Iamblichus

P. 50. Better worth saving than ten thousand corporeal eyes.

Iamblichus here alludes to what Plato says in the seventh book of his Republic, respecting the mathematical disciplines. For he there says, “that the soul through these disciplines has an organ purified and enlightened, which is blinded and buried by studies of another kind, an organ better worth saving than ten thousand eyes, since truth becomes visible through this alone.”

P. 58. That in which the Sirens subsist.

“The divine Plato, (says Proclus in his MS. Scholia on the Cratylus,) knew that there are three kinds of Sirens; the celestial, which is under the government of Jupiter; that which produces generation, and is under the government of Neptune; and that which is cathartic, and is under the government of Pluto. It is common to all these to incline all things through an harmonic motion to their ruling Gods. Hence, when the soul is in the heavens, the Sirens are desirous of uniting it to the divine life which florishes there. But it is proper that souls living in generation should sail beyond them, like the Homeric Ulysses, that they may not be allured by generation, of which the sea is an image. And when souls are in Hades, the Sirens are desirous of uniting them through intellectual conceptions to Pluto. So that Plato knew that in the kingdom of Hades there are Gods, dÆmons, and souls, who dance as it were round Pluto, allured by the Sirens that dwell there.” See more concerning the Sirens in my translation of Proclus on the Theology of Plato, Book the 6th.

P. 60. That it is requisite to put the shoe on the right foot first.

This audition is taken from what forms the 12th Symbol in the Protreptics of Iamblichus, and is as follows: “When stretching forth your feet to have your sandals put on, first extend your right foot; but when about to use a foot bath, first extend your left foot.” “This Symbol, (says Iamblichus,) exhorts to practical prudence, admonishing us to place worthy actions about us as right-handed; but entirely to lay aside and throw away such as are base, as being left-handed.”

P. 60. That it is not proper to walk in the public ways.

This is the 5th Symbol in the Protreptics of Iamblichus, but is there differently expressed: for it is, “Declining from the public ways, walk in unfrequented paths.” On which Iamblichus observes: “I think that this Symbol also contributes to the same thing as the preceding, [which is, ‘Disbelieve, nothing wonderful concerning the Gods, nor concerning divine dogmas’]. For this exhorts us to abandon a popular and merely human life; but thinks fit that we should pursue a separate and divine life. It also signifies that it is necessary to look above common opinions; but very much to esteem such as are private and arcane; and that we should despise merely human delight; but ardently pursue that felicitous mode of conduct which adheres to the divine will. It likewise exhorts us to dismiss human manners as popular, and to exchange for these the religious cultivation of the Gods, as transcending a popular life.”

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;

——facilis descensus Averno.

Noctes atque dies patet atri janua Ditis:

Sed revocare gradum, superasque evadere ad auras,

Hoc opus, hic labor est.

i.e.

The gates of Hell are open night and day,

Smooth the descent, and easy is the way;

But to return, and view the cheerful skies,

In this, the mighty task and labor lies.

Dryden.

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 Phoenicians, 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 a?sa? arsai, whence is derived a????? arithmos number. Hence a?a?s??? 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 (ap??atastase??) 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 foetus 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,

A—————————B
C—————————D
"
E

“Let these chords be perfectly equal, and equally stretched, so as to be in unison, i.e. so that there may be only one sound, though there are two strings. But it is requisite that they should be placed upon some oblong and polished rule. The ancients called this rule an harmonic rule, or also a monochord, by which instrument all consonances and dissonances, and likewise musical intervals, were tried. Let now one of these chords be bisected in E. Afterwards under the point E place what is vulgarly called the tactus, but which was denominated by the ancients, from its figure, a hemisphere. The tactus, therefore, being placed under E, press there the chord, so that one half of it only, as for instance ED, may be wholly struck and resound. Having therefore struck each of the chords at the same time, viz. the whole of AB, and the half ED, so that they may resound at one and the same time, you will hear the sweetest of all consonances, composed from the sound of the whole chord AB, and the sound of the half ED. This consonance the ancients called diapason, i.e. through all [the chords], because in the musical instruments of the ancients, the two extreme chords, i.e. the most grave, and the most acute of all the chords, contained this consonance; so that, from the gravest chord having made a transition through all the chords to the supreme and most acute of all, they would hear this sweetest consonance. It was, likewise, said to be in a duple ratio of the proportion of one sound to the other. For the sound of the chord AB is doubly greater or more grave than the sound of the half ED. For as sounding bodies are to each other, so are their sounds. But the chord AB is the double of ED. This, however, is now commonly called the octave, because from the first sound, and that the gravest, which is called ut, as far as to that sound which corresponds to it in the consonance diapason, there are these eight sounds, ut, re, mi, fa, sol, re, mi, fa. And of these the first ut, and the last fa, which is the eighth, produce the consonance diapason, or the double, or the octave.

“Again, let the same chord CD be divided into three equal parts in the points F, G.

“FD, therefore, will be two-thirds as well of the whole CD as of the whole AB. Let the tactus now be placed in F, and let AB and FD be struck at the same time, and a consonance very sweet and perfect will indeed be heard, yet not so sweet as the diapason. This the ancients called diapente (i.e. through five chords), because the first and the fifth chord produce this consonance. But according to proportion it is called sesquialter, because the chord AB is sesquialter to FD, and consequently the sounds of these chords also are in the same ratio. But sesquialter ratio is when the greater quantity AB contains the less FD once, and the half of it besides. It is, indeed, commonly called the fifth, because it is composed from the first sound ut, and the fifth, sol.

“Again, let the same chord be cut into four equal parts in the points H, E, I,

“so that the chord HD, may be three-fourths of the whole CD. The tactus, therefore, being placed in H, let AB and HD be struck at one and the same time, and a consonance will be heard, indeed, yet more imperfect than the preceding two. This was called by the ancients diatessaron, i.e. through four chords or sounds, for a similar reason to that by which the former were denominated. With reference, however, to the ratio of the chords and sounds, it is called sesquitertian, because the greater AB contains the less once, and a third part of it besides. But it is now commonly called a fourth, because it is found between the first sound ut, and the fourth fa. If now the point F be added in the preceding figure, and at one and the same time two chords HD and FD are compared in arithmetical ratios, we shall find that the greater HD will have to the less FD a sesquioctave[105] ratio, and the sound of the greater HD to the less FD will have the same ratio, i.e. in modern terms, that between fa and sol there is a sesquioctave ratio. But if these two sounds are heard together, they will be discordant to the ear. Again, the distance between these sounds fa, sol, or between the chords HD and FD, or between the two harmonic intervals HD and FD, the ratio of which was sesquioctave, was called by the ancients a tone. Afterwards they divided the whole of CD into nine equal parts, the first of which is divided in K, so that the whole CD may have to the remainder KD, which contains eight of those parts, a sesquioctave ratio. This, in like manner, will be the interval of a tone, the first sound of which, i. e, of the whole CD, is now called ut, but the second sound of the rest of the chord KD is called re. Afterwards they in a similar manner divided the remainder KD into nine parts, the first part of which is marked in the point L. And for the same reason between the chord KD and the chord KD, and their sounds, there will be a sesquioctave ratio. The sound of the chord LD is now called mi; but the interval which remains between the chord LD and the chord HD has not a sesquioctave ratio, but less than it almost by half, and therefore an interval of this kind was called a semitone, and also diesis or a division. But that interval which remains between the points F and E they divided after the same manner, as the space between C and H was divided, and they again found the same sounds. Let those divisions be marked by the points M and N; and here, also, between N and E, or between mi and fa, there is in like manner another semitone. These eight sounds, therefore, are ut, re, mi, fa, sol, re, mi, fa, which compose the whole diapason. For as we have before observed, between ut and the last fa is the consonance diapason, or between the chord CD or AB, and the chord ED. But from the intervals which are between the sounds there are two semitones, viz. one between mi and fa, denoted by the letters L, N, and the other between the last mi and fa, denoted by the letters N, E. The remaining five intervals are entire tones. It must, also, be observed, that from ut to the first sol is the consonance diapente, which contains three tonic intervals, and one semitone; nevertheless in all there are five sounds, ut, re, mi, fa, sol.

“Again, from sol to the last fa there are four sounds, sol, re, mi, fa, which are perfectly similar to the first four, ut, re, mi, fa. Nevertheless these are more grave, but those are more acute. And as from ut to the first fa is the diatessaron, so likewise from sol to the last fa is another diatessaron, from which, in the last place, it must be observed, it follows that the two consonances diatessaron and diapente constitute the whole diapason; or that the diapason is divided into one diatessaron, and one diapente. For from ut to sol is the diapente, but from sol to the last fa is the diatessaron. This will also be the case if we should say that from ut to the first fa is the diatessaron, as is evident from the division of the chord; but from the first fa to the last fa is the diapente, as is evident from the four intervals of the chord, three of which are tones, and the remaining interval is a semitone, which also in the other diapente were contained between ut and sol.

“Now again, let the tactus be placed in I; but I is the fourth part of the whole CD. Let, also, AB and ID be struck at one and the same time, and the sweetest consonance, called bisdiapason, will be produced; which is so denominated, because it is composed from two diapasons, of which the first is between AB or CD, and ED, but the second is between ED and ID; for the ratio of these is double as well as of those. The ratio, also, of the bisdiapason is quadruple, as is evident from the division; and is commonly called a fifteenth, because from the first ut to this sound, which is also denominated fa, there would be fifteen sounds, if the interval EI were divided after the same manner as the first CE is divided.

“Farther still, let GD be a third part of the whole CD, and let the tactus be placed in G. Then at one and the same time let AB and GD be struck, and a sweet consonance will be heard, which is called diapasondiapente, because it is composed from one diapason contained by the interval CE, or the two chords CD, ED, and one diapente, contained by the interval EG, or the chords ED, GD. For the chord ED is sesquialter to the chord GD; which ratio constitutes the nature of the diapente. The proportion, also, of this consonance is triple. For the chord AB or CD is triple of GD; and it is commonly called the twelfth, because between ut and sol, denoted by the letter G, there would be twelve sounds, if the interval EG received its divisions. From all which it is manifest by the experience of the ear, that there are altogether five consonances, three simple, the diapason, the diapente, and the diatessaron; but two composite, the bisdiapason, and the diapasondiapente.”

In the last place, it is necessary to observe that those ancient Greeks differently denominated these sounds, ut, re, &c. For the first, i.e. the gravest sound or chord, which is now called ut, they, denominated hypate, and the others in the following order:

P. 109. I swear by him who the tetractys found.

The tetrad was called by the Pythagoreans every number, because it comprehends in itself all the numbers as far as to the decad, and the decad itself; for the sum of 1, 2, 3, and 4, is 10. Hence both the decad and the tetrad were said by them to be every number; the decad indeed in energy, but the tetrad in capacity. The sum likewise of these four numbers was said by them to constitute the tetractys, in which all harmonic ratios are included. For 4 to 1, which is a quadruple ratio, forms the symphony bisdiapason; the ratio of 3 to 2, which is sesquialter, forms the symphony diapente; 4 to 3, which is sesquitertian, the symphony diatessaron; and 2 to 1, which is a duple ratio, forms the diapason.

In consequence, however, of the great veneration paid to the tetractys by the Pythagoreans, it will be proper to give it a more ample discussion, and for this purpose to show from Theo of Smyrna,[106] how many tetractys there are: “The tetractys,” says he, “was not only principally honored by the Pythagoreans, because all symphonies are found to exist within it, but also because it appears to contain the nature of all things.” Hence the following was their oath: “Not by him who delivered to our soul the tetractys, which contains the fountain and root of everlasting nature.” But by him who delivered the tetractys they mean Pythagoras; for the doctrine concerning it appears to have been his invention. The above-mentioned tetractys, therefore, is seen in the composition of the first numbers 1. 2. 3. 4. But the second tetractys arises from the increase by multiplication of even and odd numbers beginning from the monad.

Of these, the monad is assumed as the first, because, as we have before observed, it is the principle of all even, odd, and evenly-odd numbers, and the nature of it is simple. But the three successive numbers receive their composition according to the even and the odd; because every number is not alone even, nor alone odd. Hence the even and the odd receive two tetractys, according to multiplication; the even indeed, in a duple ratio; for 2 is the first of even numbers, and increases from the monad by duplication. But the odd number is increased in a triple ratio; for 3 is the first of odd numbers, and is itself increased from the monad by triplication. Hence the monad is common to both these, being itself even and odd. The second number, however, in even and double numbers is 2; but in odd and triple numbers 3. The third among even numbers is 4; but among odd numbers is 9. And the fourth among even numbers is 8; but among odd numbers is 27.

{ 1. 2. 4. 8. }
{ 1. 3. 9. 27. }

In these numbers the more perfect ratios of symphonies are found; and in these also a tone is comprehended. The monad, however, contains the productive principle of a point. But the second numbers 2 and 3 contain the principle of a side, since they are incomposite, and first, are measured by the monad, and naturally measure a right line. The third terms are 4 and 9, which are in power a square superficies, since they are equally equal. And the fourth terms 8 and 27 being equally equally equal, are in power a cube. Hence from these numbers, and this tetractys, the increase takes place from a point to a solid. For a side follows after a point, a superficies after a side, and a solid after a superficies. In these numbers also, Plato in the TimÆus constitutes the soul. But the last of these seven numbers, i.e. 27, is equal to all the numbers that precede it; for 1 + 2 + 3 + 4 + 8 + 9 = 27. There are, therefore, two tetractys of numbers, one of which subsists by addition, but the other by multiplication, and they comprehend musical, geometrical, and arithmetical ratios, from which also the harmony of the universe consists.

