Passages similar to: Secret Teachings of All Ages — Pythagorean Mathematics
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Western Esoteric
Secret Teachings of All Ages
Pythagorean Mathematics (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.
Chapter 17: Of the horrible, lamentable, and miserable Fall of Adam and Eve in Paradise. Man 's Looking-Glass. (48)
And out of this Limbus (at the Time when the Earth was corporised) went forth the four Elements, as out of a Fountain; and that which was discovered [...
(48) And out of this Limbus (at the Time when the Earth was corporised) went forth the four Elements, as out of a Fountain; and that which was discovered [or manifested] by the Virgin (the Wisdom of God) in the Innumerability, were the Stars, as are the Quintessence zof the four Elements, not separated from the four Elements, but qualifying [or mixing Virtues] one with another, a and yet extracted from the four Productions, with their sharp Essences; and they are the Seeking [Longing or Hunger] of the four Elements, or, as I may express it by a Similitude, [they are] the Man, and the Elements are the Woman; and the Heart of these Things is the Element, in one only Substance, and the Essences in that [one Element] are the Virtues [or Power] of the Wonders of the Wisdom of God, and are called Paradise, an exulting Joy.
The mode however of teaching through symbols, was considered by Pythagoras as most necessary. For this form of erudition was cultivated by nearly all...
(1) The mode however of teaching through symbols, was considered by Pythagoras as most necessary. For this form of erudition was cultivated by nearly all the Greeks, as being most ancient. But it was transcendently honored by the Egyptians, and adopted by them in the most diversified manner. Conformably to this, therefore, it will be found, that great attention was paid to it by Pythagoras, if any one clearly unfolds the significations and arcane conceptions of the Pythagoric symbols, and thus developes the great rectitude and truth they contain, and liberates them from their enigmatic form. For they are adapted according to a simple and uniform doctrine, to the great geniuses of these philosophers, and deify in a manner which surpasses human conception.
For those who came from this school, and especially the most ancient Pythagoreans, and also those young men who were the disciples of Pythagoras when he was an old man, viz. Philolaus and Eurytus, Charondas and Zaleucus, and Brysson, the elder Archytas also, and Aristæus, Lysis and Empedocles, Zanolxis and Epimenides, Milo and Leucippus, Alcmæon, Hippasus and Thymaridas, and all of that age, consisting of a multitude of learned men, and who were above measure excellent,—all these adopted this mode of teaching, in their discourses with each other, and in their commentaries and annotations. Their writings also, and all the books which they published, most of which have been preserved even to our time , were not composed by them in a popular and vulgar diction, and in a manner usual with all other writers, so as to be immediately understood, but in such a way as not to be easily apprehended by those that read them.
For they adopted that taciturnity which was instituted by Pythagoras as a law, in concealing after an arcane mode, divine mysteries from the uninitiated, and obscuring their writings and conferences with each other. Hence he who selecting these symbols does not unfold their meaning by an apposite exposition, will cause those who may happen to meet with them to consider them as ridiculous and inane, and as full of nugacity and garrulity. When, however, they are unfolded in a way conformable to these symbols, and become obvious and clear even to the multitude, instead of being obscure and dark, then they will be found to be analogous to prophetic sayings, and to the oracles of the Pythian Apollo. They will then also exhibit an admirable meaning, and will produce a divine afflatus in those who unite intellect with erudition.
Nor will it be improper to mention a few of them, in order that this mode of discipline may become more perspicuous: Enter not into a temple negligently, nor in short adore carelessly, not even though you should stand at the very doors themselves . Sacrifice and adore unshod. Declining from the public ways, walk in unfrequented paths. Speak not about Pythagoric concerns without light. And such are the outlines of the mode adopted by Pythagoras of teaching through symbols.
Chapter 12: Of the Nativity and Proceeding forth or Descent of the Holy Angels, as also of their Government, Order, and Heavenly joyous Life. (166)
II. The elements signify or denote the wonderful proportion, variety, change and alteration of the form and posture of heaven: For as the deep...
(166) II. The elements signify or denote the wonderful proportion, variety, change and alteration of the form and posture of heaven: For as the deep between the stars and earth always alter and change in their form, suddenly it is fair, bright and light, suddenly it is lowery and dark, now wind, then rain, now snow, suddenly the deep is blue or azure, suddenly greenish, by and by whitish, then suddenly again dusky.
All things accord in number: which he very frequently uttered to all his disciples. Or again, Friendship is equality; equality is friendship . Or in...
(2) All things accord in number:
which he very frequently uttered to all his disciples. Or again, Friendship is equality; equality is friendship . Or in the word cosmos , i. e. the world ; or by Jupiter, in the word philosophy , or in the so much celebrated word tetractys . All these and many other inventions of the like kind, were devised by Pythagoras for the benefit and amendment of his associates; and they were considered by those that understood them to be so venerable, and so much the progeny of divine inspiration, that the following was adopted as an oath by those that dwelt together in the common auditory:
Chapter 3: Of the most blessed Triumphing, Holy, Holy, Holy Trinity, GOD the Father, Son, and Holy Ghost, ONE only God. (69)
And as the three elements, fire, air and water, proceed from the sun and stars, and are one body in one another, and cause the living motion, and the ...
(69) And as the three elements, fire, air and water, proceed from the sun and stars, and are one body in one another, and cause the living motion, and the spirit of all the creatures of this world.
Now the Pythagorean symbols were connected with the Barbarian philosophy in the most recondite way. For instance, the Samian counsels "not to have a...
(1) Now the Pythagorean symbols were connected with the Barbarian philosophy in the most recondite way. For instance, the Samian counsels "not to have a swallow in the house;" that is, not to receive a loquacious, whispering, garrulous man, who cannot contain what has been communicated to him. "For the swallow, and the turtle, and the sparrows of the field, know the times of their entrance," says the Scripture; and one ought never to dwell with trifles. And the turtle-dove murmuring shows the thankless slander of fault-finding, and is rightly expelled the house.
Pythagoras saith:—We posit another government which is not from another root, but it differs in name. And know, all ye seekers after this Science and...
(13) Pythagoras saith:—We posit another government which is not from another root, but it differs in name. And know, all ye seekers after this Science and ‘Wisdom, that whatsoever the envious may have enjoined in their books concerning the’ composition of natures which agree together,* in savour there is only one, albeit to sight they are as diverse as possible. Know, also, that the thing which they have described in so many ways follows and attains its companion without fire, even as the magnet follows the iron, to which the said thing is not vainly compared, nor to a seed, nor to a matrix, for it is also like unto these. And this same thing, which followst its companion without fire, causes many colours to appear when embracing it, for this reason, that the said one thing enters into every regimen, and is found everywhere, being a stone, and also not a stone; common ”* and precious; hidden and concealed, yet known by everyone; of one name and of many names, which is the Spume of the Moon. This stone, therefore, is not a stone, because it is more precious; without it Nature never operates anything; its name is one, yet we have called it by many names on account of the excellence of its nature.*
The Turba answereth:—O! Master! wilt thou not mention some of those names for the guidance of seekers?
And he:—It is called White Ethelia, White Copper, and that which flies from the fire and alone whitens copper. Break up, therefore, the White Stone, and afterwards coagulate it with milk.* Then pound the calx in the mortar, taking care that the humidity does not escape from the vessel; but coagulate it in the vessel until it shall become a cinder. Cook also with Spume of Luna and regulate. For ye shall find the stone broken, and already imbued with its own water.t This, therefore, is the stone which we call by all names, which assimilates the work and drinks it, and is the stone out of which also all colours appear. Take, therefore, that same gum,} which is from the scoriz, and mix with cinder of calx, which you have ruled, and with the feeces which you know, moistening with permanent water. Then look and see whether it has become a powder, but if not, roast in a fire stronger than the first fire, until it be pounded. Then imbue with permanent water, and the more the colours vary all the more suffer them to be heated. Know, moreover, that if you take white quicksilver, or the Spume of Luna, and do as ye are bidden, breaking up with a gentle fire, the same is coagulated, and becomes a stone. Out of this stone, therefore, when it is broken up, many colours will appear to you. But herein, if any ambiguity occur to you in our discourse, do as ye are bidden, ruling the same until: a white and coruscating stone shall be produced, and so ye find your purpose.
Betus saith:—O disciples, ye have discoursed excellently!* PyTHAGoRAS answers:—Seeing that they are philosophers, O Belus, why hast thou called them...
(20) Betus saith:—O disciples, ye have discoursed excellently!*
PyTHAGoRAS answers:—Seeing that they are philosophers, O Belus, why hast thou called them disciples?
He answereth:—lIt is in honour of their Master, lest I should make them equal with him. Then
PytHaGcoras saith:—Those who, in conjunction with us, have composed this book which is called the Turba, ought not to betermed disciples.
Then he:— Master, they have frequently described Permanent Water, and the making of the White and the Red in many ways, albeit under many names; but in the modes after which they have conjoined weights, compositions, and regimens, they agree with the hidden truth. Behold, what is said concerning this despised thing! A report has gone abroad that the Hidden Glory of the Philosophers is a stone and not astone, and that it is called by many names, lest the foolish should recognise it, Certain wise men have designated it after one fashion, namely, according to the place where it is generated; others have adopted another, founded upon its colour, some of whom have termed it the Green Stone;* by other some it is called the Stone of the most intense Spirit of Brass, not to be mixed with bodies; by yet others its description has been further varied, because itis sold for coins by lapidaries who are called saven; some have named it Spume of Luna;t some have distinguished it astronomically or arithmetically; it has already received a thousand titles, of which the best is:— “That which is produced out of metals.” So also others have called it the Heart of the Sun, and yet others have declared it to be that which is brought forth out of quicksilver with the milk of volatile things.
Timaeus: the equilateral triangle is constructed as a third. The reason why is a longer story; but should anyone refute us and discover that it is...
(54) Timaeus: the equilateral triangle is constructed as a third. The reason why is a longer story; but should anyone refute us and discover that it is not so, we begrudge him not the prize. Accordingly, let these two triangles be selected as those wherefrom are contrived the bodies of fire and of the other elements,— one being the isosceles, and the other that which always has the square on its greater side three times the square on the lesser side. Moreover, a point about which our previous statement was obscure must now be defined more clearly. It appeared as if the four Kinds,
He also promulgated purifications, and initiations as they are called, which contain the most accurate knowledge of the Gods. And farther still, it is...
(9) And, in short, it is said that Pythagoras was emulous of the Orphic mode of writing and [piety of] disposition; and that he honored the Gods in a way similar to that of Orpheus, placing them in images and in brass, not conjoined to our forms, but to divine receptacles; because they comprehend and provide for all things; and have a nature and morphe similar to the universe. He also promulgated purifications, and initiations as they are called, which contain the most accurate knowledge of the Gods. And farther still, it is said, that he was the author of a compound divine philosophy and worship of the Gods; having learnt indeed some things from the followers of Orpheus, but others from the Egyptian priests; some from the Chaldæans and Magi; some from the mysteries performed in Eleusis, in Imbrus, Samothracia, and Delos; and some also from those which are performed by the Celtæ, and in Iberia.
It is also said that the Sacred Discourse of Pythagoras is extant among the Latins, and is read not to all, nor by all of them, but by those who are promptly disposed to learn what is excellent, and apply themselves to nothing base. He likewise ordained that men should make libations thrice, and observed that Apollo delivered oracles from the tripod, because the triad is the first number. That sacrifices also should be made to Venus on the sixth day, because this number is the first that partakes of every number , and, when divided in every possible way, receives the power of the numbers subtracted and of those that remain. But that it is necessary to sacrifice to Hercules on the eighth day of the month from the beginning, looking in so doing to his being born in the seventh month.
He further asserted, that it was necessary that he who entered a temple should be clothed with a pure garment, and in which no one had slept; because sleep in the same manner as the black and the brown, is an indication of sluggishness; but purity is a sign of equality and justice in reasoning. He also ordered, that if blood should be found involuntarily spilt in a temple, a lustration should be made, either in a golden vessel, or with the water of the sea; the former of these [i. e. gold] being the most beautiful of things, and a measure by which the price of all things is regulated; but the latter as he conceived being the progeny of a moist nature, and the nutriment of the first and more common matter.
He likewise said, that it was not proper to bring forth children in a temple; because it is not holy that in a temple the divine part of the soul should be bound to the body. He further ordained, that on a festive day neither the hair should be cut, nor the nails paired; not thinking it fit that we should leave the service of the Gods for the purpose of increasing our good. He also said, that a louse ought not to be killed in a temple; conceiving that a divine power ought not to participate of any thing superfluous and corruptible. But that the Gods should be honored with cedar, laurel, cypress, oak, and myrtle; and that the body should not be purified with these, nor should any of them be divided by the teeth.
He likewise ordained, that what is boiled should not be roasted; signifying by this that mildness is not in want of anger. But he would not suffer the bodies of the dead to be burned; following in this the Magi, being unwilling that any thing divine should communicate with a mortal nature. He likewise thought it was holy for the dead to be carried out in white garments; obscurely signifying by this the simple and first nature, according to number and the principle of all things. But above all things he ordained, that an oath should be taken religiously; since that which is behind is long. And he said, that it is much more holy to be injured than to kill a man: for judgment is deposited in Hades, where the soul and its essence, and the first nature of things are [properly] estimated.
Farther still, he ordered that sepulchral chests [i. e. biers] should not be made of cypress, because the sceptre of Jupiter was made of this wood, or for some other mystic reason. He likewise ordained that libations should be performed before the table of Jupiter the Saviour, and of Hercules and the Dioscuri; in so doing celebrating Jupiter as the presiding cause and leader of this nutriment; Hercules, as the power of nature; and the Dioscuri, as the symphony of all things. But he said, that libations should not be offered with closed eyes. For he did not think it fit, that any thing beautiful should be undertaken with shame and bashfulness. Moreover, when it thundered, he ordained that the earth should be touched, in remembrance of the generation of things.
But he ordered that temples should be entered from places on the right hand, and that they should be departed out of from the left hand. For he asserted that the right hand is the principle of what is called the odd number, and is divine; but that the left hand is a symbol of the even number, and of that which is dissolved. And such is the mode which he is said to have adopted in the cultivation of piety. But other particulars which we have omitted concerning it, may be conjectured from what has been said. So that I shall cease to speak further on this subject.
Chapter 17: Of the horrible, lamentable, and miserable Fall of Adam and Eve in Paradise. Man 's Looking-Glass. (7)
For the Element is without Understanding, and that is that [which is attracted or] concreted in the Will of God, wherein the eternal Wisdom of God doe...
(7) For the Element is without Understanding, and that is that [which is attracted or] concreted in the Will of God, wherein the eternal Wisdom of God does [sparkle or] discover itself in infinitum [infinitely,] and in that spring up Colours, Arts, Virtues, and the eternal Wonders; out of which [Element] in the Beginning (in the Kindling of the Fire in the stern Fierceness) are the four Elements proceeded.
Chapter 3: Of the most blessed Triumphing, Holy, Holy, Holy Trinity, GOD the Father, Son, and Holy Ghost, ONE only God. (43)
Now consider further the circle or sphere of the stars, they denote the various powers and wisdom of the Father, and they also are made by the power...
(43) Now consider further the circle or sphere of the stars, they denote the various powers and wisdom of the Father, and they also are made by the power and wisdom of the Father.
The Symbol is interpreted as follows: (1) The Infinite Unmanifest manifests itself in the Elemental Soul; (2) the Elemental Soul takes upon itself...
(3) The Symbol is interpreted as follows: (1) The Infinite Unmanifest manifests itself in the Elemental Soul; (2) the Elemental Soul takes upon itself the outward form of Mineral Substance; (3) The Mineral Soul evolves from itself the Plant Soul; (4) the Plant Soul evolves from itself the Animal Soul; (5) the Animal Soul evolves from itself the Human Soul; (6) the Human Soul unfolds into the Soul of the Demi-Gods; (7) the Soul of the Demi-Gods unfolds into the Soul of the Gods; and finally, the Soul of the Gods once more is resolved into Pure Spirit, which is represented by the blank space at the centre of the symbol. This statement will be more clearly apprehended by those who have carefully studied the preceding chapters conveying instruction concerning the Seven Planes of Consciousness, and much of the information contained in those chapters is to be taken into consideration in the study of the present chapter.
Timaeus: since it is in all ways the sharpest and most acute of all; and it must also be the lightest, since it is composed of the fewest identical...
(56) Timaeus: since it is in all ways the sharpest and most acute of all; and it must also be the lightest, since it is composed of the fewest identical parts; and the second comes second in point of these same qualities, and the third third. Thus, in accordance with the right account and the probable, that solid which has taken the form of a pyramid shall be the element and seed of fire; the second in order of generation we shall affirm to be air, and the third water. Now one must conceive all these to be so small that none of them,
Wherefore the wisest of the Egyptian priests decided that the temple of Athene should be hypaethral, just as the Hebrews constructed the temple...
(8) Wherefore the wisest of the Egyptian priests decided that the temple of Athene should be hypaethral, just as the Hebrews constructed the temple without an image. And some, in worshipping God, make a representation of heaven containing the stars; and so worship, although Scripture says, "Let of Eurysus the Pythagorean, which is as follows, who in his book On Fortune, having said that the "Creator, on making man, took Himself as an exemplar," added, "And the body is like the other things, as being made of the same material, and fashioned by the best workman, who wrought it, taking Himself as the archetype." And, in fine, Pythagoras and his followers, with Plato also, and most of the other philosophers, were best acquainted with the Lawgiver, as may be concluded from their doctrine. And by a happy utterance of divination, not without divine help, concurring in certain prophetic declarations, and, seizing the truth in portions and aspects, in terms not obscure, and not going beyond the explanation of the things, they honoured it on as pertaining the appearance of relation with the truth. Whence the Hellenic philosophy is like the torch of wick which men kindle, artificially stealing the light from the sun. But on the proclamation of the Word all that holy light shone forth. Then in houses by night the stolen light is useful; but by day the fire blazes, and all the night is illuminated by such a sun of intellectual light.
The Truth in Symbols There are certain truths which cannot be well expressed in words, but which may be at least partially expressed in symbols. To...
(36) The Truth in Symbols There are certain truths which cannot be well expressed in words, but which may be at least partially expressed in symbols. To those who feel a desire to penetrate rather more deeply into the Mystery of. the Three Higher Planes of Consciousness, we call attention to the symbol accompanying this particular chapter of this book. There is a wealth of knowledge and important information hidden in this symbol, undiscoverable to the many but at least partially discoverable by the few. To the Few, we offer the following suggestions concerning this Symbol.
Chapter 3: Of the most blessed Triumphing, Holy, Holy, Holy Trinity, GOD the Father, Son, and Holy Ghost, ONE only God. (66)
From the sun and stars proceed the four elements, fire, air, water and earth, as hereafter I shall demonstrate plainly, when I shall write of the...
(66) From the sun and stars proceed the four elements, fire, air, water and earth, as hereafter I shall demonstrate plainly, when I shall write of the creation. Now observe:
Chapter 20: Of Adam and Eve's going forth out of Paradise, and of their entering into this World. And then of the true Christian Church upon Earth, and also of the Antichristian Cainish Church. (9)
For the holy Element continually longs, [or groans] through the four Elements, to be released from the Vanity of the four Elements; in like Manner als...
(9) For the holy Element continually longs, [or groans] through the four Elements, to be released from the Vanity of the four Elements; in like Manner also the Qualifying [or Influence] of the grim [Constellations or] Stars [labours;] and therefore it drives Man to seek such wonderful Forms [or Ways,] that the eternal Wonders of God might be manifested, which (in the Breaking of the World) shall stand all (in the P Figure) in the Shadow.
We may now consider the question whether fire is the sole element existing in that celestial realm and whether there is any outgoing thence with the...
(6) We may now consider the question whether fire is the sole element existing in that celestial realm and whether there is any outgoing thence with the consequent need of renewal.
Timaeus pronounced the material frame of the All to consist primarily of earth and fire for visibility, earth for solidity- and deduced that the stars must be mainly composed of fire, but not solely since there is no doubt they are solid.
And this is probably a true account. Plato accepts it as indicated by all the appearances. And, in fact, to all our perception- as we see them and derive from them the impression of illumination- the stars appear to be mostly, if not exclusively, fire: but on reasoning into the matter we judge that since solidity cannot exist apart from earth-matter, they must contain earth as well.
But what place could there be for the other elements? It is impossible to imagine water amid so vast a conflagration; and if air were present it would be continually changing into fire.
Admitting that two self-contained entities, standing as extremes to each other need for their coherence two intermediaries; we may still question whether this holds good with regard to physical bodies. Certainly water and earth can be mixed without any such intermediate. It might seem valid to object that the intermediates are already present in the earth and the water; but a possible answer would be, "Yes, but not as agents whose meeting is necessary to the coherence of those extremes."
None the less we will take it that the coherence of extremes is produced by virtue of each possessing all the intermediates. It is still not proven that fire is necessary to the visibility of earth and earth to the solidarity of fire.
On this principle, nothing possesses an essential-nature of its very own; every several thing is a blend, and its name is merely an indication of the dominant constituent.
Thus we are told that earth cannot have concrete existence without the help of some moist element- the moisture in water being the necessary adhesive- but admitting that we so find it, there is still a contradiction in pretending that any one element has a being of its own and in the same breath denying its self-coherence, making its subsistence depend upon others, and so, in reality, reducing the specific element to nothing. How can we talk of the existence of the definite Kind, earth- earth essential- if there exists no single particle of earth which actually is earth without any need of water to secure its self-cohesion? What has such an adhesive to act upon if there is absolutely no given magnitude of real earth to which it may bind particle after particle in its business of producing the continuous mass? If there is any such given magnitude, large or small, of pure earth, then earth can exist in its own nature, independently of water: if there is no such primary particle of pure earth, then there is nothing whatever for the water to bind. As for air- air unchanged, retaining its distinctive quality- how could it conduce to the subsistence of a dense material like earth?
Similarly with fire. No doubt Timaeus speaks of it as necessary not to the existence but to the visibility of earth and the other elements; and certainly light is essential to all visibility- we cannot say that we see darkness, which implies, precisely, that nothing is seen, as silence means nothing being heard.
But all this does not assure us that the earth to be visible must contain fire: light is sufficient: snow, for example, and other extremely cold substances gleam without the presence of fire- though of course it might be said that fire was once there and communicated colour before disappearing.
As to the composition of water, we must leave it an open question whether there can be such a thing as water without a certain proportion of earth.
But how can air, the yielding element, contain earth?
Fire, again: is earth perhaps necessary there since fire is by its own nature devoid of continuity and not a thing of three dimensions?
Supposing it does not possess the solidity of the three dimensions, it has that of its thrust; now, cannot this belong to it by the mere right and fact of its being one of the corporeal entities in nature? Hardness is another matter, a property confined to earth-stuff. Remember that gold- which is water- becomes dense by the accession not of earth but of denseness or consolidation: in the same way fire, with Soul present within it, may consolidate itself upon the power of the Soul; and there are living beings of fire among the Celestials.
But, in sum, do we abandon the teaching that all the elements enter into the composition of every living thing?
For this sphere, no; but to lift clay into the heavens is against nature, contrary to the laws of her ordaining: it is difficult, too, to think of that swiftest of circuits bearing along earthly bodies in its course nor could such material conduce to the splendour and white glint of the celestial fire.
Timaeus: by far the safest reply, in point of truth, would be that it is gold; but as for the triangle and all the other figures which were formed in...
(50) Timaeus: by far the safest reply, in point of truth, would be that it is gold; but as for the triangle and all the other figures which were formed in it, one should never describe them as “being” seeing that they change even while one is mentioning them; rather one should be content if the figure admits of even the title “suchlike” being applied to it with any safety. And of the substance which receives all bodies