Pythagoras: His Life and Teaching, a Compendium of Classical Sources

by Wasserman, James

CHAPTER 5

  THE MONAD

  The Monad is a quantity, which in the decrease of multitude, being deprived of all number, receives mansion and station. For below quantity, Monad cannot retreat.355 The Monad therefore seems to be so called, either from standing; or from remaining always in the same condition; or from its separation ( †) from multitude.

  To the Monad are attributed these names:

  Mind,356 because the mind is stable, and every way alike, and has the preeminence.357

  Hermaphrodite,358 because it is both male and female, odd and even.359 It partakes of both natures; being added to the even, it makes odd, to the odd, even.360

  God, because it is the beginning and end of all, itself having neither beginning nor end.361

  Good, for such is the nature of one.362

  Matter, receptacle of all,363 because it produces Duad, which is properly matter.364

  Chaos, Confusion, Contemperation, Obscurity, Chasm, Tartarus, Styx, Horror, Impermanence, Subterranean Gulf, Lethe, Rigid Virgin, Atlas, Axis, Sume, Pyralios, Morpho.365

  Tower of Jupiter,366 Custody of Jupiter, Throne of Jupiter.367 From the great power which the center has in the universe, being able to restrain the general circular motion, as if the custody of the Maker of all things were constituted therein.368

  Seminal Reason, 369 because this one only is one to the Retractors and is alone; and the rest are procreated of it, and it is the only seminary of all numbers.370

  Apollo Prophet.371

  Prometheus, as being author of life.372

  Geniture, because without it no number has being.373

  Substance,374 because substance is primary.375

  Cause of Truth, Simple Exemplar, Constitution of Symphony.376

  In greater and lesser, Equal; in intention and remission, Middle; in multitude, Mean.377 In time, Now, the present378 because it consists in one part of time which is always present.379

  Ship, Chariot, Friend, Life, Beatitude.380

  Form (or Species), because it circumscribes, comprehends, and terminates,381 and because it produces the rest of the effects.382

  Jupiter,383 because he is father and head of the gods,384 whence the Pythagorean verse:

  Hear noble number, sire of gods and men.

  Love, Concord, Piety, Friendship, because it is so connected, that it cannot be divided into parts.385

  Proteus, as containing all forms.386

  Mnemosyne.387

  Vesta, or Fire.388 For the nature of Monad, like Vesta, is seated in the midst of the world and keeps that seat, inclining to no side.

  Polyonymous.389

  CHAPTER 6

  THE DUAD

  The names of the Duad are these:

  Genius, Evil.390

  Darkness, Sinister, Unequal, Unstable, Moveable.391

  Boldness,392 Fortitude, 393 Contention,394 because it proceeds to action, and first separates itself from the Monad.395

  Matter,396 because indefinite. Indeterminate Duad proceeds from Monad as matter. The cause of tumour and division.397

  Cause of Dissimilars.398

  Partition between Multitude and Monad.399

  Equal, because in composition and permission, this only makes equality.400 Two and two are equal to twice two.

  Unequal, Defect, Superfluity,401 according to the motion of matter.402

  Only Inform, Indefinite, Indeterminate.403 Because from a triangle and triad, polygons are actually procreated to infinitity; in Monad they exist all potentially together; but of two right lines or angles is made no figure.404

  Only Principle of Purity, yet not even, nor evenly even, nor unevenly even, nor evenly uneven.405

  Erato, 406 because through love applying itself to Monad, as the species it procreated the rest of the effects.407

  Harmony.408

  Tolerance,409 because it first underwent separation.410

  Root, but not in act.411

  Feet of Fountain-abounding Ida.412

  Top, Phanes.413

  Justice, because of its two equal parts.414

  Isis, Nature, Rhea, Jove's mother, Fountain of Distribution, Phrygia, Lydia, Dindymene, Ceres, Eleusinia.415

  Diana, 416 because the Moon takes many settings from all the Fixed Stars, and because she is forked, and called half-moon.417

  Love, Dictinna, Aeria, Asteria, DiSamos, Station, Venus, Dione, Micheia, Cythereia, Ignorance, Ignobility, Falsity, Permission, Otherness, Contention, Diffidence, Fat, Death,418 Impulse.419

  Opinion, because it is true and false.420

  Motion, Generation, Mutation, Division.421 (Meursius reads † Judgment) Longitude,422 or rather, First Longitude,423 Augmentation, Composition, Communion. 424

  Misfortune, Enduring, because it first suffered separation,425 Discord.426

  Imposition.427

  Marriage, Juno; Juno being both Wife and Sister to Jupiter.428

  Soul, from motion hither and thither.429

  Science, for all demonstration, and all credit of Science, and all Syllogism collects from some things granted, the thing in question, and easily demonstrates another; the comprehension of which things is Science.430

  Maia.431

  CHAPTER 7

  THE TRIAD

  The Triad is the first number actually odd: the first perfect number. It is middle and proportion.432 It causes the power of the Monad to proceed to act and achieve extension. It is the first and proper joining together of unities.433 For which reason Pythagoras said, Apollo gave oracles from a tripod; and he advised to offer libation three times.

  The Names of the triad are these:

  First Latitude, not simply Latitude.434

  Saturnia, Latona, Cornucopiae, Ophion, Thetis, Harmonia, Hecate, Erana, Charitia, Polyhymnia, Pluto, Arctus, Helice. Not descending to the Ocean, Damatrame, Dioscoria, Metis, Tridume, Triton, President of the Sea, Tritogenia, Achelous, Naclis, Agyiopeza (perhaps “silver-footed,”† as before, Thetis), Curetis, Crataeis, Symbenia, Mariadge, Gorgonia, Phorcia, TriSamos, Lydius.435

  Marriage, Friendship, Peace, Concord,436 because it collects and unites, not similars, but contraries.437

  Justice.438

  Prudence, Wisdom; because men order the present, foresee the future, and learn Experience by the past.439

  Piety,440 Temperance.441 All Virtues depend upon this number, and proceed from it.

  It is the Mind. It is the Cause of Wisdom and Understanding. It is Knowledge which is most proper to number.

  It is the power and composition of all music, and much more of geometry. It has all power in Astronomy, and the nature and knowledge of celestials, containing and impelling it to the production of substance.

  The cube of this number, Pythagoras affirmed to have the power of the lunar circle, inasmuch as the Moon goes round her orb in twenty-seven days, which the number Ternio, in Greek , the triad gives in its cube.442

  CHAPTER 8

  THE TETRAD

  The Tetrad was much honored by the Pythagoreans.443 It was esteemed the most perfect number,444 the primary and earliest formed, which they called the root of all things, and the fountain of nature.445

  The Tetrads are all intellectual and have an emergent order. They are, for that reason, the empyreal prefecture; they go round about the world as the Empyrean passes through all.446

  Even God himself Pythagoras expressed by the Tetrad.

  How God is a Tetrad, you will clearly find in the sacred discourse ascribed to Pythagoras, wherein God is described as the number of numbers.447 For if all beings subsist by his eternal counsel, it is manifest, that number in every species of beings depends upon their causes. The first number is there, from thence derived hither. The determinate stop of number is the Decad, for he who would reckon further, must return to one, two, three, and number a second Decad. In like manner, a third to make up thirty, and so on; till having numbered the tenth Decad, he comes to a 100. Again, he reckons from 100 in the same manner, and so may proceed to infinite by revolution of the Decad.

 
; Now the Tetrad is the power of the Decad; for, before we arrive at the perfection of the Decad, we find a united perfection in the Tetrad—the Decad being made up by addition of one, two, three, and four.

  Moreover, the Tetrad is an arithmetical mean between one and seven, equally exceeding and exceeded in number. It wants three of seven, and exceeds one by three. Monad, as being the mother of numbers, contains all their powers within itself.

  The Hebdomad [i.e., the number seven]—as being motherless, and a virgin—possesses the second place in dignity. For it is not made up of any number within the Decad—as four is of twice two; six of twice three; eight of twice four; nine thrice three; and ten of twice five. Neither does it make up any number within the Decad—as two makes four; three makes six; five makes ten.

