Above these three kinds—absolute, contrary, relative—there must necessarily be some Supreme Genus; every genus is before the species which are under it. For if the Genus be taken away, the species are taken away also; but the removal of the species takes not away the genus; the species depending on the genus, not the genus on the species. The transcending genus of those things which are understood by themselves (according to the Pythagoreans) is the One. That exists and is considered absolutely, so they say. Of contraries, equal and unequal, holds the place of a genus; for in them is considered the nature of all contrarieties. By example, of rest in equality, it admits not intension and remission; of motion or inequality, it admits intension and remission. In like manner, natural inequality is the instable extremity; preternatural inequality admits intension and remission. The same of health and sickness, straightness and crookedness. The relative consists of excess and defect as their genus; great and greater, much and more, high and higher, are understood by excess: little and less, low and lower, by defect.
Now forasmuch as absolutes, contraries, and relatives appear to be subordinate to other genera (that is, to one, to equality and inequality, to excess and defect), let us examine whether those genera may be reduced to others. Equality is reducible to one, for one is equal in itself; inequality is either in excess or defect; of unequals, one exceeds, the other is deficient. Excess and defect are reducible to the indeterminate Duad; for the first excess and defect is in two, in the excedent and the deficient. Thus the principles of all things appear above all the rest in the first Monad and the indeterminate Duad.
Of these are generated the Arithmetical Monad and Duad. From the first Monad, one; from the Monad and the indeterminate Duad, two. The Duad, being not yet constituted amongst Numbers, neither was there two before it was taken out of the indeterminate Duad. From the indeterminate Duad, together with the Monad, was produced the Duad which is in Numbers. Out of these, in the same manner proceeded the rest of the Numbers: one continually stepping forward, the indeterminate Duad generating two, and extending Numbers to an infinite multitude.
Hereupon they affirm that, in principles, Monad has the nature of the efficient cause, Duad of passive matter. And after the same manner as they produced Numbers, which consists of them, they composed the world also and all things in it.
A Point is correspondent to the Monad. The Monad is indivisible, so is the Point; the Monad is the principle of Numbers, so is the Point of Lines. A Line is correspondent to the Duad; both are considered by transition. A line is length without breath, extended between two points. A Superficies corresponds to the Triad. Besides length, whereby it was a Duad, it receives a third distance, breadth. Again, settling down three points: two opposite, the third at the juncture of the lines made by the two, we represent a superficies. The solid figure and the body (as a pyramid) answer the Tetrad. If we lay down, as before, three points, and set over them another point—behold the pyramidical form of a solid body, which has three dimensions, length, breadth, thickness.
Some there are who affirm that a body consists of one point; the point by fluxion makes a line; the line by fluxion makes a superficies; the superficies moved to thickness makes a body in three dimensions. This sect of the Pythagoreans differs from the former. They held that of two principles—the Monad and the Duad—were made Numbers; of Numbers were made Points, Lines, Superficies, and Solids. These hold that all things come from one point—for of it is made a line, of the line a superficies, of the superficies a body.
Thus are solid bodies produced of numbers precedent to them. Moreover, of them consist Solids, Fire, Water, Air, Earth, and in a word, the whole World; which is governed according to Harmony—as they affirm again—recurring to Numbers which comprise the proportions that constitute perfect Harmony.792 Harmony is a system consisting of three concords: the Diatessaron, the Diapente, the Diapason; the proportions of these three concords are found in the first four numbers: one, two, three, four. The Diatessaron consists in a sesquitertia proportion. The Diapason is in sesquialtera. The Diapente is in duple. Four being sesquitertius to three (as consisting of three and one third) has a Diatessaron proportion; three being sesquialter to two (as containing two and its half), a Diapente; four being the double of the Monad of two, a Diapason. The Tetractys affording the analogy of these concords, which make perfect harmony, according to which all things are governed, they styled it:
The root and fountain of eternal nature.
Moreover, whatsoever is comprehended by man (say they) either is a body or incorporeal; but neither of these is comprehended without the notion of numbers. A body, having a triple dimension, denotes the number three. Besides of bodies, some are by connection: as ships, chains, buildings; others by union comprised under one habit: as plants and animals; others by aggregation: as armies and herds. All these have numbers, as consisting of plurality. Moreover of bodies: some have simple qualities, others multiplex. Examples include an apple, various colors to the sight, juice to the taste, odor to the smell; these also are of the nature of numbers. It is the same of incorporeals. Time, an incorporeal, is comprehended by number: years, months, days, and hours. The like of a Point, a Line, a Superficies, as we said already.
Likewise to numbers are correspondent both naturals and artificials. We judge everything by criteria, which are the measures of numbers. If we take away number, we take away the cubit, which consists of two half-cubits, six palms, twenty four digits. We take away the bushel, the balance, and all other criteria, which, consisting of plurality, are kinds of number. In a word, there is nothing in life without it. All art is a collection of comprehensions. Collection implies number; it is therefore rightly said:
To number all things reference have.
That is to determinative reason, which is of the same kind with numbers, whereof all consists. Hitherto Sextus.
The sum of all (as said by Alexander in his Successions, extracted out of the Pythagorean commentaries) is this: the Monad is the principle of all things.793 From the Monad came the indeterminate Duad. As matter subjected to the cause, Monad; from the Monad and the indeterminate Duad came Numbers. From Numbers came Points. From Points came Lines; from Lines, Superficies; from Superficies, Solids; from these, solid bodies. Solid bodies are composed of four elements: Fire, Water, Air, Earth; of all which, transmutated and totally changed, the world consists.
CHAPTER 2
OF THE WORLD
The World, or comprehension of all things, Pythagoras called [“order”], from its order and beauty.794
The world795 was made by God,796 in thought, not in time.797 He gave it a beginning from fire and the fifth element. For there are five figures of solid bodies which are termed mathematical. Earth was made of a Cube; fire of a Pyramid or Tetrahedron; Air of an Octahedron; Water of an Icosahedron; the Sphere of the Universe of a Dodecahedron. In these, Plato follows Pythagoras.
The world is corruptible in its own nature, for it is sensible and corporeal.798 But it shall never be corrupted, by reason of the providence and preservation of God.799 Fate is the cause of the order of the universe and all particulars.800 Necessity encompasses the world.
The world is animate, intelligible, spherical, enclosing the earth in the midst of it.801
The Pythagoreans affirm802 that what is without heaven is infinite; for beyond the world there is a Vacuum, into which, and out of which, the world respires.803
The right side of the world is the east, whence motion begins; the left is the West.804
CHAPTER 3
OF THE SUPERIOR OR AETHERIAL PARTS OF THE WORLD
Pythagoras first called heaven [“order”],† as being perfect in all kinds of animals and adorned with all kinds of pulchritude.805
In the fixed sphere resides the first Cause: whatsoever is next him, they affirm to be best, and firmly compounded and ordered; that which is furthest from him, the worst.806 There is a constant order observed as low as the Moon, but all things beneath the Moon are moved promiscuously
.
For the air which is diffused about the earth is unmoved and unwholesome, and all things that are in it are mortal. But the air which is above is perpetually in motion, and pure, and healthful; and all that are in it are immortal, and consequently divine.807
This they call, the free Aether (immediately above the Moon). Aether, they perceived, as being void of matter and an eternal body; free, because it is not obnoxious and filled with material disturbances.808
Hence it follows that the Sun, Moon, and the rest of the stars, according to Pythagoras, are gods.
The Pythagoreans held that every star is a world in the infinite Aether, which contains earth, air, and Aether. This opinion was also held by the followers of Orpheus, that every star is a world.809
The Sun is spherical, eclipsed by the Moons coming under him.810
The body of the Moon is of a fiery nature; she receives her light from the Sun.811 The eclipse of the Moon is a reverberation or obstruction from the Antichthon.
