P. 61. Do not assist a man in laying a burden down.

This in the Protreptics is the 11th Symbol, and is explained by Iamblichus as follows: “This Symbol exhorts to fortitude; for whoever takes up a burden, signifies that he undertakes an action of labor and energy; but he who lays one down, of rest and remission. So that the Symbol has the following meaning; Do not become either to yourself or another the cause of an indolent and effeminate mode of conduct; for every useful thing is acquired by labor. But the Pythagoreans celebrate this Symbol as Herculean, thus denominating it from the labors of Hercules. For during his association with men, he frequently returned from fire and every thing dreadful, indignantly rejecting indolence. For rectitude of conduct is produced from acting and operating, but not from sluggishness.”

P. 61. Do not draw near to a woman for the sake of begetting children, if she has gold.

In the Protreptics of Iamblichus (Symbol 35.) this is expressed as follows: “Draw not near to that which has gold, in order to produce children.” On which Iamblichus observes: “The Symbol does not here speak of a woman, but of that sect and philosophy which has much of the corporeal in it, and a gravitating tendency downwards. For gold is the heaviest of all things in the earth, and pursues a tendency to the middle, which is the peculiarity of corporeal weight. But the term to draw near, not only signifies to be connected with, but always to approach towards, and to be seated near another.”

P. 61. Speak not about Pythagoric concerns without light.

This is the 13th Symbol in the Protreptics, and is thus explained by Iamblichus: “This Symbol exhorts to the possession of intellectual prudence. For this is similar to the light of the soul, to which being indefinite it gives bound, and leads, as it were, from darkness into light. It is proper, therefore, to place intellect as the leader of every thing beautiful in life, but especially in Pythagoric dogmas; for these cannot be known without light.”

P. 61. Wear not the image of God in a ring.

This in the Protreptics is the 24th Symbol; but instead of wear, it is there inscribe. But Iamblichus’ explanation of it is as follows: “This Symbol conformably to the foregoing conception, employs the following exhortation: Philosophize, and before every thing consider the Gods as having an incorporeal subsistence. For this is the most principal root of the Pythagoric dogmas, from which nearly all of them are suspended, and by which they are strengthened even to the end. Do not therefore think that the Gods use such forms as are corporeal, or that they are received by a material subject, and by body as a material bond, like other animals. But the engravings in rings exhibit the bond which subsists through the ring, its corporeal nature and sensible form, and the view as it were of some partial animal, which becomes apparent through the engraving; from which especially we should separate the genus of the Gods, as being eternal and intelligible, and always subsisting according to the same and in a similar manner, as we have particularly, most fully, and scientifically shown in our treatise concerning the Gods.”[97]

P. 61. Nor is it proper to sacrifice a white cock; for this also is a suppliant, and is sacred to the moon.

In the Protreptics, the 18th Symbol is partly the same with, and partly different from this. For it is, “Nourish a cock; but sacrifice it not; for it is sacred to the sun and the moon.” And Iamblichus explains it as follows: “This Symbol advises us to nourish and strengthen the body and not neglect it, dissolving and destroying the mighty tokens of the union, connexion, sympathy, and consent of the world. So that it exhorts us to engage in the contemplation and philosophy of the universe. For though the truth concerning the universe is naturally occult, and sufficiently difficult of investigation, it must, however, at the same time, be inquired into and investigated by man, and especially through philosophy. For it is truly impossible to be discovered through any other pursuit. But philosophy receiving certain sparks, and as it were viatica, from nature, excites and expands them into magnitude, rendering them more conspicuous through the disciplines which it possesses. Hence, therefore, we should philosophize.”

P. 61. It is proper to sacrifice, and to enter temples, unshod.

This in the Protreptics is the 3rd Symbol; but is thus enunciated by Iamblichus, “Sacrifice and adore unshod.” On which Iamblichus observes: “This Symbol signifies that we ought to worship the Gods, and acquire a knowledge of them in an orderly and modest manner, and in a way not surpassing our condition on the earth. It also signifies that, in worshipping them, and acquiring this knowledge, we should be free from bonds, and properly liberated. But the Symbol exhorts that sacrifice and adoration should be performed not only in the body, but also in the energies of the soul; so that these energies may neither be detained by passions, nor by the imbecility of the body, nor by generation, with which we are externally surrounded. But every thing pertaining to us should be properly liberated, and prepared, for the participation of the Gods.”

P. 77. Enter not into a temple negligently, nor, in short, adore carelessly, not even though you should stand at the very doors themselves.

This in the Protreptics is the 2nd Symbol, and is explained by Iamblichus as follows: “If the similar is friendly and allied to the similar, it is evident that since the Gods have a most principal essence among wholes, we ought to make the worship of them a principal object. But he who does this for the sake of any thing else, gives a secondary rank to that which takes the precedency of all things, and subverts the whole order of religious worship and knowledge. Besides, it is not proper to rank illustrious goods in the subordinate condition of human utility, nor to place our concerns in the order of an end, but things more excellent, whether they be works or conceptions, in the condition of an appendage.”

P. 79. These, therefore, he ordered not to eat the heart.

This is the 30th Symbol in the Protreptics, and is thus explained by Iamblichus: “This Symbol signifies that it is not proper to divulse the union and consent of the universe. And still further, it signifies this, Be not envious, but philanthropic, and communicative: and from this it exhorts us to philosophize. For philosophy alone among the sciences and arts, is neither pained with the goods of others, nor rejoices in the evils of neighbours, these being allied and familiar by nature, subject to the like passions, and exposed to one common fortune. It likewise evinces that the future is equally unlooked for by all men. Hence, it exhorts us to sympathy and mutual love, and to be truly communicative, as it becomes rational animals.”

P. 79. Nor the brain.

This is the 31st Symbol in the Protreptics, and which Iamblichus thus explains: “This Symbol also resembles the former: for the brain is the ruling instrument of intellectual prudence. The Symbol, therefore, obscurely signifies that we ought not to dilacerate nor mangle things and dogmas, which have been the objects of judicious deliberation. But these will be such as have been the subject of intellectual consideration, becoming thus equal to objects of a scientific nature. For things of this kind are to be surveyed, not through the instruments of the irrational form of the soul, such as the heart and the liver; but through the pure rational nature. Hence, to dilacerate these by opposition, is inconsiderate folly; but the Symbol rather exhorts us to venerate the fountain of intelligence, and the most proximate organ of intellectual perception, through which we shall possess contemplation, science, and wisdom; and by which we shall truly philosophize, and neither confound nor obscure the vestiges which philosophy produces.”

P. 79. To abstain from mallows, &c.

The 38th Symbol in the Protreptics is: “Transplant mallows in your garden, but eat them not.” On which Iamblichus observes as follows: “This Symbol obscurely signifies that plants of this kind turn with the sun, and it thinks fit that this should be noticed by us. It also adds, transplant, that is to say, observe its nature, its tendency towards, and sympathy with, the sun; but rest not satisfied, nor dwelt upon this, but transfer, and as it were transplant your conception to kindred plants and pot-herbs, and also to animals which are not kindred, to stones and rivers, and, in short, to natures of every kind. For you will find them to be prolific and multiform, and admirably abundant; and this to one who begins from the mallows, as from a root and principle, is significant of the union and consent of the world. Not only, therefore, do not destroy or obliterate observations of this kind; but increase and multiply them as if they were transplanted.”

P. 80. Thus too he ordered them to abstain from the fish Melanurus.[98]

The 6th Symbol in the Protreptics is, “Abstain from melanurus; for it belongs to the terrestrial Gods.” And this, according to Iamblichus, admonishes us to embrace the celestial journey, to conjoin ourselves to the intellectual Gods, to become separated from a material nature, and to be led as it were in a circular profession to an immaterial and pure life. It further exhorts us to adopt the most excellent worship of the Gods, and especially that which pertains to the primary[99] Gods.

P. 80. And also not to receive the fish Erythynus.

This in the Protreptics is the 33rd Symbol, and which Iamblichus thus explains: “This Symbol seems to be merely referred to the etymology of the name. Receive not an unblushing and impudent man; nor on the contrary one stupidly astonished, and who in every thing blushes, and is humble in the extreme, through the imbecility of his intellect and reasoning power. Hence this also is understood, Be not yourself such a one.”

P. 80. He likewise exhorted them to abstain from beans.

In the Protreptics this is the 37th Symbol; and Iamblichus has not developed for us the more mystical signification of this symbol. For he only says that “it admonishes us to beware of every thing which is corruptive of our converse with the Gods and divine prophecy.” But Aristotle appears to have assigned the true mystical reason why the Pythagoreans abstained from beans. For he says, (apud Laert.) “that Pythagoras considered beans as a symbol of generation [i. e. of the whole of a visible and corporeal nature,] which subsists according to a right line, and is without inflection; because a bean alone of almost all spermatic plants, is perforated through the whole of it, and is not obstructed by any intervening joints.” Hence he adds, “it resembles the gates of Hades.” For these are perpetually open without any impediment to souls descending into generation. The exhortation, therefore, to abstain from beans, is equivalent to admonishing us to beware of a continued and perpetual descent into the realms of generation. Hence the true meaning of the following celebrated lines in Virgil;

i. e.

P. 98. Such as infallible predictions of earthquakes, rapid expulsions of pestilence, &c. &c.

Since Pythagoras, as Iamblichus informs us, p. 9. was initiated in all the mysteries of Byblus and Tyre, in the sacred operations of the Syrians, and in the mysteries of the Phœnicians, and also (p. 12.) that he spent two and twenty years in the adyta of temples in Egypt, associated with the Magi in Babylon, and was instructed by them in their venerable knowledge;—it is not at all wonderful that he was skilled in magic or theurgy, and was therefore able to perform things which surpass merely human power, and which appear to be perfectly incredible to the vulgar. For “magic,” (as we learn from Psellus in his MS. treatise on Dæmons) “formed the last part of the sacerdotal science.” He farther likewise informs us, “that magic investigates the nature, power, and quality of every thing sublunary; viz. of the elements and their parts, of animals, all-various plants, and their fruits, of stones, and herbs: and in short, it explores the essence and power of every thing. From hence, therefore, it produces its effects. And it forms statues which procure health, makes all-various figures, and things which become the instruments of disease. If asserts too, that eagles and dragons contribute to health; but that cats, dogs, and crows, are symbols of vigilance, to which therefore they contribute. But for the fashioning of certain parts, wax and clay are used. Often, too, celestial fire is made to appear through magic; and then statues laugh, and lamps are spontaneously enkindled.” See the original in the Notes to my Pausanias, p. 325. And that theurgy was employed by the ancients in their mysteries, I have fully proved in my treatise On the Eleusinian and Bacchic Mysteries.[100]

Conformably to this, Plato also in the First Alcibiades says, that the magic of Zoroaster consisted in the worship of the Gods, on which passage, I shall present the reader with what I have said, in the first volume of my Plato, p. 63, as it will enable him to see that the theurgy of the ancients is founded in a theory equally scientific and sublime.

“The following account of magic by Proclus, originally formed, as it appears to me, a part of the Commentary written by him on the present passage. For the MS. Commentary of Proclus, which is extant on this dialogue, does not extend to more than a third part of it; and this Dissertation on Magic, which is only extant in Latin, was published by Ficinus the translator, immediately after his Excerpta from this Commentary. So that it seems highly probable, that the manuscript from which Ficinus translated his Excerpta, was much more perfect, than that which has been preserved to us, in consequence of containing this account of the magic of the ancients.

“In the same manner as lovers gradually advance from that beauty which is apparent in sensible forms, to that which is divine; so the ancient priests, when they considered that there is a certain alliance and sympathy in natural things to each other, and of things manifest to occult powers, and discovered that all things subsist in all, they fabricated a sacred science from this mutual sympathy and similarity. Thus they recognized things supreme in such as are subordinate, and the subordinate in the supreme: in the celestial regions, terrene properties subsisting in a causal and celestial manner; and in earth celestial properties, but according to a terrene condition. For how shall we account for those plants called heliotropes, that is, attendants on the sun, moving in correspondence with the revolution of its orb, but selenitropes, or attendants on the moon, turning in exact conformity to her motion? It is because all things pray, and hymn the leaders of their respective orders; but some intellectually, and others rationally; some in a natural, and others after a sensible manner. Hence the sun-flower, as far as it is able, moves in a circular dance towards the sun; so that if any one could hear the pulsation made by its circuit in the air, he would perceive something composed by a sound of this kind, in honor of its king, such as a plant is capable of framing. Hence, too, we may behold the sun and moon in the earth, but according to a terrene quality; but in the celestial regions, all plants, and stones, and animals, possessing an intellectual life according to a celestial nature. Now the ancients, having contemplated this mutual sympathy of things, applied for occult purposes, both celestial and terrene natures, by means of which, through a certain similitude, they deduced divine virtues into this inferior abode. For, indeed, similitude itself is a sufficient cause of binding things together in union and consent. Thus, if a piece of paper is heated, and afterwards placed near a lamp, though it does not touch the fire, the paper will be suddenly inflamed, and the flame will descend from the superior to the inferior parts. This heated paper we may compare, to a certain relation of inferiors to superiors; and its approximation to the lamp, to the opportune use of things according to time, place, and matter. But the procession of fire into the paper, aptly represents the presence of divine light, to that nature which is capable of its reception. Lastly, the inflammation of the paper may be compared to the deification of mortals, and to the illumination of material natures, which are afterwards carried upwards like the enkindled paper, from a certain participation of divine seed.

“Again, the lotus, before the rising of the sun, folds its leaves into itself, but gradually expands them on its rising: unfolding them in proportion to the sun’s ascent to the zenith; but as gradually contracting them, as that luminary descends to the west. Hence this plant, by the expansion and contraction of its leaves, appears no less to honor the sun, than men by the gesture of their eye-lids, and the motion of their lips. But this imitation and certain participation of supernal light, is not only visible in plants, which possess nothing more than a vestige of life, but likewise in particular stones. Thus the sun-stone, by its golden rays, imitates those of the sun; but the stone called the eye of heaven, or of the sun, has a figure similar to the pupil of an eye, and a ray shines from the middle of the pupil. Thus too the lunar stone, which has a figure similar to the moon when horned, by a certain change of itself, follows the lunar motion. Lastly, the stone called helioselenus, i. e. of the sun and moon, imitates, after a manner, the congress of those luminaries, which it images by its color. So that all things are full of divine natures; terrestrial natures receiving the plenitude of such as are celestial, but celestial of supercelestial essences;[101] while every order of things proceeds gradually in a beautiful descent from the highest to the lowest. For whatever particulars are collected into one above the order of things, are afterwards dilated in descending, various souls being distributed under their various ruling divinities.

“In the next place, there are many solar animals, such as lions and cocks, which participate, according to their nature, of a certain solar divinity; whence it is wonderful how much inferiors yield to superiors in the same order, though they do not yield in magnitude and power. Hence it is said, that a cock is very much feared, and as it were reverenced, by a lion; the reason of which we cannot assign from matter or sense, but from the contemplation alone of a supernal order. For thus we shall find that the presence of the solar virtue accords more with a cock than with a lion. This will be evident from considering that the cock, as it were, with certain hymns, applauds and calls to the rising sun, when he bends his course to us from the antipodes; and that solar angels sometimes appear in forms of this kind, who though they are without shape, yet present themselves to us who are connected with shape, in some sensible form. Sometimes too there are dæmons with a leonine front, who, when a cock is placed before them, unless they are of a solar order, suddenly disappear; and this, because those natures which have an inferior rank in the same order, always reverence their superiors; just as many, on beholding the images of divine men, are accustomed, from the very view, to be fearful of perpetrating any thing base.

“In fine, some things turn round correspondent to the revolutions of the sun, as the plants which we have mentioned, and others after a manner imitate the solar rays, as the palm and the date; some the fiery nature of the sun, as the laurel; and others a different property. For, indeed, we may perceive that the properties which are collected in the sun, are every where distributed to subsequent natures constituted in a solar order; that is, to angels, dæmons, souls, animals, plants, and stones. Hence the authors of the ancient priesthood discovered from things apparent, the worship of superior powers, while they mingled some things and purified others. They mingled many things indeed together, because they saw that some simple substances possessed a divine property (though not taken singly) sufficient to call down that particular power, of which they were participants. Hence, by the mingling of many things together, they attracted upon us a supernal influx; and by the composition of one thing from many, they produced an assimilation to that one which is above many; and composed statues from the mixture of various substances conspiring in sympathy and consent. Besides this, they collected composite odours, by a divine art, into one, comprehending a multitude of powers, and symbolizing with the unity of a divine essence; considering that division debilitates each of these, but that mingling them together, restores them to the idea of their exemplar.

“But sometimes one herb, or one stone, is sufficient to a divine operation. Thus, a thistle is sufficient to procure the sudden appearance of some superior power; but a laurel, raccinum, (or a thorny kind of sprig) the land and sea onion, the coral, the diamond, and the jasper, operate as a safeguard. The heart of a mole is subservient to divination, but sulphur and marine water to purification. Hence, the ancient priests, by the mutual relation and sympathy of things to each other, collected their virtues into one, but expelled them by repugnancy and antipathy; purifying when it was requisite with sulphur and bitumen, and sprinkling with marine water. For sulphur purifies, from the sharpness of its odour; but marine water, on account of its fiery portion. Besides this, in the worship of the Gods, they offered animals, and other substances congruous to their nature; and received, in the first place, the powers of dæmons, as proximate to natural substances and operations; and by these natural substances they convoked into their presence those powers to which they approached. Afterwards, they proceeded from dæmons to the powers and energies of the Gods; partly, indeed, from dæmoniacal instruction, but partly by their own industry, interpreting convenient symbols, and ascending to a proper intelligence of the Gods. And lastly, laying aside natural substances and their operations, they received themselves into the communion and fellowship of the Gods.”

It will doubtless be objected by most of the present period, who believe in nothing beyond the information of their senses, that plants, animals, and stones, no longer possess those wonderful sympathetic powers, which are mentioned by Proclus in the above extract. In answer to any such objector, whose little soul, (in the language of the Emperor Julian) is indeed acute, but sees nothing with a vision healthy and sound, it must be said, that this is not at all wonderful at a period, when, as the author of the Asclepian dialogue justly observes, “there is a lamentable departure of divinity from man, when nothing worthy of heaven, or celestial concerns, is heard or believed, and when every divine voice is by a necessary silence dumb.”[102] But to the philosophic reader, it must be observed, that as in the realms of generation, or in other words, the sublunary region, wholes, viz. the spheres of the different elements, remain perpetually according to nature; but their parts are sometimes according, and sometimes contrary to nature; this must also be true of the parts of the earth. When those circulations therefore take place, during which the parts of the earth subsist according to nature, and which are justly called, by Plato, fertile periods, the powers of plants, animals, and stones, magically sympathize with superior natures, in consequence of a more abundant participation of them, through a greater degree of aptitude to receive, and alliance to the participated powers. But during those circulations, in which the parts of the earth subsist contrary to nature, as at present, and which Plato calls barren periods, the powers of plants, animals, and stones, no longer possess a magic sympathy, and consequently are no longer capable of producing magical operations.

P. 106. The eternal essence of number is the most providential principle of the universe, &c.

The following account of the manner in which the Pythagoreans philosophized about numbers, is extracted from my Theoretic Arithmetic, and the information contained in it is principally derived from the great Syrianus.

“The Pythagoreans, turning from the vulgar paths, and delivering their philosophy in secret to those alone who were worthy to receive it, exhibited it to others through mathematical names. Hence, they called forms, numbers, as things which are the first separated from impartible union; for the natures which are above forms, are also above separation.[103] The all-perfect multitude of forms, therefore, they obscurely signified through the duad; but they indicated the first formal principles by the monad and duad, as not being numbers; and also by the first triad and tetrad, as being the first numbers, the one being odd, and the other even, from which by addition the decad is generated; for the sum of 1, 2, 3, and 4, is ten. But after numbers, in secondary and multifarious lives, introducing geometrical prior to physical magnitudes; these also they referred to numbers, as to formal causes and the principles of these; referring the point indeed, as being impartible, to the monad; but a line, as the first interval, to the duad; and again, a superficies, as having a more abundant interval, to the triad; and a solid to the tetrad. They also called, as is evident from the testimony of Aristotle, the first length the duad; for it is not simply length, but the first length, in order that by this they might signify cause. In a similar manner also, they denominated the first breadth, the triad; and the first depth the tetrad. They also referred to formal principles all psychical knowledge. And intellectual knowledge indeed, as being contracted according to impartible union, they referred to the monad; but scientific knowledge, as being evolved, and as proceeding from cause to the thing caused, yet through the inerratic, and always through the same things, they referred to the duad; and opinion to the triad, because the power of it is not always directed to the same thing, but at one time inclines to the true, and at another to the false. And they referred sense to the tetrad, because it has an apprehension of bodies; for in the duad, indeed, there is one interval from one monad to the other; but in the triad there are two intervals from any one monad to the rest; and in the tetrad there are three. They referred, therefore, to principles every thing knowable, viz. beings, and the gnostic powers of these. But they divided beings not according to breadth, but according to depth; into intelligibles, objects of science, objects of opinion, and sensibles. In a similar manner, also, they divided knowledge into intellect, science, opinion, and sense. The extremity, therefore, of the intelligible triad, or animal itself, as it is called by Plato in the Timæus, is assumed from the division of the objects of knowledge, manifesting the intelligible order, in which forms themselves, viz. the first forms and the principles of these, are contained, viz. the idea of the one itself, of the first length, which is the duad itself, and also the ideas of the first breadth and the first depth; (for in common the term first is adapted to all of them), viz. to the triad itself, and the tetrad itself.

“Again, the Pythagoreans and Plato did not denominate idea from one thing, and ideal number from another. But since the assertion is eminently true, that all things are similar to number, it is evident that number, and especially every ideal number, was denominated on account of its paradigmatic peculiarity. If any one, however, wishes to apprehend this from the appellation itself, it is easy to infer that idea was so called, from rendering as it were its participants similar to itself, and imparting to them form, order, beauty, and unity; and this in consequence of always preserving the same form, expanding its own power to the infinity of particulars, and investing with the same species its eternal participants. Number also, since it imparts proportion and elegant arrangement to all things, was allotted this appellation. For the ancients, says Syrianus,[104] call to adapt or compose αρσαι arsai, whence is derived αριθμος arithmos number. Hence αναρσιον anarsion among the Greeks signifies incomposite. Hence too, those Grecian sayings, you will adapt the balance, they placed number together with them, and also number and friendship. From all which number was called by the Greeks arithmos, as that which measures and orderly arranges all things, and unites them in amicable league.

“Farther still, some of the Pythagoreans discoursed about inseparable numbers alone, i. e. numbers which are inseparable from mundane natures, but others about such as have a subsistence separate from the universe, in which as paradigms they saw those numbers are contained, which are perfected by nature. But others, making a distinction between the two, unfolded their doctrine in a more clear and perfect manner. If it be requisite, however, to speak concerning the difference of these monads, and their privation of difference, we must say that the monads which subsist in quantity, are by no means to be extended to essential numbers; but when we call essential numbers monads, we must assert that all of them mutually differ from each other by difference itself, and that they possess a privation of difference from sameness. It is evident also, that those which are in the same order, are contained through mutual comparison, in sameness rather than in difference, but that those which are in different orders are conversant with much diversity, through the dominion of difference.

“Again, the Pythagoreans asserted that nature produces sensibles by numbers; but then these numbers were not mathematical but physical; and as they spoke symbolically, it is not improbable that they demonstrated every property of sensibles by mathematical names. However, says Syrianus, to ascribe to them a knowledge of sensible numbers alone, is not only ridiculous, but highly impious. For they received indeed, from the theology of Orpheus, the principles of intelligible and intellectual numbers, they assigned them an abundant progression, and extended their dominion as far as to sensibles themselves.”

Again, their conceptions about mathematical and physical number, were as follow:

“As in every thing, according to the doctrine of Aristotle, one thing corresponds to matter, and another to form, in any number, as for instance the pentad, its five monads, and in short its quantity, and the number which is the subject of participation, are derived from the duad itself; but its form, i. e. the pentad itself, is from the monad; for every form is a monad, and unites its subject quantity. The pentad itself, therefore, which is a monad, proceeds from the principal monad, forms its subject quantity, which is itself formless, and connects it to its own form. For there are two principles of mathematical numbers in our souls: the monad, which comprehends in itself all the forms of numbers, and corresponds to the monad in intellectual natures; and the duad, which is a certain generative principle of infinite power, and which on this account, as being the image of the never-failing and intelligible duad, is called indefinite. While this proceeds to all things, it is not deserted in its course by the monad, but that which proceeds from the monad continually distinguishes and forms boundless quantity, gives a specific distinction to all its orderly progressions, and incessantly adorns them with forms. And as in mundane natures, there is neither any thing formless, nor any vacuum among the species of things, so likewise in mathematical number, neither is any quantity left innumerable; for thus the forming power of the monad would be vanquished by the indefinite duad, nor does any medium intervene between the consequent numbers, and the well-disposed energy of the monad.

“Neither, therefore, does the pentad consist of substance and accident, as a white man; nor of genus and difference, as man of animal and biped; nor of five monads mutually touching each other, like a bundle of wood; nor of things mingled, like a drink made from wine and honey; nor of things sustaining position, as stones by their position complete the house; nor lastly, as things numerable, for these are nothing else than particulars. But it does not follow that numbers themselves, because they consist of indivisible monads, have nothing else besides monads, (for the multitude of points in continued quantity is an indivisible multitude, yet it is not on this account that there is a completion of something else from the points themselves); but this takes place because there is something in them which corresponds to matter, and something which corresponds to form. Lastly, when we unite the triad with the tetrad, we say that we make seven. The assertion, however, is not true: for monads conjoined with monads, produce indeed the subject of the number 7, but nothing more. Who then imparts the heptadic form to these monads? Who is it also that gives the form of a bed to a certain number of pieces of wood? Shall we not say that the soul of the carpenter, from the art which he possesses, fashions the wood, so as to receive the form of a bed, and that the numerative soul, from possessing in herself a monad which has the relation of a principle, gives form and subsistence to all numbers? But in this only consists the difference, that the carpenter’s art is not naturally inherent in us, and requires manual operation, because it is conversant with sensible matter; but the numerative art is naturally present with us, and is therefore possessed by all men, and has an intellectual matter which it instantaneously invests with form. And this is that which deceives the multitude, who think that the heptad is nothing besides seven monads. For the imagination of the vulgar, unless it first sees a thing unadorned, afterwards the supervening energy of the adorner, and lastly, above all the thing itself, perfect and formed, cannot be persuaded that it has two natures, one formless, the other formal, and still further, that which beyond these imparts form; but asserts, that the subject is one, and without generation. Hence, perhaps, the ancient theologists and Plato ascribed temporal generations to things without generation, and to things which are perpetually adorned, and regularly disposed, privation of order and ornament, the erroneous and the boundless, that they might lead men to the knowledge of a formal and effective cause. It is, therefore, by no means wonderful, that though seven sensible monads are never without the heptad, these should be distinguished by science, and that the former should have the relation of a subject, and be analogous to matter, but the latter should correspond to species and form.

“Again, as when water is changed into air, the water does not become air, or the subject of air, but that which was the subject of water becomes the subject of air, so when one number unites itself with another, as for instance the triad with the duad, the species or forms of the two numbers are not mingled, except in their immaterial reasons (or productive principles), in which at the same time that they are separate, they are not impeded from being united, but the quantities of the two numbers which are placed together, become the subject of the pentad. The triad, therefore, is one, and also the tetrad, even in mathematical numbers: for though in the ennead or number nine, you may conceive a first, second, and third triad, yet you see one thing thrice assumed; and in short, in the ennead there is nothing but the form of the ennead in the quantity of nine monads. But if you mentally separate its subject, (for form is impartible) you will immediately invest it with forms corresponding to its division; for our soul cannot endure to see that which is formless, unadorned, especially as she possesses the power of investing it with ornament.

“Since also separate numbers possess a demiurgic or fabricative power, which mathematical numbers imitate, the sensible world likewise contains images of those numbers by which it is adorned; so that all things are in all, but in an appropriate manner in each. The sensible world, therefore, subsists from immaterial and energetic reasons, and from more ancient causes. But those who do not admit that nature herself is full of productive powers, lest they should be obliged to double things themselves, these wonder how from things void of magnitude and gravity, magnitude and gravity are composed; though they are never composed from things of this kind which are void of gravity and magnitude, as from parts. But magnitude is generated from essentially impartible elements; since form and matter are the elements of bodies; and still much more is it generated from those truer causes which are considered in demiurgic reasons and forms. Is it not therefore necessary that all dimensions, and all moving masses, must from these receive their generation? For either bodies are unbegotten, like incorporeal natures; or of things with interval, things without interval are the causes; of partibles impartibles; and of sensibles and contraries, things insensible and void of contact: and we must assent to those who assert that things possessing magnitude are thus generated from impartibles. Hence the Pythagorean Eurytus, and his followers, beholding the images of things themselves in numbers, rightly attributed certain numbers to certain things, according to their peculiarity. In consequence of this, he said that a particular number is the boundary of this plant, and again, another number of this animal; just as of a triangle 6 is the boundary, of a square 9, and of a cube 8. As the musician, too, harmonizes his lyre through mathematical numbers, so nature through her own natural numbers, orderly arranges, and modulates her productions.

“Indeed, that numbers are participated by the heavens, and that there is a solar number, and also a lunar number, is manifest according to the adage, even to the blind. For the restitutions of the heavenly bodies to their pristine state (αποκαταστασεις) would not always be effected through the same things, and in the same manner, unless one and the same number bad dominion in each. Yet all these contribute to the procession of the celestial spheres, and are contained by their perfect number. But there is also a certain natural number belonging to every animal. For things of the same species would not be distinguished by organs after the same manner, nor would they arrive at puberty and old age about the same time, or generate, nor would the fœtus be nourished or increase, according to regular periods, unless they were detained by the same measure of nature. According to the best of the Pythagoreans also, Plato himself, number is the cause of better and worse generations. Hence though the Pythagoreans sometimes speak of the squares and cubes of natural numbers, they do not make them to be monadic, such as the number 9, and the number 27; but they signify through these names, from similitude, the progression of natural numbers into, and dominion about, generations. In like manner, though they call them equal or double, they exhibit the dominion and symphony of ideas in these numbers. Hence different things do not use the same number, so far as they are different, nor do the same things use a different number, so far as they are the same.

“In short, physical numbers are material forms divided about the subject which receives them. But material powers are the sources of connexion and modification to bodies. For form is one thing, and the power proceeding from it another. For form itself is indeed impartible and essential; but being extended, and becoming bulky, it emits from itself, as if it were a blast, material powers which are certain qualities. Thus, for instance, in fire, the form and essence of it is impartible, and is truly the image of the cause of fire: for in partible natures, the impartible has a subsistence. But from form which is impartible in fire, and which subsists in it as number, an extension of it accompanied with interval takes place about matter, from which the powers of fire are emitted, such as heat, or refrigeration, or moisture, or something else of the like kind. And these qualities are indeed essential, but are by no means the essence of fire. For essences do not proceed from qualities, nor are essence and power the same thing. But the essential every where precedes power. And from this being one the multitude of powers proceeds, and the distributed from that which is undistributed; just as many energies are the progeny of one power.”

P. 107. For Pythagoras always proclaimed, that nothing admirable pertaining to the Gods or divine dogmas, should be disbelieved.

This in the Protreptics forms the fourth symbol, and is thus explained by Iamblichus:—“This dogma sufficiently venerates and unfolds the transcendency of the Gods, affording us a viaticum, and recalling to our memory that we ought not to estimate divine power from our judgment. But it is likely that some things should appear difficult and impossible to us, in consequence of our corporeal subsistence, and from our being conversant with generation and corruption; from our having a momentary existence; from being subject to a variety of diseases; from the smallness of our habitation; from our gravitating tendency to the middle; from our somnolency, indigence and repletion; from our want of counsel and our imbecility; from the impediments of our soul, and a variety of other circumstances, although our nature possesses many illustrious prerogatives. At the same time however we perfectly fall short of the Gods, and neither possess the same power with them, nor equal virtue. This symbol therefore in a particular manner introduces the knowledge of the Gods, as beings who are able to effect all things. On this account it exhorts us to disbelieve nothing concerning the Gods. It also adds, nor about divine dogmas; viz. those belonging to the Pythagoric philosophy. For these being secured by disciplines and scientific theory, are alone true and free from falsehood, being corroborated by all-various demonstration, accompanied with necessity. The same symbol, also, is capable of exhorting us to the science concerning the Gods: for it urges us to acquire a science of that kind, through which we shall be in no respect deficient in things asserted about the Gods. It is also able to exhort the same things concerning divine dogmas, and a disciplinative progression. For disciplines alone give eyes to, and produce light about, all things, in him who intends to consider and survey them. For from the participation of disciplines, one thing before all others is effected, viz. a belief in the nature, essence, and power of the Gods, and also in those Pythagoric dogmas, which appear to be prodigious to such as have not been introduced to, and are uninitiated in, disciplines; So that the precept disbelieve not is equivalent to participate and acquire those things through which you will not disbelieve; that is to say, acquire disciplines and scientific demonstrations.”

P. 88. After this manner therefore it is said that music was discovered by Pythagoras.

The following particulars relative to music are added for the purpose of elucidating what is said about it in this chapter.

“Take two brazen chords, such as are used in harps; for those chords which are made from the intestines of sheep are for the most part either false or obnoxious to the change of the air,