But the third tetractys is that which according to the same analogy or proportion comprehends the nature of all magnitude. For what the monad was in the former tetractys, that a point is in this. What the numbers 2 and 3, which are in power a side, were in the former tetractys, that the extended species of a line, the circular and the right, are in this; the right line indeed subsisting in conformity to the even number, since it is terminated[107] by two points; but the circular in conformity to the odd number, because it is comprehended by one line which has no end. But what in the former tetractys the square numbers 4 and 9 were, that the two-fold species of planes, the rectilinear and the circular, are in this. And what the cube numbers 8 and 27 were in the former, the one being an even, but the other an odd number, that the two solids, one of which has a hollow superficies, as the sphere and the cylinder, but the other a plane superficies, as the cube and pyramid, are in this tetractys. Hence, this is the third tetractys, which gives completion to every magnitude, from a point, a line, a superficies, and a solid.

The fourth tetractys is of the simple bodies fire, air, water, and earth, which have an analogy according to numbers. For what the monad was in the first tetractys, that fire is in this. But the duad is air, the triad is water, and the tetrad is earth. For such is the nature of the elements according to tenuity and density of parts. Hence fire has to air the ratio of 1 to 2; but to water, the ratio of 1 to 3; and to earth, the ratio of 1 to 4. In other respects also they are analogous to each other.

The fifth tetractys is of the figures of the simple bodies. For the pyramid, indeed, is the figure of fire; the octaedron, of air; the icosaedron, of water; and the cube, of earth.

The sixth tetractys is of things rising into existence through the vegetative life. And the seed, indeed, is analogous to the monad and a point. But if it increases in length it is analogous to the duad and a line; if in breadth, to the triad and a superficies; but if in thickness, to the tetrad and a solid.

The seventh tetractys is of communities; of which the principle indeed, and as it were monad, is man; the duad is a house; the triad a street; and the tetrad a city. For a nation consists of these. And these indeed are the material and sensible tetractys.

The eighth tetractys consists of the powers which form a judgment of things material and sensible, and which are of a certain intelligible nature. And these are, intellect, science, opinion, and sense. And intellect, indeed, corresponds in its essence to the monad; but science to the duad; for science is the science of a certain thing. Opinion subsists between science and ignorance; but sense is as the tetrad. For the touch which is common to all the senses being fourfold, all the senses energize according to contact.

The ninth tetractys is that from which the animal is composed, the soul and the body. For the parts of the soul, indeed, are the rational, the irascible, and the epithymetic, or that which desires external good; and the fourth is the body in which the soul subsists.

The tenth tetractys is of the seasons of the year, through which all things rise into existence, viz. the spring, the summer, the autumn, and the winter.

And the eleventh is of the ages of man, viz. of the infant, the lad, the man, and the old man.

Hence there are eleven tetractys. The first is that which subsists according to the composition of numbers. The second, according to the multiplication of numbers. The third subsists according to magnitude. The fourth is of the simple bodies. The fifth is of figures. The sixth is of things rising into existence through the vegetative life. The seventh is of communities. The eighth is the judicial power. The ninth is of the parts of the animal. The tenth is of the seasons of the year. And the eleventh is of the ages of man. All of them however are proportional to each other. For what the monad is in the first and second tetractys, that a point is in the third; fire in the fourth; a pyramid in the fifth; seed in the sixth; man in the seventh; intellect in the eighth; and so of the rest. Thus, for instance, the first tetractys is 1. 2. 3. 4. The second is the monad, a side, a square, and a cube. The third is a point, a line, a superficies, and a solid. The fourth is fire, air, water, earth. The fifth the pyramid, the octaedron, the icosaedron, and the cube. The sixth, seed, length, breadth and depth. The seventh, man, a house, a street, a city. The eighth, intellect, science, opinion, sense. The ninth, the rational, the irascible, and the epithymetic parts, and the body. The tenth, the spring, summer, autumn, winter. The eleventh, the infant, the lad, the man, and the old man.

The world also, which is composed from these tetractys, is perfect, being elegantly arranged in geometrical, harmonical, and arithmetical proportion; comprehending every power, all the nature of number, every magnitude, and every simple and composite body. But it is perfect, because all things are the parts of it, but it is not itself the part of any thing. Hence, the Pythagoreans are said to have first used the before-mentioned oath, and also the assertion that “all things are assimilated to number.”

P. 111. 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.

Because 6 consists of 1, 2 and 3, the two first of which are the principles of all number, and also because 2 and 3 are the first even and odd, which are the sources of all the species of numbers; the number 6 may be said to partake of every number. In what Iamblichus afterwards adds, I suppose he alludes to 6 being a perfect number and therefore equal to all its parts.

P. 134. Not to step above the beam of the balance.

This is the 14th Symbol in the Protreptics of Iamblichus, whose explanation of it is as follows: “This symbol exhorts us to the exercise of justice, to the honoring equality and moderation in an admirable degree, and to the knowledge of justice as the most perfect virtue, to which the other virtues give completion, and without which none of the rest are of any advantage. It also admonishes us, that it is proper to know this virtue not in a careless manner, but through theorems and scientific demonstrations. But this knowledge is the business of no other art and science than the Pythagoric philosophy alone, which in a transcendent degree honors disciplines before every thing else.”

The following extract also from my Theoretic Arithmetic, (p. 194.), will in a still greater degree elucidate this symbol. The information contained in it is derived from the anonymous author of a very valuable work entitled Te??????e?a ?????t???? Theologumena ArithmeticÆ, and which has lately been reprinted at Leipsic, “The Pythagoreans called the pentad providence and justice, because it equalizes things unequal, justice being a medium between excess and defect, just as 5 is the middle of all the numbers that are equally distant from it on both sides as far as to the decad, some of which it surpasses, and by others is surpassed, as may be seen in the following arrangement:

1. 4. 7.
2. 5. 8.
3. 6. 9.

“For here, as in the middle of the beam of a balance, 5 does not depart from the line of the equilibrium, while one scale is raised, and the other is depressed.

“In the following arrangement also, viz. 1, 2, 3, 4, 5, 6, 7, 8, 9, it will be found that the sum of the numbers which are posterior, is triple the sum of those that are prior to 5; for 6 + 7 + 8 + 9 = 30; but 1 + 2 + 3 + 4 = 10. If therefore the numbers on each side of 5 represent the beam of a balance, 5 being the tongue of it, when a weight depresses the beam, an obtuse angle is produced by the depressed part with the tongue, and an acute angle by the elevated part of the beam. Hence it is worse to do than to suffer an injury: and the authors of the injury verge downward as it were to the infernal regions; but the injured tend upward as it were to the Gods, imploring the divine assistance. Hence the meaning of the Pythagoric symbol is obvious, “Pass not above the beam of the balance.” Since however injustice pertains to inequality, in order to correct this, equalization is requisite, that the beam of the balance may remain on both sides without obliquity. But equalization is effected by addition and subtraction. Thus if 4 is added to 5, and 4 is also taken from 5, the number 9 will be produced on one side, and 1 on the other, each of which is equally distant from 5. Thus too, if 3 is added to 5, and is also subtracted from it, on the one side 8 will be produced, and on the other 2. If 2 is added to 5, and likewise taken from it, 7 and 3 will be produced. And by adding 1 to 5, and subtracting 3 from it, 6 and 4 will be the result; in all which instances, the numbers produced are equidistant from 5, and the sum of each couple is equal to 10.”

P. 161. Such as dig not fire with a sword.

This is the 9th Symbol in the Protreptics, and is thus explained by Iamblichus. “This symbol exhorts to prudence. For it excites in us an appropriate conception with respect to the propriety of not opposing sharp words to a man full of fire and wrath, nor contending with him. For frequently by words you will agitate and disturb an ignorant man, and will yourself suffer things dreadful and unpleasant.” Heraclitus also testifies to the truth of this symbol. For he says, “It is difficult to fight with anger: for whatever is necessary to be done redeems the soul.” And this he says truly. For many, by gratifying anger, have changed the condition of their soul, and have made death preferable to life. But by governing the tongue, and being quiet, friendship is produced from strife, the fire of anger being extinguished; and you yourself will not appear to be destitute of intellect.”

P. 200. But this follows from the whole being naturally prior to the part, and not the part to the whole.

For whole co-subverts, but is not co-subverted by part: since if whole is taken away, part also is taken away; but the contrary does not follow.

P. 231. Such therefore as hope the intellective and gnostic part of virtue, are denominated skilful and intelligent; but such as have the ethical and pre-elective part of it, are denominated useful and equitable.

The following account of the virtues is extracted from the Notes to my Translation of the PhÆdo of Plato: The first of the virtues are the physical, which are common to brutes, being mingled with the temperaments, and for the most part contrary to each other; or rather pertaining to the animal. Or it may be said that they are illuminations from reason, when not impeded by a certain bad temperament: or that they are the result of energies in a former life. Of these Plato speaks in the Politicus and the Laws. The ethical virtues, which are above these, are ingenerated by custom and a certain right opinion, and are the virtues of children when well educated. These virtues also are to be found in some brute animals. They likewise transcend the temperaments, and on this account are not contrary to each other. These virtues Plato delivers in the Laws. They pertain however at the same time both to reason and the irrational nature. In the third rank above these are the political virtues, which pertain to reason alone; for they are scientific. But they are the virtues of reason adorning the irrational part as its instrument; through prudence adorning the gnostic, through fortitude the irascible, and through temperance the epithymetic power, (or the power which is the source of desire;) but adorning all the parts of the irrational nature through justice. And of these virtues Plato speaks much in the Republic. These virtues too follow each other. Above these are the cathartic virtues, which pertain to reason alone, withdrawing from other things to itself, throwing aside the instruments of sense as vain, repressing also the energies through these instruments, and liberating the soul from the bonds of generation. Plato particularly unfolds these virtues in the PhÆdo. Prior to these however are the theoretic virtues, which pertain to the soul, introducing itself to natures superior to itself, not only gnostically, as some one may be induced to think from the name, but also orectically: for it hastens to become, as it were, intellect instead of soul; and intellect possesses both desire and knowledge. These virtues are the converse of the political: for as the latter energize about things subordinate according to reason, so the former about things more excellent according to intellect. These virtues Plato delivers in the TheÆtetus.

According to Plotinus, there is also another gradation of the virtues besides these, viz, the paradigmatic. For, as our eye, when it is first illuminated by the solar light, is different from that which illuminates, as being illuminated, but afterwards is in a certain respect united and conjoined with it, and becomes, as it were, solar-form; so also our soul at first indeed is illuminated by intellect, and energizes according to the theoretic virtues, but afterwards becomes, as it were, that which is illuminated, and energizes uniformly according to the paradigmatic virtues. And it is the business indeed of philosophy to make us intellect; but of theurgy to unite us to intelligibles, so that we may energize paradigmatically. And as when possessing the physical virtues, we know mundane bodies (for the subjects to virtues of this kind are bodies); so from possessing the ethical virtues, we know the fate of the Universe, because fate is conversant with irrational lives. For the rational soul is not under fate; and the ethical virtues are irrational, because they pertain to the irrational part. According to the political virtues we know mundane affairs, and according to the cathartic supermundane; but as possessing the theoretic we know intellectual, and from the paradigmatic intelligible natures. Temperance also pertains to the ethical virtues; justice to the political, on account of compacts; fortitude to the cathartic, through not verging to matter; and prudence to the theoretic. Observe too, that Plato in the PhÆdo calls the physical virtues servile, because they may subsist in servile souls; but he calls the ethical s?????af?a? adumbrations, because their possessors only know that the energies of such virtues are right, but do not know why they are so. It is well observed too here, by Olympiodorus, that Plato calls the cathartic and theoretic virtues, those which are in reality true virtues. He also separates them in another way, viz. that the political are not telestic, i.e. do not pertain to mystic ceremonies, but that the cathartic and theoretic are telestic. Hence, Olympiodorus adds, the cathartic virtues are denominated from the purification which is used in the mysteries; but the theoretic from perceiving things divine. On this account he accords with the Orphic verses, that

For initiation is the divinely-inspired energy of the virtues. Olympiodorus also further observes, that by the thyrsus-bearers, Plato means those that energize according to the political virtues, but by the Bacchuses those that exercise the cathartic virtues. For we are bound in matter as Titans, through the great partibility of our nature; but we rise from the dark mire as Bacchuses. Hence we become more prophetic at the time of death: and Bacchus is the inspective guardian of death, because he is likewise of every thing pertaining to the Bacchic sacred rites.

All the virtues likewise exhibit their proper characters, these being every where common, but subsisting appropriately in each. For the characteristic property of fortitude is the not declining to things subordinate; of temperance, a conversion from an inferior nature; of justice, a proper energy, and which is adapted to being; and of prudence, the election and selection of things good and evil. Olympiodorus farther observes, that all the virtues are in the Gods. For many Gods, says he, are adorned with their appellations; and all goodness originates from the Gods. Likewise, prior, to things which sometimes participate the virtues, as is our case, it is necessary there should be natures which always participate them. In what order, therefore, do the virtues appear? Shall we say in the psychical? For virtue is the perfection of the soul; and election and pre-election are the energies and projections of the soul. Hence the ChaldÆan oracles conjoin fontal virtue with fontal soul, or in other words, with soul subsisting according to cause. But may it not also be said, that the virtues naturally wish to give an orderly arrangement to that which is disordered? If this be admitted, they will originate from the demiurgic order. How then will they be cathartic there? May we not say, Olympiodorus adds, that through the cathartic virtues considered according to their causal subsistence in Jupiter the demiurgus, he is enabled to abide in his accustomed mode, as Plato says in the TimÆus? And farther still, according to ancient theologists, he ascends to the tower of Saturn, who is a pure intellect.

As this distribution of the virtues, however, is at present no less novel than important, the following discussion of them from the ?f??a? p??? ta ???ta, or Auxiliaries to Intelligibles, of Porphyry, is added for the sake of the genuinely philosophic reader:

“There is one kind of virtues pertaining to the political character, and another to the man who tends to contemplation, and on this account is called theoretic, and is now a beholder. And there are also other virtues pertaining to intellect, so far as it is intellect, and separate from soul. The virtues indeed of the political character, and which consist in the moderation of the passions, are characterised by following and being obedient to the reasoning about that which is becoming in actions. Hence, looking to an innoxious converse with neighbours, they are denominated, from the aggregation of fellowship, political. And prudence indeed subsists about the reasoning part; fortitude about the irascible part; temperance, in the consent and symphony of the epithymetic with the reasoning part; and justice in each of these performing its proper employment with respect to governing and being governed. But the virtues of him who proceeds to the contemplative life, consist in a departure from terrestrial concerns. Hence also, they are called purifications, being surveyed in the refraining from corporeal actions, and avoiding sympathies with the body. For these are the virtues of the soul elevating itself to true being. The political virtues, therefore, adorn the mortal man, and are the forerunners of purifications. For it is necessary that he who is adorned by these, should abstain from doing any thing precedaneously in conjunction with body. Hence in purifications, not to opine with body, but to energize alone, gives subsistence to prudence; which derives its perfection through energizing intellectually with purity. But not to be similarly passive with the body, constitutes temperance. Not to fear a departure from body as into something void, and nonentity, gives subsistence to fortitude. But when reason and intellect are the leaders, and there is no resistance [from the irrational part,] justice is produced. The disposition therefore, according to the political virtues, is surveyed in the moderation of the passions; having for its end to live as man conformable to nature. But the disposition according to the theoretic virtues, is beheld in apathy;[108] the end of which is a similitude to God.

“Since, however, of purification one kind consists in purifying, but another pertains to those that are purified, the cathartic virtues are surveyed according to both these significations of purification; for they purify the soul, and are present with purification. For the end of purification is to become pure. But since purification, and the being purified, are an ablation of every thing foreign, the good resulting from them will be different from that which purifies; so that if that which is purified was good prior to the impurity with which it is defiled, purification is sufficient. That, however, which remains after purification, is good, and not purification. The nature of the soul also was not good, but is that which is able to partake of good, and is boniform. For if this were not the case, it would not have become situated in evil. The good, therefore, of the soul consists in being united to its generator; but its evil, in an association with things subordinate to itself. Its evil also is two-fold; the one arising from an association with terrestrial natures; but the other from doing this with an excess of the passions. Hence all the political virtues, which liberate the soul from one evil, may be denominated virtues, and are honorable. But the cathartic are more honorable, and liberate it from evil, so far as it is soul. It is necessary, therefore, that the soul when purified should associate with its generator. Hence the virtue of it after its conversion consists in a scientific knowledge of [true] being; but this will not be the case unless conversion, precedes.

“There is therefore another genus of virtues after the cathartic and political, and which are the virtues of the soul energizing intellectually. And here, indeed, wisdom and prudence consist in the contemplation of those things which intellect possesses. But justice consists in performing what is appropriate in a conformity to, and energizing according to intellect. Temperance is an inward conversion of the soul to intellect. And fortitude is apathy; according to a similitude of that to which the soul looks, and which is naturally impassive. These virtues also, in the same manner as the others, alternately follow each other.

“The fourth species of the virtues, is that of the paradigms subsisting in intellect; which are more excellent than the psychical virtues, and exist as the paradigms of these; the virtues of the soul being the similitudes of them. And intellect indeed is that in which all things subsist at once as paradigms. Here, therefore, prudence is science; but intellect that knows [all things] is wisdom. Temperance is that which is converted to itself. The proper work of intellect, is the performance of its appropriate duty, [and this is justice[109]]. But fortitude is sameness, and the abiding with purity in itself, through an abundance of power. There are therefore four genera of virtues; of which, indeed, some pertain to intellect, concur with the essence of it, and are paradigmatic. Others pertain to soul now looking to intellect, and being filled from it. Others belong to the soul of man, purifying itself, and becoming purified from the body, and the irrational passions. And others are the virtues of the soul of man, adorning the man, through giving measure and bound to the irrational nature, and producing moderation in the passions. And he, indeed, who has the greater virtues has also necessarily the less; but the contrary is not true, that he who has the less has also the greater virtues. Nor will he who possesses the greater, energize precedaneously according to the less, but only so far as the necessities of the mortal nature require. The scope also of the virtues, is, as we have said, generically different in the different virtues. For the scope of the political virtues, is to give measure to the passions in their practical energies according to nature. But the scope of the cathartic virtues, is entirely to obliterate the remembrance of the passions. And the scope of the rest subsists analogously to what has been before said. Hence, he who energizes according to the practical virtues, is a worthy man: but he who energizes according to the cathartic virtues, is a dÆmoniacal man, or is also a good dÆmon. He who energizes according to the intellectual virtues alone, is a God. But he who energizes according to the paradigmatic virtues, is the father of the Gods. We, therefore, ought especially to pay attention to the cathartic virtues, since we may obtain these in the present life. But through these, the ascent is to the more honorable virtues. Hence it is requisite to survey to what degree purification may be extended. For it is a separation from body, and from the passive motion of the irrational part. But how this may so effected, and to what extent, must now be said.

“In the first place, indeed, it is necessary that he who intends to acquire this purification, should, as the foundation and basis of it, know himself to be a soul bound in a foreign thing, and in a different essence. In the second place, as that which is raised from this foundation, he should collect himself from the body, and as it different places, so as to be disposed in a manner perfectly impassive with respect to the body. For he who energizes uninterruptedly according to sense, though he may not do this with an adhering affection, and the enjoyment resulting from pleasure, yet at the same time his attention is dissipated about the body, in consequence of becoming through sense[110] in contact with it. But we are addicted to the pleasures or pains of sensibles, in conjunction with a promptitude, and converging sympathy; from which disposition it is requisite to be purified. This, however, will be effected by admitting necessary pleasures, and the sensations of them, merely as remedies, or as a liberation from pain, in order that [the rational part] may not be impeded [in its energies.] Pain also must be taken away. But if this is not possible, it must be mildly diminished. And it will be diminished, if the soul is not co-passive with it. Anger, likewise, must as much as possible be taken away; and must by no means be premeditated. But if it cannot be entirely removed, deliberate choice must not be mingled with it, but the unpremeditated motion must be the impulse of the irrational part. That however which is unpremeditated is imbecile and small. All fear, likewise, must be expelled. For he who acquires this purification, will fear nothing. Here, however, if it should take place, it will be unpremeditated. Anger therefore and fear must be used for the purpose of admonition. But the desire of every thing base must be exterminated. Such a one also, so far as he is a cathartic philosopher, will not desire meats and drinks. Neither must there be the unpremeditated in natural venereal connexions; but if this should take place, it must only be as far as to that precipitate imagination which energizes in sleep. In short, the intellectual soul itself of the purified man, must be liberated from all these [corporeal propensities.] He must likewise endeavour that what is moved to the irrational nature of corporeal passions, may be moved without sympathy, and without animadversion; so that the motions themselves may be immediately dissolved, through their vicinity to the reasoning power. This, however, will not take place while the purification is proceeding to its perfection; but will happen to those in whom reason rules without opposition. Hence in these, the inferior part will so venerate reason, that it will be indignant if it is at all moved, in consequence of not being quiet when its master is present, and will reprove itself for its imbecility. These, however, are yet only moderations of the passions, but at length terminate in apathy, for when co-passivity is entirely exterminated, then apathy is present with him who is purified from it. For passion becomes moved, when reason imparts excitation, through verging [to the irrational nature.]”

P. 279. The theorems of philosophy are to be enjoyed, as much as possible, as if they were ambrosia and nectar, &c. &c.

This Sentence in the original of Arcerius is as follows: t?? ?ata f???s?f?a? ?e???at?? ap??a?ste??, ef’ ?s?? ????, ?a?ape? a??s?a? ?a? ?e?ta???· a???at?? te ?a? t? ap’ a?t?? ?d? ?a? t? ?e??? t? e?a??????? d??ata? te p??e??, ?a? e? ? aÏd????, aÏd??? ?e ep?st???a?.

In the edition of the Protreptics by Kiessling, which I did not see, till the greater part of this work was printed, s?f?a? is substituted for f???s?f?a?, but in my opinion very erroneously; and this German editor, from not perceiving the necessity of reading a???at?? te ?a? t? ap’ a?t?? ?d? ?a? ?e???, t? e?a???????, ?. ?. instead of retaining the reading of Arcerius, has made nonsense of this part of the Sentence. For his version of it is: “Nam et sincera est eorum dulcedo, et divinam naturam, animum magnum efficere possunt.”