The Pythagoreans affirm that the Moon seems earthly because she is round-about inhabited as our earth. But the creatures are larger and fairer, exceeding us in size fifteen times, neither have they any excrements, and their day is so much longer.812
Some of the Pythagoreans affirm that a comet is one of the planets that appears not in heaven but after a long time, and is near the Sun, as it happens also to Mercury. For because it recedes but little from the Sun, often when it should appear, it is hid; so as it appears not but after a long time.813 Or, as Plutarch expresses it, a comet is one of those stars which are not always apparent, but rise after a certain period. Others hold that it is the reflection of our sight on the Sun, like images in glasses.814
The rainbow he asserted to be the splendor of the Sun.815
Celestial bodies frequently appear in ancient art. This silver denarius was issued by Juba II and his wife Cleopatra Selene, the only daughter of Marc Antony and Cleopatra VII, who were made co-rulers of the Kingdom of Mauretania by Rome's first emperor, Augustus. It represents Juba II with his portrait on the obverse and Cleopatra Selene with a star above a crescent (alluding to the goddess Selene) on its reverse.
Photo courtesy of Classical Numismatic Group, Inc.
OF THE SUBLUNARY PARTS OF THE WORLD
Of the inferior sublunary parts of the world, the anonymous Pythagorean places first the sphere of fire, then that of air, next that of water, last that of Earth.816
The bodies of all the elements are round, except that of fire, which is conical.817
Below the Moon all things move in a disorderly manner. Evil therefore necessarily exists about the region of the Earth; that being settled lowest as the basis of the world, the receptacle of the lowest things.818
The air, which is diffused about the Earth is unmoved and unwholesome, and all things in it are mortal.819
There, is generation and corruption. For things are produced by alteration, mutation, and resolution of the elements. Motion is a difference or diversity in matter.820
In the world, there is equally proportioned, light and darkness, heat and cold, dryness and humidity. When they are exuberant, the excess of heat causes summer; of cold, winter. When they are equal, then are the best seasons of the year: whereof that which is growing up is the spring, healthful; that which is decaying is autumn, unhealthful.821 Even of the day, the morning is growing up, the evening decaying, and therefore more unwholesome.
CHAPTER 1
OF LIVING, AND ANIMATE CREATURES
There penetrates a beam from the Sun through the Aether which is cold and dry.822 (They call the air, “cold aether,” and the Sun and humidity, “gross aether.”) This beam penetrates to the Abyss, and thereby all things vivificate. All things live inasmuch as they participate of heat (wherefore even plants are living creatures). But all things have not soul. The soul is a portion of aether, of heat, and cold, for it participates of cold aether. The soul differs from life. She is immortal, because that from which she is taken is immortal. Thus Alexander in his successions, out of the commentaries of the Pythagoreans.
CHAPTER 2
OF THE GENERATION OF ANIMATE CREATURES
Animate creatures are generated of one another by seed (but of earth nothing can be generated).823 Seed is a distillation from the brain of the foam of the most useful part of the blood, the superfluity of the aliment, as blood and marrow. This being injected [“in the womb”], purulent matter, moisture, and blood issue from the brain, whereof flesh, nerves, bones, hair, and the whole body consists. (The power of seed is incorporeal as the motive mind; but the effused matter corporeal.) From the vapor comes the soul and sense; it is first compacted and coagulated in forty days. And being perfected according to harmonical proportions in seven, nine, or ten months (at the farthest), the Infant is brought forth, having all proportions of life; of which (aptly connected according to the proportions of harmony) it consists; all things happening to it at certain times. Thus Alexander, out of the Pythagorean commentaries.
The proportions themselves are more exactly delivered by Censorinus thus.824 Pythagoras said that generally there are two kinds of births: one lesser, of seven months; which comes into the world the 207th day after the conception. The other greater, of ten months; which is brought forth in the 274th day. The first and lesser is chiefly contained in the number six. For that which is conceived of the seed (as he says) the six first days, is a milky substance; the next eight days, bloody; which eight with the six make the first concord, Diatessaron. The third degree is of nine days; in which time, it is made flesh. These to the first six are in sesquialtera proportion, and make the second concord, Diapente. Then follow twelve days more in which the body is fully formed. These to the same six consist in duple proportion, and make the Diatessaron concord. These four numbers, six, eight, nine, twelve, added together make thirty-five days; nor without reason is the number six the foundation of generation. For the Greeks call it we perfect; because its three parts perfect it. Now as the beginnings of the seed and that milky foundation of conception is first completed by this number, so this is the beginning of the man now formed. And, as it were, another foundation of maturity which is of thirty-five days, being multiplied by six, makes 220 days in which this maturity is fulfilled.
The other (greater) birth is contained in the greater number seven. And as the beginning of the former is in six days, after which the seed is converted into blood, so that of this is in seven. And as there the members of the Infant are formed in thirty-five days; so here in about forty. These forty days being multiplied by the first seven, make 280 days, that is forty weeks. But forasmuch as the birth happens on the first day of the last week, six days are subtracted, and the 274th observed.
He held that mankind had ever been; and never had beginning.825
CHAPTER 3
THE SOUL: ITS PARTS AND FIRST OF THE IRRATIONAL PART
The power of number, being greatest in nature,826 Pythagoras defined the soul as a self-moving number.827
Of the Pythagoreans, some affirm that the soul is the motes in the air; others, that it is that which moves those motes.828
The soul is most generally divided into two parts, rational, and irrational, but more especially into three.829 For the irrational they divide into irascible and desiderative. These are termed [“intelligence”], [“reason”], and [“passion”]. [“intelligence”] and [“passion”] are in other living creatures, [“reason”] only in man.830
Yet, the souls of all animate creatures are rational, even of those which we term irrational. But they act not according to reason because of the ill temperament of the body and want of speech: as in apes and dogs, who talk but cannot speak.831
The beginning of the soul comes from the heat of the brain. That part which is the heart is [“passion”], but [“reason”] and [“intelligence”] are in the brain. The senses are distillations from these: the rational part is immortal, the rest mortal. The soul is nourished by blood, and the faculties of the soul are spirits. Both t
he soul and her faculties are invisible, for Aether is invisible. The fetters of the soul are veins, arteries, and nerves. But when she is strong, and composed within herself, her fetters are reasons and actions.
Every sense is derived from its proper element. Sight is from Aether, hearing from air, smelling from fire, taste from water, touch from earth.832
Sense in general, and particulary sight, is a vapor very hot. For this reason we are said to see through air and through water, for the heat pierces the cold. For if that which is in the eyes were a cold vapor, it would fight with the air—which is like it hot. In some places, he calls the eyes the gates of the Sun; the same he determined concerning hearing and the rest of the senses.
Sight is the judge of colors.833 Color they call the superficies of a body. The kinds of color are black, white, red, pale.834 Or, as the anonymous writer delivers the opinion of Pythagoras, ten: black, white, and the rest between them, yellow, tawney, pale, red, blue, green, bright, grey.835 The differences of colors are derived from the mixture of the elements, and, in living creatures, from variety of place and of air.
The image in a mirror is made by reflection of the sight.836 This, being extended to the brass, and meeting with a thick smooth body, is pushed back and returns into itself, as when the hand is stretched forth and again brought back to the shoulder.837
Hearing is the judge of voice, sharp and flat.838 Voice is incorporeal; for not air, but the figure and superficies of air, by a stroke becomes voice. But no superficies is a body.839 And though it follows the motion of the body, voice itself has no body; as when a rod is bent, the superficies suffers nothing, the matter only is bent.
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