Additional Notes
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 primary99 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 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,
“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 sesquioctave105 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:
| Ut, | Hypate, | i. e. | Principalis. |
| Re, | Parhypate, | — | Postprincipalis. |
| Mi, | Lychanos, | — | Index. |
| Fa, | Mese, | — | Media. |
| Sol, | Paramese, | — | Postmedia. |
| Re, | Trite, | — | Tertia. |
| Mi, | Paranete, | — | Antepenultima. |
| Fa, | Nete, | — | Ultima, vel suprema. |
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 terminated107 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 Θεολογουμενα Αριθμητικης 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 σκιογραφιαι 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
The soul that uninitiated dies,
Plung’d in the blackest mire in Hades lies.
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 Αφορμαι προς τα νοητα, 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 justice109]. 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 sense110 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: των κατα φιλοσοφιαν θεωρηματων απολαυστεον, εφ’ οσον οιον, καθαπερ αμβροσιας και νεκταρος· ακηρατον τε γαρ το απ’ αυτων ηδυ και το θειον το μεγαλοψυχον δυναται τε ποιειν, και ει μη αïδιους, αïδιων γε επιστημονας.
In the edition of the Protreptics by Kiessling, which I did not see, till the greater part of this work was printed, σοφιαν is substituted for φιλοσοφιαν, but in my opinion very erroneously; and this German editor, from not perceiving the necessity of reading ακηρατον τε γαρ το απ’ αυτων ηδυ και θειον, το μεγαλοψυχον, κ. λ. 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.”
Footnotes
1Οιδα μεν ουν και Πλατωνα τον μεγαν, και μετα τουτον ανδρα τοις χρονοις μεν, ου τῃ μην φυσει, καταδεεστερον, τον Χαλκιδεα φημι τον Ιαμβλιχον, κ. λ. Julian. Orat. IV.
Thus too the celebrated Bullialdus, in his Notes on Theo of Smyrna, speaks of Iamblichus as a man of a most acute genius.
2There is a Greek and Latin edition of this admirable work by Gale, under the title of Iamblichus De Mysteriis.
3Αλλα και το της λεξεως κομματικον, και αφοριστικον, και το των εννοιων πραγματικον, και γλαφυρον, και ενθουν, κ. λ. See the Testimonies prefixed by Gale to his edition of the above-mentioned work.
4This Sopater succeeded Plotinus in his philosophical school.
5The exact time of Iamblichus’ death is unknown. It is however certain that it was during the reign of Constantine; and according to the accurate Fabricius, prior to the year of Christ 333. Vid. Biblioth. Græc. Tom. IV. p. 283.
6This Sextus is probably the same that Seneca so greatly extols, and from whom he derives many of those admirable sentences with which his works abound. Vid. Senecæ Epistolas, 59, 64, 98, et lib. 2 de Irâ, c. 36, et lib. 3. c. 36.
7All these were published in one vol. 12mo. by Mr. Bridgman, under the title of Translations from the Greek, in the year 1804, and well deserve to be perused by the liberal reader.
8i. e. Having black leaves.
9i. e. It must not be admitted, that Apollo was actually connected with Pythaïs; for this would be absurd in the extreme; but the assertion of Epimenides, Eudoxus, and Xenocrates must be considered as one of those mythological narrations in which heroes are said to have Gods for their fathers, or Goddesses for their mothers, and the true meaning of it is as follows: According to the ancient theology, between those perpetual attendants of a divine nature called essential heroes, who are impassive and pure, and the bulk of human souls who descend to earth with passivity and impurity, it is necessary there should be an order of human souls who descend with impassivity and purity. For as there is no vacuum either in incorporeal or corporeal natures, it is necessary that the last link of a superior order, should coalesce with the summit of one proximately inferior. These souls were called by the ancients, terrestrial heroes, on account of their high degree of proximity and alliance to such as are essentially heroes. Hercules, Theseus, Pythagoras, Plato, &c. were souls of this kind, who descended into mortality both to benefit other souls, and in compliance with that necessity by which all natures inferior to the perpetual attendants of the Gods are at times obliged to descend.
