself, who in His creative aspect is always symbolized by the triangle. The monad passing into the duad was thus capable of becoming the parent of progeny, for the duad was the womb of Meru, within which the world was incubated and within which it still exists in embryo.

(107) As the monad is the father, so the duad is the mother; therefore, the duad has certain points in common with the goddesses Isis, Rhea (Jove's mother), Phrygia, Lydia, Dindymene (Cybele), and Ceres; Erato (one of the Muses); Diana, because the moon is forked; Dictynna, Venus, Dione, Cytherea; Juno, because she is both wife and sister of Jupiter; and Maia, the mother of Mercury.

(105) The following symbolic names were given to the duad--2--because it has been divided, and is two rather than one; and when there are two, each is opposed to the other: genius, evil, darkness, inequality, instability, movability, boldness, fortitude, contention, matter, dissimilarity, partition between multitude and monad, defect, shapelessness, indefiniteness, indeterminate ness, harmony, tolerance, root, feet of fountain-abounding idea, top, Phanes, opinion, fallacy, alterity, diffidence, impulse, death, motion, generation, mutation, division, longitude, augmentation, composition, communion, misfortune, sustentation, imposition, marriage, soul, and science.

(102) By the Pythagoreans monad was called chaos, obscurity, chasm, Tartarus, Styx, abyss, Lethe, Atlas, Axis, Morpho (a name for Venus), and Tower or Throne of Jupiter, because of the great power which abides in the center of the universe and controls the circular motion of the planers about itself. Monad is also called germinal reason, because it is the origin of all the thoughts in the universe. Other names given to it were: Apollo, because of its relation to the sun; Prometheus, because he brought man light; Pyralios, one who exists in fire; geniture, because without it no number can exist; substance, because substance is primary; cause of truth; and constitution of symphony: all these because it is the primordial one.

(75) The one was defined by the Platonists as "the summit of the many." The one differs from the monad in that the term monad is used to designate the sum of the parts considered as a unit, whereas the one is the term applied to each of its integral parts.

(5) As a manifold, then, this God, the Intellectual-Principle, exists within the Soul here, the Soul which once for all stands linked a member of the divine, unless by a deliberate apostasy.

Bringing itself close to the divine Intellect, becoming, as it were, one with this, it seeks still further: What Being, now, has engendered this God, what is the Simplex preceding this multiple; what the cause at once of its existence and of its existing as a manifold; what the source of this Number, this Quantity?

Number, Quantity, is not primal: obviously before even duality, there must stand the unity.

The Dyad is a secondary; deriving from unity, it finds in unity the determinant needed by its native indetermination: once there is any determination, there is Number, in the sense, of course, of the real Number. And the soul is such a number or quantity. For the Primals are not masses or magnitudes; all of that gross order is later, real only to the sense-thought; even in seed the effective reality is not the moist substance but the unseen- that is to say Number and the Reason-Principle .

Thus by what we call the Number and the Dyad of that higher realm, we mean Reason Principles and the Intellectual-Principle: but while the Dyad is, as regards that sphere, undetermined- representing, as it were, the underly of The One- the later Number - that which rises from the Dyad and The One- is not Matter to the later existents but is their forming-Idea, for all of them take shape, so to speak, from the ideas rising within this. The determination of the Dyad is brought about partly from its object- The One- and partly from itself, as is the case with all vision in the act of sight: intellection is vision occupied upon The One.

(124) The tetrad (the elements) plus the monad equals the pentad. The Pythagoreans taught that the elements of earth, fire, air, and water were permeated by a substance called ether--the basis of vitality and life. Therefore, they chose the five-pointed star, or pentagram, as the symbol of vitality, health, and interpenetration.

(11) It may be suggested that the decad is nothing more than so many henads; admitting the one henad why should we reject the ten? As the one is a real existence why not the rest? We are certainly not compelled to attach that one henad to some one thing and so deprive all the rest of the means to unity: since every existent must be one thing, the unity is obviously common to all. This means one principle applying to many, the principle whose existence within itself we affirmed to be presupposed by its manifestation outside.

But if a henad exists in some given object and further is observed in something else, then that first henad being real, there cannot be only one henad in existence; there must be a multiplicity of henads.

Supposing that first henad alone to exist, it must obviously be lodged either in the thing of completest Being or at all events in the thing most completely a unity. If in the thing of completest Being, then the other henads are but nominal and cannot be ranked with the first henad, or else Number becomes a collection of unlike monads and there are differences among monads . If that first henad is to be taken as lodged in the thing of completest unity, there is the question why that most perfect unity should require the first henad to give it unity.

Since all this is impossible, then, before any particular can be thought of as a unit, there must exist a unity bare, unrelated by very essence. If in that realm also there must be a unity apart from anything that can be called one thing, why should there not exist another unity as well?

Each particular, considered in itself, would be a manifold of monads, totalling to a collective unity. If however Nature produces continuously- or rather has produced once for all- not halting at the first production but bringing a sort of continuous unity into being, then it produces the minor numbers by the sheer fact of setting an early limit to its advance: outgoing to a greater extent- not in the sense of moving from point to point but in its inner changes- it would produce the larger numbers; to each number so emerging it would attach the due quantities and the appropriate thing, knowing that without this adaptation to Number the thing could not exist or would be a stray, something outside, at once, of both Number and Reason.

(54) German philosophy had its inception with Gottfried Wilhelm von Leibnitz, whose theories are permeated with the qualities of optimism and idealism. Leibnitz's criteria of sufficient reason revealed to him the insufficiency of Descartes' theory of extension, and he therefore concluded that substance itself contained an inherent power in the form of an incalculable number of separate and all-sufficient units. Matter reduced to its ultimate particles ceases to exist as a substantial body, being resolved into a mass of immaterial ideas or metaphysical units of power, to which Leibnitz applied the term monad. Thus the universe is composed of an infinite number of separate monadic entities unfolding spontaneously through the objectification of innate active qualities. All things are conceived as consisting of single monads of varying magnitudes or of aggregations of these bodies, which may exist as physical, emotional, mental, or spiritual substances. God is the first and greatest Monad; the spirit of man is an awakened monad in contradistinction to the lower kingdoms whose governing monadic powers are in a semi-dormant state.

(6) The self-existent Super-goodness then, as projecting the first gift of self-existent being, is celebrated by the elder and first of the participations; and being itself is from It, and in It; as also the sources of things being, and all the things that be, and the things howsoever sustained by being, and that irresistibly, and comprehensively and uniformly. For even in a monad, every number preexists in the form of a unit, and the monad holds every number in itself singly. And every number is united in the monad, but so far as it advances from the monad, so far it is distributed and multiplied. And in a centre, all the lines of the circle coexist within one union, and the point holds all the straight lines in itself, uniformly united, both to each other, and to the one source from which they proceeded, and in the centre itself they are completely united; but standing slightly distant from it, they are slightly separated; but when more apart, more so. And in one word, the nearer they are to the centre, the more they are united to it and to each other? and the more they stand apart from it, the more they stand apart from each other.

(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.

(122) One quality has always generated the others alike, and none of them have vanished or gone out of sight, just as it is in the whole God; and then the whole body, as it is also in the Ternary, generated itself just as the Deity generateth itself, without or distinct from the body in the Ternary.