  But the Tetrad, lying between the unbegotten Monad and the motherless Hebdomad, comprehends all powers, both of the productive and produced numbers. For this of all numbers under ten is made of a certain number, and makes a certain number; the Duad doubled makes a Tetrad, the Tetrad doubled makes eight.

  Besides, the first solid figure is found in a Tetrad. For a point is correspondent to Monad, a line to Duad (because drawn from one point to another), a superficies to Triad (because it is the most simple of all rectilinear figures). But a solid properly agrees with the Tetrad. For the first pyramid is in a Tetrad; the base is triangular, so that at the bottom is a three, at the top one.

  Furthermore, the judicative power in things is four: mind, science, opinion, and sense. For all beings are determined to be either mind, science, opinion, or sense. For which reason Pythagoras affirmed the soul of man to consist of a Tetrad.448

  Finally, the Tetrad connects all beings, elements, numbers, seasons of the year, Coaevous society. Neither can we name anything which depends not on the Tetractys as its root and principle. For it is, as we have said, the maker and cause of all things—intelligible God, author of celestial and sensible good. The knowledge of these things was delivered to the Pythagoreans by Pythagoras himself. Hitherto Hierocles.

  For this reason the word “Tetractys” was used by Pythagoras and his disciples as a great oath. They, likewise, out of respect to their master, forbearing his name, did swear by the person that communicated the Tetractys to them.

  Eternal Nature's Fountain I attest,

  Who the Tetractys to our Soul express't.

  But Plutarch interprets this Tetractys (which he says was also called , World) to be thirty-six, which consists of the first four odd numbers, thus:449

  The names of the Tetrad are these:

  Another Goddess, Multideity, Pantheos, Fountain of Natural Effects.450

  Key-keeper of Nature: because the universal constitution cannot be without it. To these sciences it confers constitution and settlement, and reconciles them. Yea, it is nature itself and truth.451

  Nature of Aeolus452 from its various property.453

  Hercules, Impetuosity, Most Strong, Masculine, Ineffeminate, Mercury, Vulcan, Bacchus, Soritas, Maiades, Erinnius, Socus, Dioscorus, Bassarius, Two-mother'd, of Feminine Form, of Virile performance, Bacchation.454

  Harmony455 because it has a sesquitertia.456

  Urania the Muse.457 World.458

  Body: as a Point is one, a Line two, a Superficies three.

  Soul, because it consists of mind, science, opinion and sense.459

  First Profundity, as it is a body.460

  Justice. The property of justice is compensation and equality. This number is the first evenly even. And whatsoever is the first in any kind is most that thing. This, they said, was the Tetrad, because being quadrate, it is divided into equals and is itself equal.461

  CHAPTER 9

  THE PENTAD

  The Pentad is the first combination of both kinds of number, even and odd—two and three.462 Its names are these:

  Reconciliation,463 because the fifth element, Aether, is free from the disturbances of the other four.464

  Alteration, Light, because it changed that which was separated threefold into the Identity of its Sphere, moving circularly and engendering light.465

  Justice,466 because it divides ten into two equal parts.467

  The least and top of livelihood.468

  Nemesis,469 because it distributes conveniently celestial, divine, and natural elements.470

  Bubastia,471 because worshipped at Bubastus in Egypt.472

  Venus, Gamelia, Androgynia, Cytherea, Zoneia,473 Marriage,474 because it connects a masculine and feminine number:475 consisting of two (the first even), and three (the first odd).476

  , President of Circles.477

  Semi-Goddess,478 not only as being the half of ten (which is divine), but for that it is placed in the middle.479

  Tower of Jupiter.

  Didymaea, or Twin,480 because it divides ten into two.481

  Firm Axis.482

  Immortal, Pallas, implying the fifth essence.483

  , Cordial 484 from similitude with the heart.485

  Providence, because it makes unequals equal.486

  Tρooς, Sound, the fifth being the first diasteme.487

  Nature: because multiplied by itself, it returns into itself. For as Nature, receiving wheat in seed—and introducing many forms by altering and changing it—at last returns it wheat at the end of the whole mutation, restoring the beginning; so, while other numbers multiplied in themselves are increased and end in other numbers; only five and six multiplied by themselves, represent and retain themselves.488

  This number represent all superior and inferior beings. For it is either the supreme God, or the mind-born of God, wherein are contained the species of all things; or the Soul of the World, which is the fountain of all souls, or celestials, down to us; or it is terrestial nature. And so the Pentad is replete with all things.489

  CHAPTER 10

  THE HEXAD

  The Pythagoreans held the number Six to be perfect, respecting (as Clement Alexandrinus conceives) the creation of the world according to the Prophet.

  The names of the Hexad, are these:

  Form of Form, Articulation of the Universe, Maker of the Soul, Harmony,490 because it has the power to produce a vital habit. Whence it is called Hexad, ; and Harmony, because all Souls are Harmonic.491

  Regarding , † Perfection of Parts,492 the Pythagoreans called it thus, imitating Orpheus—either as being the only number under ten which is whole and equal in its parts; or because the whole Universe is divided into parts by it.493

  Venus,494 because it procreates harmony. Six to twelve is a diapason concord. Six to nine is a hemiolius. Six to eight is epitrites, that is a diatessaron concord. Whence it is named Venus, who was the Mother of Harmony.495

  [“yoke”],496 [“wedding”],497 Marriage,498 because of the mixture of the first even and first odd.499 For as marriage procreates by a male and female, so this number is generated of three (which is odd and called male), and of two (which is even and called female); for two times three make six.500 It produces children like the parents.501

  [“central oarsman”],† [“friendship”],502 or , Conciliation, because it conciliates the male and female.503

  Health,504 a triple triangle, which being alternately conjoined within itself constitutes a figure of five lines. They used it as a symbol to those of their own sect, and called it , Health.505

  Anvil;506 quasi unwearied; because the principal triangles of the mundane elements have a share in it, being each of them Six, if measured by three perpendiculars.507

  [“Hecate's missile”], being compounded of, and, as it were, [“hurled forth”],† the triad which is called Hecate.508

  Trioditis: from the nature of that goddess; or because the Hexad first assumes the three motions of intervals, being divided into two parts, each of which is on each side.509

  the distribution of all time, of things above the earth, and under the earth, which is done by the Hexad in the Zodiac. Or because Time is of the nature of the Triad, consisting of three parts, and the Hexad consists
of two Triads.510

  Persaea, Triform.511

  Amphitrite;512 because it has a triad on each side.513

  Neighbor to Justice,514 as being nearest to 5 (which is named Justice.515)

  Thalia, the Muse,516 because of the harmony of the rest.517

  Panacaea,518 in respect to health mentioned already; or, a Panarceia (omni-sufficience, endued with parts sufficient for totality).519

  Middle-Right, being in the midst between two and ten, equidistant from both.520

  World, because the world, as the Hexad, is often seen to consist of contraries by harmony.521

  CHAPTER 11

  THE HEPTAD

  The Heptad was so called, quasi worthy of veneration;522 for Pythagoras held this number to be most proper to religion.523 He also held that it is perfect.524 And thence it was, as the Pythagoreans conceived, that creatures born in the seventh month live.525

  The names of the Heptad, are these.

  Fortune, Occasion,526 because it occurs casually and opportunely to everything.527 Whatsoever is best amongst sensible things, by which the seasons of the year and their periods are orderly complete. Participates of the Hebdomad,528 the Moon having seven days, measures all time.529

  , Motherless, Virgin,530 Minerva, as being a virgin, unmarried, not born of a mother (odd number), nor of a father (even number); but out of the crown of the father of all, Monad.531

  Mars,532 [“citadel”].533

  Ageleia,534 an epither of Minerva.535

  [“The Unwearied”]†.536

  Custody,537 because the stars which guard the universe are seven.538

  , Tritogenia, [“Blue-eyed”],† [“Protectress”],† [“in full armor”], [“worker”],† [“much desired”], [“sound of limbs“],† Stock of Amalphea, Aegis, Osiris, Dream, Voice, Sound, Clio the Muse, Judgment, Adrastia.539

  leading to the end†;540 because by it all are led to the end.541

  CHAPTER 12

  THE OGDOAD

  The Ogdoad, they said, was the first cube, and the only number evenly even under ten.542

  The Names of it are these: