(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.

(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.

(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.

(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.

(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.

(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!

(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) 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:

(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.

(13) But seeing men are gods, and have the knowledge of God the only Father, from whom they are proceeded or descended, and in whom they live, therefore I despise not the canons, rules and formulae of their philosophy, astrology, and theology: For I find, that for the most part they [the philosophers, etc.] stand upon a right ground, and I will diligently endeavour to go according to their rules and formulae.

(18) The study of geometry, music, and astronomy was considered essential to a rational understanding of God, man, or Nature, and no one could accompany Pythagoras as a disciple who was not thoroughly familiar with these sciences. Many came seeking admission to his school. Each applicant was tested on these three subjects, and if found ignorant, was summarily dismissed.

(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.

(4) Accept, therefore, this, which is said indeed incidentally, but is a sufficient reply to the whole of your conception concerning the theurgic art. Those assertions, also, of yours pertain to the same thing, in which you say, “ that the science of the Gods is sacred and useful, and call the ignorance of things honourable and beautiful darkness, but the knowledge of them light; and also add, that the ignorance of these things fills men with all evils, through inerudition and audacity, but the knowledge of them is the cause of all good .” For all these assertions tend to the same thing with the preceding, and obtain together with them an appropriate discussion. It is necessary, therefore to omit them, and to pass on to the inquiries concerning divination, and concisely dissolve them.

(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.

(1) That the circuit of the stars indicates definite events to come but without being the cause direct of all that happens, has been elsewhere affirmed, and proved by some modicum of argument: but the subject demands more precise and detailed investigation for to take the one view rather than the other is of no small moment.

The belief is that the planets in their courses actually produce not merely such conditions as poverty, wealth, health and sickness but even ugliness and beauty and, gravest of all, vices and virtue and the very acts that spring from these qualities, the definite doings of each moment of virtue or vice. We are to suppose the stars to be annoyed with men- and upon matters in which men, moulded to what they are by the stars themselves, can surely do them no wrong.

They will be distributing what pass for their good gifts, not out of kindness towards the recipients but as they themselves are affected pleasantly or disagreeably at the various points of their course; so that they must be supposed to change their plans as they stand at their zeniths or are declining.

More absurdly still, some of them are supposed to be malicious and others to be helpful, and yet the evil stars will bestow favours and the benevolent act harshly: further, their action alters as they see each other or not, so that, after all, they possess no definite nature but vary according to their angles of aspect; a star is kindly when it sees one of its fellows but changes at sight of another: and there is even a distinction to be made in the seeing as it occurs in this figure or in that. Lastly, all acting together, the fused influence is different again from that of each single star, just as the blending of distinct fluids gives a mixture unlike any of them.

Since these opinions and others of the same order are prevalent, it will be well to examine them carefully one by one, beginning with the fundamental question:

(3) On completing, then, the whole of what we propose in the commentaries, on which, if the Spirit will, we ministering to the urgent need, (for it is exceedingly necessary, before coming to the truth, to embrace what ought to be said by way of preface), shall address ourselves to the true gnostic science of nature, receiving initiation into the minor mysteries before the greater; so that nothing may be in the way of the truly divine declaration of sacred things, the subjects requiring preliminary detail and statement being cleared away, and sketched beforehand. The science of nature, then, or rather observation, as contained in the gnostic tradition according to the rule of the truth, depends on the discussion concerning cosmogony, ascending thence to the department of theology. Whence, then, we shall begin our account of what is handed down, with the creation as related by the prophets, introducing also the tenets of the heterodox, and endeavouring as far as we can to confute them. But it shall be written if God will, and as He inspires; and now we must proceed to what we proposed, and complete the discourse on ethics.

(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.

(5) When they tell us that a certain cold star is more benevolent to us in proportion as it is further away, they clearly make its harmful influence depend upon the coldness of its nature; and yet it ought to be beneficent to us when it is in the opposed Zodiacal figures.

When the cold planet, we are told, is in opposition to the cold, both become meanacing: but the natural effect would be a compromise.

And we are asked to believe that one of them is happy by day and grows kindly under the warmth, while another, of a fiery nature, is most cheerful by night- as if it were not always day to them, light to them, and as if the first one could be darkened by night at that great distance above the earth's shadow.

Then there is the notion that the moon, in conjunction with a certain star, is softened at her full but is malignant in the same conjunction when her light has waned; yet, if anything of this order could be admitted, the very opposite would be the case. For when she is full to us she must be dark on the further hemisphere, that is to that star which stands above her; and when dark to us she is full to that other star, upon which only then, on the contrary, does she look with her light. To the moon itself, in fact, it can make no difference in what aspect she stands, for she is always lit on the upper or on the under half: to the other star, the warmth from the moon, of which they speak, might make a difference; but that warmth would reach it precisely when the moon is without light to us; at its darkest to us it is full to that other, and therefore beneficent. The darkness of the moon to us is of moment to the earth, but brings no trouble to the planet above. That planet, it is alleged, can give no help on account of its remoteness and therefore seems less well disposed; but the moon at its full suffices to the lower realm so that the distance of the other is of no importance. When the moon, though dark to us, is in aspect with the Fiery Star she is held to be favourable: the reason alleged is that the force of Mars is all-sufficient since it contains more fire than it needs.

The truth is that while the material emanations from the living beings of the heavenly system are of various degrees of warmth- planet differing from planet in this respect- no cold comes from them: the nature of the space in which they have their being is voucher for that.

The star known as Jupiter includes a due measure of fire , in this resembling the Morning-star and therefore seeming to be in alliance with it. In aspect with what is known as the Fiery Star, Jupiter is beneficent by virtue of the mixing of influences: in aspect with Saturn unfriendly by dint of distance. Mercury, it would seem, is indifferent whatever stars it be in aspect with; for it adopts any and every character.

But all the stars are serviceable to the Universe, and therefore can stand to each other only as the service of the Universe demands, in a harmony like that observed in the members of any one animal form. They exist essentially for the purpose of the Universe, just as the gall exists for the purposes of the body as a whole not less than for its own immediate function: it is to be the inciter of the animal spirits but without allowing the entire organism and its own especial region to run riot. Some such balance of function was indispensable in the All- bitter with sweet. There must be differentiation- eyes and so forth- but all the members will be in sympathy with the entire animal frame to which they belong. Only so can there be a unity and a total harmony.

And in such a total, analogy will make every part a Sign.

(2) [Now,] seeing that the hollow roundness of the Cosmos is borne round into the fashion of a sphere; by reason of its [very] quality or form, it never can be altogether visible unto itself. So that, however high a place in it thou shouldest choose for looking down below, thou could’st not see from it what is at bottom, because in many places it confronts [the senses], and so is thought to have the quality [of being visible throughout]. For it is solely owing to the forms of species, with images of which it seems insculpted, that it is thought [to be] as though ’twere visible [throughout]; but as a fact ’tis ever to itself invisible.

(4) Plato regarded philosophy as the greatest good ever imparted by Divinity to man. In the twentieth century, however, it has become a ponderous and complicated structure of arbitrary and irreconcilable notions--yet each substantiated by almost incontestible logic. The lofty theorems of the old Academy which Iamblichus likened to the nectar and ambrosia of the gods have been so adulterated by opinion--which Heraclitus declared to be a falling sickness of the mind--that the heavenly mead would now be quite unrecognizable to this great Neo-Platonist. Convincing evidence of the increasing superficiality of modern scientific and philosophic thought is its persistent drift towards materialism. When the great astronomer Laplace was asked by Napoleon why he had not mentioned God in his Traité de la Mécanique Céleste, the mathematician naively replied: "Sire, I had no need for that hypothesis!"