(15) The same holds also of astronomy. For treating of the description of the celestial objects, about the form of the universe, and the revolution of the heavens, and the motion of the stars, leading the soul nearer to the creative power, it teaches to quickness in perceiving the seasons of the year, the changes of the air, and the appearance of the stars; since also navigation and husbandry derive from this much benefit, as architecture and building from geometry. This branch of learning, too, makes the soul in the highest degree observant, capable of perceiving the true and detecting the false, of discovering correspondences and proportions, so as to hunt out for similarity in things dissimilar; and conducts us to the discovery of length without breadth, and superficial extent without thickness, and an indivisible point, and transports to intellectual objects from those of sense.

(69) The Pythagoreans declared arithmetic to be the mother of the mathematical sciences. This is proved by the fact that geometry, music, and astronomy are dependent upon it but it is not dependent upon them. Thus, geometry may be removed but arithmetic will remain; but if arithmetic be removed, geometry is eliminated. In the same manner music depends upon arithmetic, but the elimination of music affects arithmetic only by limiting one of its expressions. The Pythagoreans also demonstrated arithmetic to be prior to astronomy, for the latter is dependent upon both geometry and music. The size, form, and motion of the celestial bodies is determined by the use of geometry; their harmony and rhythm by the use of music. If astronomy be removed, neither geometry nor music is injured; but if geometry and music be eliminated, astronomy is destroyed. The priority of both geometry and music to astronomy is therefore established. Arithmetic, however, is prior to all; it is primary and fundamental.

(58) An interesting application of the Pythagorean doctrine of geometric solids as expounded by Plato is found in The Canon. "Nearly all the old philosophers," says its anonymous author, "devised an harmonic theory with respect to the universe, and the practice continued till the old mode of philosophizing died out. Kepler (1596), in order to demonstrate the Platonic doctrine, that the universe was formed of the five regular solids, proposed the following rule. 'The earth is a circle, the measurer of all. Round it describe a dodecahedron; the circle inclosing this will be Mars. Round Mars describe a tetrahedron; the sphere inclosing this will be Jupiter. Describe a cube round Jupiter; the sphere containing this will be Saturn. Now inscribe in the earth an icosahedron; the circle inscribed in it will be Venus. Inscribe an octahedron in Venus; the circle inscribed in it will be Mercury' (Mysterium Cosmographicum, 1596). This rule cannot be taken seriously as a real statement of the proportions of the cosmos, fox it bears no real resemblance to the ratios published by Copernicus in the beginning of the sixteenth century. Yet Kepler was very proud of his formula, and said he valued it more than the Electorate of Saxony. It was also approved by those two eminent authorities, Tycho and Galileo, who evidently understood it. Kepler himself never gives the least hint of how his precious rule is to be interpreted." Platonic astronomy was not concerned with the material constitution or arrangement of the heavenly bodies, but considered the stars and planers primarily as focal points of Divine intelligence. Physical astronomy was regarded as the science of "shadows," philosophical astronomy the science of "realities."

(4) But what slipped from our view in the midst of our discourse, the Good is Cause of the celestial movements in their commencements and terminations, of their not increasing, not diminishing, and completely changeless, course, and of the noiseless movements, if one may so speak, of the vast celestial transit, and of the astral orders, and the beauties and lights, and stabilities, and the progressive swift motion of certain stars, and of the periodical return of the two luminaries, which the Oracles call "great," from the same to the same quarter, after which our days and nights being marked, and months and years being measured, mark and number and arrange and comprehend the circular movements of time and things temporal. But, what would any one say of the very ray of the sun? For the light is from the Good, and an image of the Goodness, wherefore also the Good is celebrated under the name of Light; as in a portrait the original is manifested. For, as the goodness of the Deity, beyond all, permeates from the highest and most honoured substances even to the lowest, and yet is above all, neither the foremost outstripping its superiority, nor the things below eluding its grasp, but it both enlightens all that are capable, and forms and enlivens, and grasps, and perfects, and is measure of things existing, and age, and number, and order, and grasp, and cause, and end; so, too, the brilliant likeness of the Divine Goodness, this our great sun, wholly bright and ever luminous, as a most distant echo of the Good, both enlightens whatever is capable of participating in it, and possesses the light in the highest degree of purity, unfolding to the visible universe, above and beneath, the splendours of its own rays, and if anything does not participate in them, this is not owing to the inertness or deficiency of its distribution of light, but is owing to the inaptitude for light-reception of the things which do not unfold themselves for the participation of light. No doubt the ray passing over many things in such condition, enlightens the things after them, and there is no visible thing which it does not reach, with the surpassing greatness of its own splendour. Further also, it contributes to the generation of sensible bodies, and moves them to life, and nourishes, and increases, and perfects, and purifies and renews; and the light is both measure and number of hours, days, and all our time. For it is the light itself, even though it was then without form, which the divine Moses declared to have fixed that first Triad of our days. And, just as Goodness turns all things to Itself, and is chief collector of things scattered, as One-springing and One-making Deity, and all things aspire to It, as Source and Bond and End, and it is the Good, as the Oracles say, from Which all things subsisted, and are being brought into being by an all-perfect Cause; and in Which all things consisted, as guarded and governed in an all-controlling route; and to Which all things are turned, as to their own proper end; and to Which all aspire --the intellectual and rational indeed, through knowledge, and the sensible through the senses, and those bereft of sensible perception by the innate movement of the aspiration after life, and those without life, and merely being, by their aptitude for mere substantial participation; after the same method of its illustrious original, the light also collects and turns to itself all things existing--things with sight -- things with motion--things enlightened--things heated--things wholly held together by its brilliant splendours--whence also, Helios, because it makes all things altogether (ἀολλῆ), and collects things scattered. And all creatures, endowed with sensible perceptions, aspire to it, as aspiring either to see, or to be moved and enlightened, and heated, and to be wholly held together by the light. By no means do I affirm, after the statement of antiquity, that as being God and Creator of the universe, the sun, by itself, governs the luminous world, but that the invisible things of God are clearly seen from the foundation of the world, being understood by the things that are made, even His eternal power and Deity.

(34) There are two distinct systems of astrological philosophy. One of them, the Ptolemaic, is geocentric: the earth is considered the center of the solar system, around which the sun, moon, and planets revolve. Astronomically, the geocentric system is incorrect; but for thousands of years it has proved its accuracy when applied to the material nature of earthly things. A careful consideration of the writings of the great occultists and a study of their diagrams reveal the fact that many of them were acquainted with another method of arranging the heavenly bodies.

(52) In ridiculing the geocentric system of astronomy expounded by Claudius Ptolemy, modem astronomers have overlooked the philosophic key to the Ptolemaic system. The universe of Ptolemy is a diagrammatic representation of the relationships existing between the various divine and elemental parts of every creature, and is not concerned with astronomy as that science is now comprehended. In the above figure, special attention is called to the three circles of zodiacs surrounding the orbits of the planets. These zodiacs represent the threefold spiritual constitution of the universe. The orbits of the planets are the Governors of the World and the four elemental spheres in the center represent the physical constitution of both man and the universe, Ptolemy's scheme of the universe is simply a cross section of the universal aura, the planets and elements to which he refers having no relation to those recognized by modern astronomers.

(1) It is also said, that Pythagoras was the first who called himself a philosopher; this not being a new name, but previously instructing us in a useful manner in a thing appropriate to the name. For he said that the entrance of men into the present life, resembled the progression of a crowd to some public spectacle. For there men of every description assemble with different views; one hastening to sell his wares for the sake of money and gain; but another that he may acquire renown by exhibiting the strength of his body; and there is also a third class of men, and those the most liberal, who assemble for the sake of surveying the places, the beautiful works of art, the specimens of valor, and the literary productions which are usually exhibited on such occasions.

Thus also in the present life, men of all-various pursuits are collected together in one and the same place. For some are influenced by the desire of riches and luxury; others by the love of power and dominion; and others are possessed with an insane ambition for glory. But the most pure and unadulterated character, is that of the man who gives himself to the contemplation of the most beautiful things, and whom it is proper to call a philosopher. He adds, that the survey of all heaven, and of the stars that revolve in it, is indeed beautiful, when the order of them is considered. For they derive this beauty and order by the participation of the first and the intelligible essence.

But that first essence is the nature of number and reasons [i. e. productive principles,] which pervades through all things, and according to which all these [celestial bodies] are elegantly arranged, and fitly adorned. And wisdom indeed, truly so called, is a certain science which is conversant with the first beautiful objects, and these divine, undecaying, and possessing an invariable sameness of subsistence; by the participation of which other things also may be called beautiful. But philosophy is the appetition of a thing of this kind. The attention therefore to erudition is likewise beautiful, which Pythagoras extended, in order to effect the correction of mankind.

(18) A writer has said of this Cosmic Principle: "There is always a correspondence between the laws and phenomena of the various planes of life and being. The grasping of this truth gives one the means of solving many a dark paradox, many a hidden secret of Nature. There are planes beyond our knowing, but when we apply the Principle of Correspondence to them we are able to understand much that otherwise would be unknowable to us. This principle is of universal application and manifestation, on the various planes of the material, mental and spiritual universe—it is an universal law. The ancient Hermetists considered this principle as one of the most important mental instruments by which man was able to pry aside the obstructions which hid from view the Unknown. Its use even tore aside the Veil of Isis to the extent that a glimpse of the face of the goddess might be caught. Just as a knowledge of the principles of Geometry enables a man to measure distant suns and their movements, while seated in an observatory, so a knowledge of the Principle of Correspondence enables man to reason intelligently from the Known to the Unknown. Studying the moneron, he understands the archangel.

(60) And the chambers of the winds, and how the winds are divided, and how they are weighed, and (how) the portals of the winds are reckoned, each according to the power of the wind, and the power of the lights of the moon, and according to the power that is fitting: and the divisions of the stars according to their names, and how all the divisions are divided.

(17) After discovering the operation of certain principles in one thing we may safely reason by analogy based upon the assumption that these principles exist in other things on a higher plane, and thus discover the nature of the unknown " x ." Thus the occultist reasons that there is Law and Order manifest on every plane of being; that there is a Principle of Vibration manifest on every plane of being; that there is a Principle of Rhythm manifest on every plane of being; that there is a Principle of Cycles manifest on every plane of being; that there is a Principle of Polarity manifest on every plane of being; that there is a Principle of Sex manifest on every plane of being. And the further that human investigation is pushed into the Unknown, the greater is the proof of the existence of these Cosmic Principles reasoned out by the ancient occultists upon the fundamental basis of the Principle of Correspondence.

(1) [Trismegistus] ’Tis in this way, Asclepius;—by mixing it, by means of subtle expositions, with divers sciences not easy to be grasped,—such as arithmetic, and music, and geometry. But Pure Philosophy, which doth depend on godly piety alone, should only so far occupy itself with other arts, that it may [know how to] appreciate the working out in numbers of the fore-appointed stations of the stars when they return, and of the course of their procession. Let her, moreover, know how to appreciate the Earth’s dimensions, its qualities and quantities, the Water’s depths, the strength of Fire, and the effects and nature of all these. [And so] let her give worship and give praise unto the Art and Mind of God.

(28) By perfectly concentrated Meditation on the fixed pole-star comes a knowledge of the motions of the stars.

(11) To Pythagoras music was one of the dependencies of the divine science of mathematics, and its harmonies were inflexibly controlled by mathematical proportions. The Pythagoreans averred that mathematics demonstrated the exact method by which the good established and maintained its universe. Number therefore preceded harmony, since it was the immutable law that governs all harmonic proportions. After discovering these harmonic ratios, Pythagoras gradually initiated his disciples into this, the supreme arcanum of his Mysteries. He divided the multitudinous parts of creation into a vast number of planes or spheres, to each of which he assigned a tone, a harmonic interval, a number, a name, a color, and a form. He then proceeded to prove the accuracy of his deductions by demonstrating them upon the different planes of intelligence and substance ranging from the most abstract logical premise to the most concrete geometrical solid. From the common agreement of these diversified methods of proof he established the indisputable existence of certain natural laws.

(19) Without going deeply into the matter of the application of this particular Cosmic Principle, we may say that one of the fundamental facts of being discovered by the ancient occultists by the application of the said principle is this: That in every thing there is to be found (1) Substance, or Body; (2) Motion or Active Energy; and (3) Consciousness or Awareness. Therefore, when dealing with planes of being of which, at the time, they had but little knowledge, the ancient occultists always assumed the existence in everything on the unknown plane of these three great forms of manifestation. And all future esoteric investigation and discovery tended to disclose facts corroborating and sustaining the original assumption derived by analogy, and the discoveries of modern science have invariably tended in the same direction.

(15) An astronomer who, by his knowledge, can map the stars and describe their courses, derives more pleasure from his knowledge than the chess player from his. Seeing, then, that nothing is higher than God, how great must be the delight which springs from the true knowledge of Him!

(2) For time always proceeding the divine mode of knowledge becomes evanescent, through being frequently mingled and contaminated with much of what is mortal. This divine mode is indeed [in astrology also], and a certain clear indication of truth, though it is but small, is at the same time preserved in it. For it places before our eyes manifest signs of the mensuration of the divine periods, when it predicts the eclipses of the sun and moon, and the concursions of the moon with the fixed stars, and when the experience of the sight is seen to accord with the prediction. Moreover, the observations of the celestial bodies through the whole of time, both by the Chaldeans and by us, testify that this science is true. Indications, also, more known than these might be adduced, if the present discussion was precedaneously about these particulars. But as they are superfluous, and do not pertain to the knowledge of the peculiar dæmon, I shall, as it is fit so to do, omit them, and pass on to things more appropriate than these.

(2) Moreover, the lations of the stars approximate to the eternal circulations of the heavens, not only locally, but also in powers, and the irradiations of light. But these are moved conformably to the mandates of the celestial Gods. For the most pure, agile, and supreme part of the air, is adapted to be enkindled [ i. e. is most inflammable], so that when the Gods assent, it is immediately set on fire. And if some one thinks that certain effluxions of the celestial bodies are imparted to the air, his opinion will not be discordant with what is frequently effected by the divine art. The union, also, and sympathy of the universe, and the simultaneous motion of the most remote parts, as if they were near, and belonged to one animal, cause these signs to be sent from the Gods to men in the most luminous manner, primarily, indeed, through the heavens, but afterwards through the air.

(7) But, if the stars announce the future- as we hold of many other things also- what explanation of the cause have we to offer? What explains the purposeful arrangement thus implied? Obviously, unless the particular is included under some general principle of order, there can be no signification.

We may think of the stars as letters perpetually being inscribed on the heavens or inscribed once for all and yet moving as they pursue the other tasks allotted to them: upon these main tasks will follow the quality of signifying, just as the one principle underlying any living unit enables us to reason from member to member, so that for example we may judge of character and even of perils and safeguards by indications in the eyes or in some other part of the body. If these parts of us are members of a whole, so are we: in different ways the one law applies.

All teems with symbol; the wise man is the man who in any one thing can read another, a process familiar to all of us in not a few examples of everyday experience.

But what is the comprehensive principle of co-ordination? Establish this and we have a reasonable basis for the divination, not only by stars but also by birds and other animals, from which we derive guidance in our varied concerns.

All things must be enchained; and the sympathy and correspondence obtaining in any one closely knit organism must exist, first, and most intensely, in the All. There must be one principle constituting this unit of many forms of life and enclosing the several members within the unity, while at the same time, precisely as in each thing of detail the parts too have each a definite function, so in the All each several member must have its own task- but more markedly so since in this case the parts are not merely members but themselves Alls, members of the loftier Kind.

Thus each entity takes its origin from one Principle and, therefore, while executing its own function, works in with every other member of that All from which its distinct task has by no means cut it off: each performs its act, each receives something from the others, every one at its own moment bringing its touch of sweet or bitter. And there is nothing undesigned, nothing of chance, in all the process: all is one scheme of differentiation, starting from the Firsts and working itself out in a continuous progression of Kinds.

(1) Let him imagine, who would well conceive What now I saw, and let him while I speak Retain the image as a steadfast rock, The fifteen stars, that in their divers regions The sky enliven with a light so great That it transcends all clusters of the air; Let him the Wain imagine unto which Our vault of heaven sufficeth night and day, So that in turning of its pole it fails not; Let him the mouth imagine of the horn That in the point beginneth of the axis Round about which the primal wheel revolves,— To have fashioned of themselves two signs in heaven, Like unto that which Minos' daughter made, The moment when she felt the frost of death; And one to have its rays within the other, And both to whirl themselves in such a manner That one should forward go, the other backward; And he will have some shadowing forth of that True constellation and the double dance That circled round the point at which I was; Because it is as much beyond our wont, As swifter than the motion of the Chiana Moveth the heaven that all the rest outspeeds.

(1) Of his wisdom, however, the commentaries written by the Pythagoreans afford, in short, the greatest indication; for they adhere to truth in every thing, and are more concise than all other compositions, so that they savour of the ancient elegance of style, and the conclusions are exquisitely deduced with divine science. They are also replete with the most condensed conceptions, and are in other respects various and diversified both in the form and the matter. At one and the same time likewise, they are transcendently excellent, and without any deficiency in the diction, and are in an eminent degree full of clear and indubitable arguments, accompanied with scientific demonstration, and as it is said, the most perfect syllogism; as he will find to be the case, who, proceeding in such paths as are fit, does not negligently peruse them.

This science, therefore, concerning intelligible natures and the Gods, Pythagoras delivers in his writings from a supernal origin. Afterwards, he teaches the whole of physics, and unfolds completely ethical philosophy and logic. He likewise delivers all-various disciplines, and the most excellent sciences. And in short there is nothing pertaining to human knowledge which is not accurately discussed in these writings. If therefore it is acknowledged, that of the [Pythagoric] writings which are now in circulation, some were written by Pythagoras himself, but others consist of what he was heard to say, and on this account are anonymous, but are referred to Pythagoras as their author;—if this be the case, it is evident that he was abundantly skilled in all wisdom.

But it is said that he very much applied himself to geometry among the Egyptians. For with the Egyptians there are many geometrical problems; since it is necessary that from remote periods, and from the time of the Gods themselves, on account of the increments and decrements of the Nile, those that were skilful should have measured all the Egyptian land which they cultivated. Hence also geometry derived its name. Neither did they negligently investigate the theory of the celestial orbs, in which likewise Pythagoras was skilled. Moreover, all the theorems about lines appear to have been derived from thence. For it is said that what pertains to computation and numbers, was discovered in Phœnicia. For some persons refer the theorems about the celestial bodies to the Egyptians and Chaldeans in common.

It is said therefore, that Pythagoras having received and increased all these [theories,] imparted the sciences, and at the same time demonstrated them to his auditors with perspicuity and elegance. And he was the first indeed that denominated philosophy, and said that it was the desire, and as it were love of wisdom. But he defined wisdom to be the science of the truth which is in beings. And he said that beings are immaterial and eternal natures, and alone possess an efficacious power, such as incorporeal essences. But that the rest of things are only homonymously beings, and are so denominated through the participation of real beings, and such are corporeal and material forms, which are generated and corrupted, and never truly are.

And that wisdom is the science of things which are properly beings, but not of such as are homonymously so. For corporeal natures are neither the objects of science nor admit of a stable knowledge, since they are infinite and incomprehensible by science, and are as it were, non-beings, when compared with universals, and are incapable of being properly circumscribed by definition. It is impossible however to conceive that there should be science of things which are not naturally the objects of science. Hence it is not probable that there will be a desire of science which has no subsistence, but rather that desire will be extended to things which are properly beings, which exist with invariable permanency, and are always consubsistent with a true appellation.

For it happens that the perception of things which are homonymously beings, and which are never truly what they seem to be, follows the apprehension of real beings; just as the knowledge of particulars follows the science of universals. For he who knows universals properly, says Archytas, will also have a clear perception of the nature of particulars. Hence things which have an existence are not alone, nor only-begotten, nor simple, but they are seen to be various and multiform. For some of them are intelligible and incorporeal natures, and which are denominated beings; but others are corporeal and fall under the perception of sense, and by participation communicate with that which has a real existence. Concerning all these therefore, he delivered the most appropriate sciences, and left nothing [pertaining to them] uninvestigated.

He likewise unfolded to men those sciences which are common [ to all disciplines ,] as for instance the demonstrative, the definitive, and that which consists in dividing, as may be known from the Pythagoric commentaries. He was also accustomed to pour forth sentences resembling Oracles to his familiars in a symbolical manner, and which in the greatest brevity of words contained the most abundant and multifarious meaning, like the Pythian Apollo through certain oracles, or like nature herself through seeds small in bulk, the former exhibiting conceptions, and the latter effects, innumerable in multitude, and difficult to be understood. Of this kind is the sentence, The beginning is the half of the whole , which is an apothegm of Pythagoras himself.

But not only in the present hemistich, but in others of a similar nature, the most divine Pythagoras has concealed the sparks of truth; depositing as in a treasury for those who are capable of being enkindled by them, and with a certain brevity of diction, an extension of theory most ample and difficult to be comprehended, as in the following hemistich: