(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."

(13) Moreover, on some of the higher minor planes of this Plane of the Minerals, there is manifested the crystallization of the mineral particles according to a definite principle of design embedded in the consciousness of its particles. The crystal is built upon a definite plane, just as truly as is the acorn or the oak—and in all of these cases the pattern is but an "idea" in the consciousness of the combined particles. The Universal Builder works through the consciousness of the mineral particles just as truly and as wonderfully as through the particles of humanity which we call individual men. The study of crystals, and their formation will open up a new world of thought to the average person, and will give him a peep into the workshop of the Universal Builder in which he will see things heretofore unsuspected and undreamt.

(37) "The symmetrical solids were regarded by Pythagoras, and by the Greek thinkers after him, as of the greatest importance. To be perfectly symmetrical or regular, a solid must have an equal number of faces meeting at each of its angles, and these faces must be equal regular polygons, i. e., figures whose sides and angles are all equal. Pythagoras, perhaps, may be credited with the great discovery that there are only five such solids.* * *

(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.

(28) To the five symmetrical solids of the ancients is added the sphere (1), the most perfect of all created forms. The five Pythagorean solids are: the tetrahedron (2) with four equilateral triangles as faces; the cube (3) with six squares as faces; the octahedron (4) with eight equilateral triangles as faces; the icosahedron (5) with twenty equilateral triangles as faces; and the dodecahedron (6) with twelve regular pentagons as faces.

(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:

(38) 'Now, the Greeks believed the world [material universe] to be composed of four elements--earth, air, fire, water--and to the Greek mind the conclusion was inevitable that the shapes of the particles of the elements were those of the regular solids. Earth-particles were cubical, the cube being the regular solid possessed of greatest stability; fire-particles were tetrahedral, the tetrahedron being the simplest and, hence, lightest solid. Water-particles were icosahedral for exactly the reverse reason, whilst air-particles, as intermediate between the two latter, were octahedral. The dodecahedron was, to these ancient mathematicians, the most mysterious of the solids; it was by far the most difficult to construct, the accurate drawing of the regular pentagon necessitating a rather elaborate application of Pythagoras' great theorem. Hence the conclusion, as Plato put it, that 'this (the regular dodecahedron) the Deity employed in tracing the plan of the Universe.' (H. Stanley Redgrove, in Bygone Beliefs.)

(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.

(7) I. The Plane of the Elements On this Plane of Consciousness is manifested the actions and reactions between the subtle elements of which all material forms are composed. Here occurs the play between the atoms, the electrons, the ions, the corpuscles, and the still more tenuous particles of substance of which science has as yet no knowledge. And, going still further back, it may be said that on this plane occurs the play of phases of substance as much more tenuous and subtle than the electrons as the latter are more tenuous than the atoms. Little can be said concerning these practically unknown forms and phases of matter, although the occult teachings are quite full of them.

(53) Timaeus: of each of these Kinds which I must endeavor to explain to you in an exposition of an unusual type; yet, inasmuch as you have some acquaintance with the technical method which I must necessarily employ in my exposition, you will follow me. In the first place, then, it is plain I presume to everyone that fire and earth and water and air are solid bodies; and the form of a body, in every case, possesses depth also. Further, it is absolutely necessary that depth should be bounded by a plane surface; and the rectilinear plane is composed of triangles.

(2) Our first observations must be directed to what passes in the Sensible realm for Substance. It is, we shall agree, only by analogy that the nature manifested in bodies is designated as Substance, and by no means because such terms as Substance or Being tally with the notion of bodies in flux; the proper term would be Becoming.

But Becoming is not a uniform nature; bodies comprise under the single head simples and composites, together with accidentals or consequents, these last themselves capable of separate classification.

Alternatively, Becoming may be divided into Matter and the Form imposed upon Matter. These may be regarded each as a separate genus, or else both may be brought under a single category and receive alike the name of Substance.

But what, we may ask, have Matter and Form in common? In what sense can Matter be conceived as a genus, and what will be its species? What is the differentia of Matter? In which genus, Matter or Form, are we to rank the composite of both? It may be this very composite which constitutes the Substance manifested in bodies, neither of the components by itself answering to the conception of Body: how, then, can we rank them in one and the same genus as the composite? How can the elements of a thing be brought within the same genus as the thing itself? Yet if we begin with bodies, our first-principles will be compounds.

Why not resort to analogy? Admitted that the classification of the Sensible cannot proceed along the identical lines marked out for the Intellectual: is there any reason why we should not for Intellectual-Being substitute Matter, and for Intellectual Motion substitute Sensible Form, which is in a sense the life and consummation of Matter? The inertia of Matter would correspond with Stability, while the Identity and Difference of the Intellectual would find their counterparts in the similarity and diversity which obtain in the Sensible realm.

But, in the first place, Matter does not possess or acquire Form as its life or its Act; Form enters it from without, and remains foreign to its nature. Secondly, Form in the Intellectual is an Act and a motion; in the Sensible Motion is different from Form and accidental to it: Form in relation to Matter approximates rather to Stability than to Motion; for by determining Matter's indetermination it confers upon it a sort of repose.

In the higher realm Identity and Difference presuppose a unity at once identical and different: a thing in the lower is different only by participation in Difference and in relation to some other thing; Identity and Difference are here predicated of the particular, which is not, as in that realm, a posterior.

As for Stability, how can it belong to Matter, which is distorted into every variety of mass, receiving its forms from without, and even with the aid of these forms incapable of offspring.

This mode of division must accordingly be abandoned.

(14) The common opinion is that crystals are formed by mechanical causes, such as outside pressure, etc., but the careful student of science, as well as the occultist, knows that the formation of a crystal is a growth , and is as much the result of stored-up psychical ideas in the particles, as is the growth of plant substance or animal bodies. The student of crystallography soon becomes convinced of the presence of Life and Consciousness in the world of crystals.

(29) Although Eugenius Philalethes disclaimed membership in the Rosicrucian Fraternity, it is believed that for a number of years he was the head of that Order. In a little work called Lumen de Lumine, or A New Magical Light Discovered and Communicated to the World, published in London in 1651, Eugenius Philalethes gives a remarkable letter, presumably from the Rosicrucian Order. Accompanying the letter is an emblematic figure setting forth in symbolic form the processes and formulæ of the Philosopher's Stone. This epistle is an excellent example of the Rosicrucian system of combining abstract theological speculations with concrete chemical formulæ. With the aid of the material contained in various parts of this present book the student would do well to set himself the task of solving the riddle contained in this hieroglyph.

(183) A tiny particle of the Philosopher's Scone, if cast upon the surface of water, will, according to an appendix to the work on the universal salt by Herr von Welling, immediately begin a process of recapitulating in miniature the history of the universe, for instantly the tincture--like the Spirits of Elohim--moves upon the face of the waters. A miniature universe is formed which the philosophers have affirmed actually rises out of the water and floats in the air, where it passes through all the stages of cosmic unfoldment and finally disintegrates into dust again. Not only is it possible to prepare a medicine for metals; it is also possible to prepare a tincture for minerals by means of which pieces of granite and marble can be turned into precious stones; also stones of inferior quality may be improved.

(181) This arrangement opens an interesting field of speculation which may be of great service if intelligently carried out. These twelve "steps" leading up to the accomplishment of the Magnum Opus are a reminder of the twelve degrees of the ancient Rosicrucian Mysteries. To a certain degree, Rosicrucianism was chemistry theologized and alchemy philosophized. According to the Mysteries, man was redeemed as the result of his passage in rotation through the twelve mansions of the heavens. The twelve processes by means of which the "secret essence" may be discovered remind the student forcibly of the twelve Fellow Craftsmen who are sent forth in search of the murdered Builder of the Universe, the Universal Mercury.

(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.

(9) This diagrammatic sector represents the major gradations of energy and substance between elemental earth and absolute unconditioned force. Beginning with the superior, the fifteen graduated spheres descend in the following order: Limitless and Eternal Life; the superior, the middle, and the inferior Empyrean; the seven planets; and the four elements. Energy is symbolized by Fludd as a pyramid with its base upon the concave surface of the superior Empyrean, and substance as another Pyramid with its base upon the convex surface of the sphere (not planet) of earth. These pyramids demonstrate the relative proportions of energy and substance entering into the composition of the fifteen planes of being. It will be noted that the ascending pyramid of substance touches but does not pierce the fifteenth sphere--that of Limitless and Eternal Life. Likewise, the descending pyramid of energy touches but does not pierce the first sphere--the grossest condition of substance. The plane of the sun is denominated the sphere of equality, for here neither energy nor substance predominate. The mundane monochord consists of a hypothetical string stretched from the base of the pyramid of energy to the base of the pyramid of substance.

(55) Timaeus: And the third solid is composed of twice sixty of the elemental triangles conjoined, and of twelve solid angles, each contained by five plane equilateral triangles, and it has, by its production, twenty equilateral triangular bases. Now the first of the elemental triangles ceased acting when it had generated these three solids, the substance of the fourth Kind being generated by the isosceles triangle. Four of these combined, with their right angles drawn together to the center, produced one equilateral quadrangle; and six such quadrangles,

(71) Magnitude is divided into two parts--magnitude which is stationary and magnitude which is movable, the stationary pare having priority. Multitude is also divided into two parts, for it is related both to itself and to other things, the first relationship having priority. Pythagoras assigned the science of arithmetic to multitude related to itself, and the art of music to multitude related to other things. Geometry likewise was assigned to stationary magnitude, and spherics (used partly in the sense of astronomy) to movable magnitude. Both multitude and magnitude were circumscribed by the circumference of mind. The atomic theory has proved size to be the result of number, for a mass is made up of minute units though mistaken by the uninformed for a single simple substance.