But as, according to the arcana of ancient theology, every God beginning from on high produces his proper series as far as to the last of things, and this series comprehends many essences different from each other, such as Dæmoniacal, Heroical, Nymphical, and the like; the lowest powers of these orders, have a great communion and physical sympathy with the human race, and contribute to the perfection of all their natural operations, and particularly to their procreations. “Hence” (says Proclus in MSS. Schol. in Crat.) “it often appears, that heroes are generated from the mixture of these powers with mankind; for those that possess a certain prerogative above human nature, are properly denominated heroes.” He adds: “Not only a dæmoniacal genus of this kind sympathizes physically with men, but other kinds sympathize with other natures, as Nymphs with trees, others with fountains, and others with stags or serpents.”
Olympiodorus, in his life of Plato, observes of that philosopher, “That an Apolloniacal spectre is said to have had connexion with Perictione his mother, and that appearing in the night to his father Aristo, it commanded him not to sleep with Perictione during the time of her pregnancy; which mandate Aristo obeyed.” The like account of the divine origin of Plato, is also given by Apuleius, Plutarch, and Hesychius.
10i. e. The priests of Jupiter.
11From what has been said in the note, p. 4, respecting the divine origin of Pythagoras, it follows that he was a terrestrial hero belonging to the series of Apollo. Thus too the Esculapius who once lived on the earth, and was the inventor of medicine, proceeded, according to the ancient mythology, from the God Esculapius, who subsists in Apollo, just as the hero Bacchus proceeded from the Bacchus who subsists in Jupiter. Hence the Emperor Julian (apud Cyril.) says of Esculapius: “I had almost forgotten the greatest of the gifts of Jupiter and the Sun, but I have very properly reserved it to the last. For it is not peculiar to us only, but is common also, I think, to our kindred the Greeks. For Jupiter, in intelligibles, generated from himself Esculapius; but he was unfolded into light on the earth, through the prolific light of the sun. He therefore, proceeding from heaven to the earth, appeared uniformly in a human shape about Epidaurus. But thence becoming multiplied in his progressions, he extended his saving right hand to all the earth. He came to Pergamus, to Ionia, to Tarentum, and afterwards to Rome. Thence he went to the island Co, afterwards to Ægas, and at length to wherever there is land and sea. Nor did we individually, but collectively, experience his beneficence. And at one and the same time, he corrected souls that were wandering in error, and bodies that were infirm.”
12Those Gods, according to the Orphic theology, that contain in themselves the first principle of stability, sameness, and being, and who also were the suppliers of conversion to all things, are of a male characteristic; but those that are the causes of all-various progressions, separations, and measures of life, are of a feminine peculiarity.
13This inventor of names was called by the Egyptians Theuth, as we are informed by Plato in the Philebus and Phædrus; in the latter of which dialogues, Socrates says: “I have heard, that about Naucratis in Egypt, there was one of the ancient Gods of the Egyptians, to whom a bird was sacred, which they call Ibis; but the name of the dæmon himself was Theuth. According to tradition, this God first discovered number and the art of reckoning, geometry and astronomy, the games of chess and hazard, and likewise letters.” On this passage I observe as follows, in Vol. 3. of my translation of Plato: The genus of disciplines belonging to Mercury, contains gymnastic, music, arithmetic, geometry, astronomy, and the art of speaking and writing. This God, as he is the source of invention, is called the son of Maia; because investigation, which is implied by Maia, produces invention: and as unfolding the will of Jupiter, who is an intellectual God, he is the cause of mathesis or discipline. He first subsists in Jupiter, the artificer of the world; next among the supermundane Gods; in the third place, among the liberated Gods; fourthly, in the planet Mercury; fifthly, in the Mercurial order of dæmons; sixthly, in human souls, who are the attendants of this God; and in the seventh degree, his properties subsist in certain animals, such as the ibis, the ape, and sagacious dogs. The narration of Socrates in this place, is both allegorical and anagogic or reductory. Naucratis is a region of Egypt eminently subject to the influence of Mercury, though the whole of Egypt is allotted to this divinity. Likewise, in this city a man once florished full of the Mercurial power, because his soul formerly existed in the heavens of the Mercurial order. But he was first called Theuth, that is, Mercury, and a God, because his soul subsisted according to the perfect similitude of this divinity. But afterwards a dæmon, because from the God Mercury, through a Mercurial dæmon, gifts of this kind are transmitted to a Mercurial soul.
14Iamblichus derived this very beautiful passage from Heraclides Ponticus, as is evident from Cicero, Tusc. Quæst. lib. v. 3. who relates the same thing of Pythagoras, from the aforesaid author.
15i. e. With intelligibles properly so called.
16Iliad, lib. 17. The translation by Pope.
17“The Pythagoreans,” says Simplicius, in his Commentary on the 2d book of Aristotle’s treatise On the Heavens, said, “that an harmonic sound was produced from the motion of the celestial bodies, and they scientifically collected this from the analogy of their intervals; since not only the ratios of the sun and moon, of Venus and Mercury, but also of the other stars, were discovered by them.” Simplicius adds, “Perhaps the objection of Aristotle to this assertion of the Pythagoreans, may be solved according to the philosophy of those men, as follows:
“All things are not commensurate with each other, nor is every thing sensible to every thing, even in the sublunary region. This is evident from dogs who scent animals at a great distance, and which are not smelt by men. How much more, therefore, in things which are separated by so great an interval as those which are incorruptible from the corruptible, and celestial from terrestrial natures, is it true to say, that the sound of divine bodies is not audible by terrestrial ears? But if any one like Pythagoras, who is reported to have heard this harmony, should have his terrestrial body exempt from him, and his luminous and celestial vehicle17a and the senses which it contains purified, either through a good allotment, or through probity of life, or through a perfection arising from sacred operations, such a one will perceive things invisible to others, and will hear things inaudible by others. With respect to divine and immaterial bodies, however, if any sound is produced by them, it is neither percussive nor destructive, but it excites the powers and energies of sublunary sounds, and perfects the sense which is co-ordinate with them. It has also a certain analogy to the sound which concurs with the motion of terrestrial bodies. But the sound which is with us in consequence of the sonorific nature of the air, is a certain energy of the motion of their impassive sound. If, then, air is not passive there, it is evident that neither will the sound which is there be passive. Pythagoras, however, seems to have said that he heard the celestial harmony, as understanding the harmonic proportions in numbers, of the heavenly bodies, and that which is audible in them. Some one, however, may very properly doubt why the stars are seen by our visive sense, but the sound of them is not heard by our ears? To this we reply that neither do we see the stars themselves; for we do not see their magnitudes, or their figures, or their surpassing beauty. Neither do we see the motion through which the sound is produced; but we see as it were such an illumination of them, as that of the light of the sun about the earth, the sun himself not being seen by us. Perhaps too, neither will it be wonderful, that the visive sense, as being more immaterial, subsisting rather according to energy than according to passion, and very much transcending the other senses, should be thought worthy to receive the splendor and illumination of the celestial bodies, but that the other senses should not be adapted for this purpose. Of these, however, and such like particulars, if any one can assign more probable causes, let him be considered as a friend, and not as an enemy.”
[17a]The soul has three vehicles, one etherial, another aerial, and the third this terrestrial body. The first, which is luminous and celestial, is connate with the essence of the soul, and in which alone it resides in a state of bliss in the stars. In the second, it suffers the punishment of its sins after death. And from the third it becomes an inhabitant of earth.
18i. e. Of the discursive energy of reason, or that part of the soul that reasons scientifically, deriving the principles of its reasoning from intellect.
19Kuster, one of the editors of this Life of Pythagoras, not perceiving that these auditions are both questions and answers, has made them to be questions only, and in consequence of this was completely at a loss to conceive the meaning of οπερ εστιν η αρμονια, εν ῃ αι Σειρηνες. Hence, he thinks it should be, τι εστιν η αρμονια ῃ ηδον αι Σειρηνες; but is not satisfied with this reading after all. Something I have no doubt is wanting; but the sense of the passage is, I conceive, that which is given in the above translation.
20“Pythagoras,” (says Proclus in MSS. Schol. in Cratylum,) “being asked what was the wisest of things, said it was number; and being asked what was the next in wisdom, said, he who gave names to things. But by number, he obscurely signified the intelligible order, which comprehends the multitude of intellectual forms: for there that which is the first, and properly number, subsists after the superessential one.20a This likewise supplies the measures of essence to all beings, in which also true wisdom, and knowledge which is of itself, and which is converted to and perfects itself, subsist. And as there the intelligible, intellect, and intelligence, are the same, so there also number and wisdom are the same. But by the founder of names, he obscurely signified the soul, which indeed subsists from intellect, and is not things themselves like the first intellect, but possesses the images and essential transitive reasons of them as statues of beings. Being, therefore, is imparted to all things from intellect, which knows itself and is replete with wisdom; but that they are denominated is from soul, which imitates intellect. Pythagoras therefore said, that it was not the business of any casual person to fabricate names, but of one looking to intellect and the nature of things.”
[20a]i. e. Number according to cause, which subsists at the extremity of the intelligible order. For number according to hyparxis or essence, subsists at the summit of the order which is intelligible and at the same time intellectual. See the 3d book of my translation of Proclus on the Theology of Plato.
21The words περι πυθαγορειων are omitted in the original, but from the Protrept. of Iamblichus evidently ought to be inserted.
22The same thing is said by the Pythagoreans to have befallen the person who first divulged the theory of incommensurable quantities. See the first scholium on the 10th book of Euclid’s Elements, in Commandine’s edition, fol. 1572.
23Iamblichus, in this list of Pythagoreans, must not be supposed to enumerate those only who were contemporary with Pythagoras: since, if he did, he contradicts what he says of Philolaus in Chap. 31. viz. “that he was many ages posterior to Pythagoras;” but those in general who came from the school of Pythagoras, and were his most celebrated disciples.
24From this passage it is evident that Iamblichus had many sources of information, which are unknown to modern critics; and this circumstance alone ought to check their pedagogical impertinence.
25For αυτα here I read, conformably to the version of Obrechtus, αλλα.
26For δηγμους here, I read οδυρμους; as I do not see what morsus has to do with this place. Obrechtus has in his version “pectorisque morsus;” but I have no doubt lamentations is the proper word, which aptly associates with despondency.
27“Well-instituted polities,” (says Proclus in MS. Comment. in Alcibiad. prior.) “are averse to the art of playing on wind-instruments; and therefore neither does Plato admit it. The cause of this is the variety of this instrument, the pipe, which shows that the art which uses it should be avoided. For instruments called Panarmonia, and those consisting of many strings, are imitations of pipes. For every hole of the pipe emits, as they say, three sounds at least; but if the cavity above the holes be opened, then each hole will emit more than three sounds.”
28Odyss. lib. 4.
29Iamblichus derived what he has said in this chapter about music, from Nicomachus.
30The first part of this sentence in the original is ξενου τινος εκβεβληκοτος εν Ασκληπιειῳ Ζωνην χρυσιον εχουσαν, and in translating it I have followed the version of Obrechtus, because it appeared to me to convey the meaning of Iamblichus, though the translation is certainly forced, and not such as the natural construction of the words will admit. The translation of Arcerius is, “Cum hospes quidam in æde Æsculapii fœminam zonam auream habentem ejecisset;” and this is perfectly conformable to the natural construction of the words, but then it is void of sense.
31This history is copiously narrated in chap. 33.
33These lines are as the numbers 4, 3, 2. For 4 to 3 is sesquitertian, 3 to 2 is sesquialter, and 2 is an arithmetical medium between 4 and 3.
34For an explanation of this assertion of Plato in the Republic, see my Theoretic Arithmetic.
35“The Pythagoreans,” (says Syrianus in Aristot. Metaphys. lib. 13.) “received 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.” Hence that proverb was peculiar to the Pythagoreans, that all things are assimilated to number. Pythagoras, therefore, in the Sacred Discourse, clearly says, that “number is the ruler of forms and ideas, and is the cause of Gods and dæmons.” He also supposes, that “to the most ancient and artificially ruling deity, number is the canon, the artificial reason, the intellect also, and the most undeviating balance of the composition and generation of all things.” αυτος μεν Πυθαγορας, εν τῳ ιερῳ λογῳ, διαρρηδην μορφων και ιδεων κραντορα τον αριθμον ελεγεν ειναι, και θεων και δαιμονων αιτιον· και τῳ πρεσβυτατῳ και κρατιστευοντι τεχνιτῃ θεῳ κανονα, και λογον τεχνικον, νουν τε και σταθμαν ακλινεσταταν τον αριθμον υπεικε συστασιος και γενεσεως των παντων. Syrianus adds, “But Philolaus declared that number is the governing and self-begotten bond of the eternal permanency of mundane natures.” Φιλολαυς δε, της των κοσμικων αιωνιας διαμονης την κρατιστευουσαν και αυτογενη συοχην ειναι απεφῃνατο τον αριθμον. “And Hippasus, and all those who were destined to a quinquennial silence, called number the judicial instrument of the maker of the universe, and the first paradigm of mundane fabrication.” οι δε περι Ιππασον ακουσματικοι ειπον κριτικον κοσμουργου θεου οργανον, και παραδειγμα πρωτον κοσμοποιϊας. “But how is it possible they could have spoken thus sublimely of number, unless they had considered it as possessing an essence separate from sensible, and a transcendency fabricative, and at the same time paradigmatic?”
36i. e. To spheres; Iamblichus indicating by this, that Pythagoras as well as Orpheus considered a spherical figure as the most appropriate image of divinity. For the universe is spherical; and, as Iamblichus afterwards observes, the Gods have a nature and morphe similar to the universe; morphe, as we learn from Simplicius, pertaining to the color, figure, and magnitude of superficies. Keissling, having no conception of this meaning, and supposing the whole passage to be corrupt, has made nonsense of it by his alterations. For according to his version, Pythagoras, after the manner of Orpheus, worshipped the Gods not bound to a human form, but to divine numbers. For instead of ιδρυμασι he reads αριθμοις. But divine numbers both according to Orpheus and Pythagoras are the Gods themselves.
37i. e. Futurity is long; Pythagoras signifying by this, that those who do not take an oath religiously, will be punished in some future period, if they are not at present.
38i. e. From the time in which the Gods are fabulously said to have reigned in Egypt.
39I wonder that the learned Obrechtus should translate ηβηδον, cum omni juventute sua. Had his translation, which is on the whole very excellent, been reviewed by English or Scotch critics, they would have immediately said from this circumstance, that he did not understand Greek.
40Iamblichus here alludes to a right-angled triangle, and the Pythagoric theorem of 47. 1 of Euclid. For the square described on the longest side is equal to the two squares described on the two other sides. The longest side therefore is said by geometricians to be equal in power to the powers of the other sides. This however Kiessling not understanding, says, “that power is the space contained between the concurring lines of figures, and is the area of the triangle.” “Δυναμις idem est, quod εμβαδον, spatium, quod infra concurrentes lineas figurarum continetur, area trigoni.” But Kiessling, though a good verbalist, is a bad geometrician, and no philosopher.
41In the original δεκατον the tenth month; but as it very seldom happens that a woman is in a state of pregnancy more than nine months, it appears to me that for δεκατον we should read εκτον the sixth month, as in the above translation.
42Obrechtus by translating περι δε δοξης in this place, “De fama et gloria,” has evidently mistaken the meaning of Iamblichus.
43The wise and magnanimous Pythagoreans, Platonists, Peripatetics and Stoics, among the ancients, looked to virtue as its own reward, and performed what is right, because it is right to do so. And though they firmly believed in the immortality of the soul, their conduct was not at all influenced by the hope of future reward. This great truth indeed, that virtue brings with it its own recompense, is almost at present obsolete; and it is no unusual thing to hear a man, when afflicted, exclaiming with Methodistical cant,
“The many troubles that I meet,
In getting to a Mercy-seat!”
44These energies are called beneficent, because they are of a purifying character. Hence Plato in the Timæus says, that a deluge is the consequence of the Gods purifying the earth by water.
45Iamblichus a little before informs us, that Pythagoras suspected that Phalaris intended to put him to death, but at the same time knew that he was not destined to die by Phalaris. This being the case therefore, Pythagoras has no claim to fortitude in this instance, in being free from the fear of death. But he has great claim to it, when it is considered that he was in the power of a tyrant who might have caused him to suffer tortures worse than death.
46i. e. Humble (ταπεινης ουσης.) With the Pythagoreans, therefore, humility was no virtue, though in modern times it is considered to be the greatest of the virtues. With Aristotle likewise it is no virtue; for in his Nicomachean Ethics he says, “that all humble men are flatterers, and all flatterers are humble.”
47See the Cave of Plato, in the 7th book of his Republic.
48The original is, Μητροδωρος τε ο Θυρσου του πατρος Επιχαρμου, which Obrechtus erroneously translates, “Metrodorus Epicharmi filius Thyrsi nepos.”
49This observation applies also to those of the present day, who, from a profound ignorance of human nature, attempt to enlighten by education the lowest class of mankind. For this, as I have elsewhere observed, is an attempt to break the golden chain of beings, to disorganise society, and to render the vulgar dissatisfied with the servile situations in which God and nature intended them to be placed. See p. 73. of the introduction to my translation of Select Works of Plotinus.
50This also is asserted, as I have before observed, in the Scholia on the 10th book of Commandine’s edition of Euclid’s Elements, p. 122.
51Obrechtus has omitted to translate the words ηδη πρεσβυτην οντα, “being now an elderly man.”
52In the original ακρατος, which Obrechtus very erroneously translates impotens.
53i. e. To the Pythagoreans.
54The whole of this paragraph, the greater part of which is a repetition of what has been said elsewhere, does not certainly belong to this place.
55In the original, και την γην αναδαστον εποιησαν, which Obrechtus erroneously translates, “et agrorum divisionem introduxerunt.”
56The words within the brackets are from a Latin Manuscript, which was in the possession of Fabricius.
57In the original, ουδεν γαρ αυταρκες, ο τουτων των μοριων ποιει το ολον. This Canter erroneously translates, “Quandoquidem horum nulla pars totum queat constituere.” And Gale has noticed the error.
58Gale says in his notes, that after οφθαλμων he adds φυσιος, but he should evidently have added αρετα, as in the above translation.
59In the original συν τᾳ οξυδορκιᾳ, which Canter very defectively translates, videndi facultate.
60For ου μετριαν here, I read ασυμμετριαν.
61i. e. So far as he is considered as energizing in conjunction with the body; but so far as he has an energy independent of the body, viz. so far as he is a rational soul, the body is not to be considered as a part of his essence. And the energy of the rational soul by itself alone, without any assistance from the corporeal organs, constitutes the true man, into the definition of which body does not enter.
62Canter, in his version of these Pythagoric fragments, uniformly translates ευτυχια felicitas, contrary to the obvious meaning of the word, as is evident in this, and many other passages. It is also directly contrary to what Aristotle says in cap. 13. lib. 7. of his Nicomachean Ethics: δια δε το προσδεισθαι της τυχης, δοκει τισι ταυτον ειναι η ευτυχια τῃ ευδαιμονιᾳ, ουκ ουσα· επει και αυτη υπερβαλλουσα, εμποδιος εστι. i. e. “Because felicity requires fortune, it appears to some persons that prosperity is the same with felicity. This however is not the case; since prosperity, when it is excessive, is an impediment to felicity.” But Canter did not, I believe, pretend to have any knowledge of philosophy: and Gale, who did, has not corrected him in this and many other places in which he has erred through the want of this knowledge. Gale however, though verbally learned, was but a garrulous smatterer in philosophy, as is evident from his notes on Iamblichus de Mysteriis.
63For επιπρεπειαν here, I read απρεπειαν.
64In the original, ωστε ουδεποκα δει θαυμαινεν, ει παντ’ αντεστραμμενως ενιοκα κρινεται, τας αληθινας διαθεσιος μεταπιπτοισας, which Canter erroneously translates as follows: “Quocirca mirandum non est, si cuncta nonnunquam, verâ affectione mutatâ, aliter eveniunt.” Nor is the error noticed by Gale.
65i. e. In the etherial vehicle of the soul, which when the soul energizes intellectually is spherical, and is moved circularly. This vehicle also is αυγοειδης, or luciform, throughout diaphanous, and of a star-like nature. Hence Marcus Antoninus beautifully observes: σφαιρα ψυχης αυτοειδης, (lege αυγοειδης) οταν μητε εκτεινηται επι τι, μητε εσω συντρεχῃ μητε συνιζανῃ, αλλα φωτι λαμπηται, ῳ την αληθειαν ορᾳ την παντων, και την εν αυτῃ. Lib. II. i. e. “The sphere of the soul is then luciform, when the soul is neither extended to any thing [external] nor inwardly concurs with it, nor is depressed by it, but is illuminated with a light by which she sees the truth of all things, and the truth that is in herself.”
66M. Meibomius observes, that Canter did not see that λογιστικω should be written in this place for αλογω. Canter however was right in retaining αλογω. For the dianoetic is the same with the logistic part of the soul; and it is evident that a part of the soul different from the dianoetic is here intended to be signified. Besides, as Aristotle shows in his Nicomachean Ethics, when the irrational becomes obedient to the rational part of the soul, the former then prohibits and vanquishes base appetites in conjunction with the latter.
67viz. Such as have the theoretic virtues.
68i. e. Such as have the ethical and political virtues.
69The original is, α δε δυναμις, οιον αλκα τις τω σκανεος, ᾳ υφισταμεθα, και εμμενομες τοις πραγμασιν. This sentence in its present state is certainly unintelligible. For σκανεος therefore, I read φυσεως, and then the sense will be as in the above translation. The version of Canter is certainly absurd; for it is, “Facultas tanquam robur et causæ, quo ferimus, et in rebus permanemus.” And Gale, as usual, takes no notice of the absurdity.
70viz., The equal and that which is arranged, belong to the order of bound, and the unequal and that which is without arrangement, to the order of infinity. And bound and infinity are the two great principles of things after the ineffable cause of all. See the third book of my translation of Proclus, On the Theology of Plato.
71viz. The salvation of the universe arises from the co-adaptation of the sublunary region to the heavens.
72In the Greek επῳδας; on which Gale observes, “Forte αμαθιας, nisi aliud subsit mysterium.” But it appears to me that there is no occasion to substitute any other word for επῳδας. For in the education of youth, it is certainly requisite to unite allurement with erudition. And the substitution of αμαθιας, ignorance, is monstrous.
73In the original αυτα γαρ α διενεργουσα, instead of which Gale proposes to read αυτα γαρ αδε ενεργοισα, which still leaves the sentence involved in obscurity. But if for διενεργουσα we read διοριζουσα as in the above translation, the meaning is clear.
74For νοηται in this place, I read φυεται.
75Neither of the Latin translators North and Arcerius have understood this passage, and therefore have erroneously translated it. For the original is: και παντα τα εν τᾳ συστοιχειᾳ και ταξει τα εκεινου κατακεχωρισμενα. This North translates: “Atque omnia in rerum serie et ordine ab illo separata.” But Arcerius: “Atque omnia quæ sunt in naturæ cognatione ordineque ab illo separata.” By the things however co-ordinate with, and successive to God, Archytas means the other Gods, who, though subordinate to the supreme, yet in consequence of partaking of the same nature, are said to be co-ordinate with him. Gale, likewise, did not perceive the error of the Latin translators.
76Plato says this of God in his Laws.
77The above sentences are from Stobæi Sententiæ, p. 3. (the edition that of 1609,) and are ascribed to Pythagoras.
78The above seven sentences are to be found in p. 4. of Stobæus, and as it appears to me are erroneously ascribed to Socrates. For I conceive them to have been written either by Democrates or Demophilus.
79Stob. p. 48.
80Hence the dogma of the Stoics derived its origin, that the wise man is independent of Fortune.
81Stob. p. 65. These three sentences are ascribed to Pythagoras.
82Stob. p. 80. These two sentences are ascribed to Socrates, but I have no doubt originally formed a part of the sentences of Demophilus.
83Stob. p. 104. This sentence is ascribed to Democritus in Stobæus, but has doubtless either Democrates or Demophilus for its author.
84Stob. p. 147. The above four sentences, are in Stobæus ascribed to Socrates; but I refer them either to Democrates or Demophilus.
85This sentence in Stobæus is ascribed to Socrates, as is also the one which immediately precedes it, viz. “The wealth of the avaricious man, like the sun descending under the earth, delights no living thing.” But as this sentence is to be found among the Similitudes of Demophilus, there can be no doubt of the other belonging to the same work.
86This and the preceding sentence, are in Stobæus ascribed to Democritus, but I attribute them to Democrates or Demophilus.
87This sentence in Stobæus is ascribed to Pythagoras, but, excepting the part within the brackets, is to be found among the sentences of Demophilus.
88This sentence in Stobæus, is ascribed to Democritus, and that immediately preceding it, to Socrates; but I ascribe both of them to Democrates, or Demophilus.
89This and the preceding sentences, together with two other sentences that accompany them, are in Stobæus ascribed to Democritus; but as the other two are to be found in the Collection of Democrates, there can be no doubt that all of them are from the same author.
90For as every cause of existence to a thing, is better than that thing, so far as the one is cause and the other effect; thus also that which gives a name to any thing is better than the thing named, so far as it is named, i. e. so far as pertains to its possession of a name. For the nominator is the cause, and the name the effect.
91In the Latin it is “post dispositionem corporis.” But for dispositionem it is evidently necessary to read dissolutionem.
92This is conformable to the well-known Pythagoric precept, “Follow God.”
93“We can by no other means,” (says Porphyry De Abstinen. lib. I.) “obtain the true end of a contemplative, intellectual life than by adhering to God, if I may be allowed the expression, as if fastened by a nail, at the same time being torn away and separated from body and corporeal delights; having procured safety from our deeds, and not from the mere attention to words.”
94But intellect is the recipient of wisdom, and therefore intellect is the true man. This also is asserted by Aristotle.
95In the Latin fidelis; but as Ruffinus, the Latin translator of these sentences, frequently adulterates the true meaning of Sextus, by substituting one word for another, I have no doubt that in this sentence the original was πεπαιδευμενος eruditus, and not πιστος fidelis. My reason for so thinking is, that in one of the sentences of Demophilus it is said, “that the life of ignorant men is a disgrace,” των αμαθων ονειδος ειναι τον βιον; and this in the sentences of Sextus is, “Hominum infidelium vita, opprobrium est.” If, therefore, Ruffinus translates αμαθων, infidelium, there is every reason to suppose that he would translate πεπαιδευμενος, fidelis.
96Several of these sentences as published by Arcerius, are in a very defective state; but which, as the learned reader will perceive, I have endeavoured to amend in my translation of them.
97This work is unfortunately lost.
98According to Ælian and Suidas also, melanurus is a fish; but as the word signifies that which has a black termination, it is very appropriately used as a symbol of a material nature.
99viz. Those Gods that are characterized by the intelligible, and intellect. See my translation of Proclus, On the Theology of Plato.
100See the second edition of this work in Nos. 15 and 16 of the Pamphleteer.
101i. e. Natures which are not connected with body.
102See an extract of some length, and of the greatest importance, from this dialogue, in my translation of Select Works of Plotinus, p. 553, &c.
103Forms subsist at the extremity of the intelligible triad, which triad consists of being, life, and intellect. But being and life, with all they contain, subsist here involved in impartible union. See my Proclus on the Theology of Plato.
104In Aristot. Metaphys. Lib. 13.
105Because ¾ is to ⅔ as 9 to 8.
106In Mathemat. p. 147.
107Instead of περιττουται, it is necessary to read περατουται; the necessity of which emendation, I wonder the learned Bullialdus did not observe.
108This philosophic apathy is not, as is stupidly supposed by most of the present day, insensibility, but a perfect subjugation of the passions to reason.
109The words και δικαιοσυνη are omitted in the original. But it is evident from Plotinus, that they ought to be inserted.
110Instead of κατ’ αυτην here, it is necessary to read κατ’ αισθησιν.
The End