(44) As an illustration of the fact just stated, we may consider the two opposites known as Hot and Cold, respectively; surely there can be no two qualities apparently more distinct and separate from each other—more diametrically different from each other. But careful examination shows us that the two contrasting things are really but degrees, conditions, and states of the same thing. There is no such thing as an "absolute hot," or an "absolute cold." There are merely different degrees of this Hot-Cold pair of opposites, which for convenience we call "Heat." We cannot point out a place on the thermometer where Hot ceases and Cold begins, or vice versa. The two states or conditions blend into each other, and any statement regarding them is found to be merely comparative. If we place one hand in a bowl of very hot water, and the other in a bowl of ice-cold water, and then suddenly withdraw both hands and plunge them into a bowl of lukewarm water, what happens d Simply this, that we find that the hot-water hand feels a sensation of coolness, while the cold-water hand feels a sensation of heat—each experience resulting from the comparison with the previous experience.

(46) Sometimes there is a rapid change and shift on the scale of the opposites. Love is quickly transmuted to hate; the best friends and most ardent lovers become the bitterest enemies. And, on the other hand, persons who originally detest each other frequently become ardent lovers after a time; and old enemies, when reconciled, frequently become the closest friends. The swing is often as far in one direction as was its former swing in the opposite direction. Up changes to down, as the earth revolves; and hot becomes cold when the vibrations are changed. This also applies to hard and soft, tenuous and solid, etc., the conditions depending entirely upon the rate of vibrations and relative positions of the particles of the matter of which the things are composed. Moreover, constant emphasis or activity of one opposite frequently leads to a manifestation of the other opposite. We often fly to the other extreme of feeling and action, when we have over-emphasized the former emotional states. We get tired and disgusted with one set or condition of things, and feel a desire to fly to the opposite condition or set. Too much of a good thing often causes us to dislike it. Likewise, if we travel far enough west, we finally reach the extreme east, and vice versa. If we travel far enough north, we pass the pole and find ourselves proceeding south. At the North Pole, no matter in what direction we may travel, we always find ourselves travelling south; while at the South Pole, we can travel north only, no matter which way we may step out.

(45) We may consider the emotional states of Love and Hate as another illustration of the same principle; surely these two emotions seem irreconcilable and impossible to harmonize. But let us see! At the one end of the emotional scale of Love-Hate we find intense love, then descending on the scale we find varying and gradually lessening degrees of love. Then we find the balanced point of indifference, which seems to be neither love nor hate, but which in reality is the subtle balancing of the two emotions. Then descending the scale we find a faint degree of aversion or dislike; then a series of gradually increasing degrees of dislike, until finally real hate is met with, and so on until we reach the degree of intense and extreme hate. Yet all are seen to be but degrees on the same emotional scale of Love-Hate.

(11) Now the heat reigneth and predominateth in all powers in nature, and warmeth all, and is one source or spring in all; for if it were not so the water would be too cold, and the earth would be congealed, and there would be no air.

(16) Heat is set in opposition unto it, and qualifieth therein, as if it were one and the same thing; but cold opposeth the fierceness or rage of the heat, and allayeth the heat.

(17) After discovering the operation of certain principles in one thing we may safely reason by analogy based upon the assumption that these principles exist in other things on a higher plane, and thus discover the nature of the unknown " x ." Thus the occultist reasons that there is Law and Order manifest on every plane of being; that there is a Principle of Vibration manifest on every plane of being; that there is a Principle of Rhythm manifest on every plane of being; that there is a Principle of Cycles manifest on every plane of being; that there is a Principle of Polarity manifest on every plane of being; that there is a Principle of Sex manifest on every plane of being. And the further that human investigation is pushed into the Unknown, the greater is the proof of the existence of these Cosmic Principles reasoned out by the ancient occultists upon the fundamental basis of the Principle of Correspondence.

(16) I. The Principle of Correspondence The Principle of Correspondence manifests in a certain correspondence or analogy or agreement between manifestations of the various planes of activity in the Cosmos. It is indicated by the old Hermetic aphorism: "As above, so below; as below, so above," and by the Arcane axiom: "Ex Uno disce Omnes," or "From One know All." The Rosicrucians, and other ancient occultists, hold that the laws governing the nature and activity of the amoeba, likewise govern the nature and activity of man and beings higher than man. What is true of matter is true of energy and of mind. The occultists make a practical application of this universal principle, in the direction of studying the unknown by means of the known, with the knowledge that the same laws govern each. Thus, just as the solar system may be known by means of studying the atoms and molecules, so may the higher planes of being be studied by an examination of the lower planes in manifestation before us.

(20) But the air has its original and greatest motion from heat, and the water has its original and greatest motion from cold.

(14) Yet the heat makes the light moveable, so that it springeth and driveth forth; as is seen in winter, when the light of the sun is likewise upon the earth, but the hot rays of the sun cannot reach into the earth, and that is the reason why no fruit grows in winter. Of the Qualification of the Cold Quality.

(28) So truly does advanced modern scientific thought recognize the nature of vibrations, that the axiom is announced that "The difference in things consists entirely of difference in vibrations." This axiom is akin to the ancient occult aphorism that "Things manifest differences according to their rate of vibrations." So, it is seen, all human investigation tends to prove the truth of the old occult axiom that "Everything vibrates." IV. The Principle of Rhythm The Principle of Rhythm manifests that universal regular swing or time-beat which is apparent in all the manifested world, from its highest to its lowest manifestation. The ancient occult axiom "Everything beats time" expresses this fundamental fact of the Cosmos.

(27) Thus heat and cold are the cause and original of water and air, in which everything acteth and stands; every life and mobility stands therein. Of this I shall write plainly, concerning the creation of the stars. Of the Influences of the other Qualities in the Three Elements, Fire, Air, and Water. Of the Bitter Quality.

(15) Cold is a quality also, as well as heat; it qualifieth or operateth in all creatures whatsoever that come forth in nature, and in all whatsoever that move therein, in men, beasts, fowls, fishes, worms, leaves and grass.

(527) And suppose we make astronomy the third—what do you say? I am strongly inclined to it, he said; the observation of the seasons and of months and years is as essential to the general as it is to the farmer or sailor. I am amused, I said, at your fear of the world, which makes you guard against the appearance of insisting upon useless studies; and I quite admit the difficulty of believing that in every man there is an eye of the soul which, when by other pursuits lost and dimmed, is by these purified and re-illumined; and is more precious far than ten thousand bodily eyes, for by it alone is truth seen. Now there are two classes of persons: one class of those who will agree with you and will take your words as a revelation; another class to whom they will be utterly unmeaning, and who will naturally deem them to be idle tales, for they see no sort of profit which is to be obtained from them. And therefore you had better decide at once with which of the two you are proposing to argue. You will very likely say with neither, and that your chief aim in carrying on the argument is your own improvement; at the same time you do not grudge to others any benefit which they may receive. I think that I should prefer to carry on the argument mainly on my own behalf. Then take a step backward, for we have gone wrong in the order of the sciences. What was the mistake? he said. After plane geometry, I said, we proceeded at once to

(43) The South wind and the North wind and the East wind and the West wind

(38) A writer has said of this: "The Ego may convert the circle of its life-motion into an advancing and rising spiral, which while carrying him around the life circle will at the same time raise him a stage higher at each turn. The Mountain of Attainment, around which winds the Spiral Path, is travelled only in this way. Around and around the Pilgrims travel, seemingly retracing their steps but in reality constantly mounting upward. By advancing the Central Point, by means of the Will , the wise and the strong convert the Circles into Spirals, and thus advance and attain. This, indeed, as the old aphorism states, 'is one of the highest forms of Mental Alchemy.'" The further the student penetrates in his investigations, along the lines of the physical, the mental, or the spiritual, the more will he become convinced of the truth of the ancient occult axiom that "Everything proceeds in circles." VI. The Principle of Polarity The Principle of Polarity manifests that universal fact of "the pairs of opposites," or "the antinomies," which is apparent in all the manifested world, from its highest to its lowest manifestation. The spirit of this principle was expressed in the ancient occult axiom: "Everything has its Opposite, which is the other pole of its manifestation." The Principle of Polarity may be stated as follows: "All phenomena manifest polarity, or opposite and contrasted sets of qualities, properties, or powers, operating in opposite and contrasted directions." The ancient philosophers made this one of the chief features of their teachings, under the name of "The Opposites," "The Pairs of Opposites," or "The Antinomies," according to the usage of the respective schools. They held that every phenomenal thing possesses and manifests these pairs of opposite qualities, properties, and powers. They also held that each and every set of polarized opposites constitutes a unity consisting of a reconciliation and balancing of the opposing poles. They also held that every phenomenal thing, itself, is one of a pair of polarized opposites which, together, constitute a greater unity; and so on, either to infinity or until the opposites find final reconciliation and harmony in an Infinite Reality.

(17) Cold containeth also two sorts or species in it, which are to be observed, viz. It mitigateth the heat, makes all things pleasant, and is in all creatures a quality of life; for no creature can subsist without cold; for it is a springing, driving mobility in every thing.

(1) Since, however, we are narrating the wisdom employed by Pythagoras in instructing his disciples, it will not be unappropriate to relate that which is proximate in a following order to this, viz. how he invented the harmonic science, and harmonic ratios. But for this purpose we must begin a little higher. Intently considering once, and reasoning with himself, whether it would be possible to devise a certain instrumental assistance to the hearing, which should be firm and unerring, such as the sight obtains through the compass and the rule, or, by Jupiter, through a dioptric instrument; or such as the touch obtains through the balance, or the contrivance of measures;—thus considering, as he was walking near a brazier’s shop, he heard from a certain divine casualty the hammers beating out a piece of iron on an anvil, and producing sounds that accorded with each other, one combination only excepted.

But he recognized in those sounds, the diapason, the diapente, and the diatessaron, harmony. He saw, however, that the sound which was between the diatessaron and the diapente was itself by itself dissonant, yet, nevertheless, gave completion to that which was the greater sound among them. Being delighted, therefore, to find that the thing which he was anxious to discover had succeeded to his wishes by divine assistance, he went into the brazier’s shop, and found by various experiments, that the difference of sound arose from the magnitude of the hammers, but not from the force of the strokes, nor from the figure of the hammers, nor from the transposition of the iron which was beaten. When, therefore, he had accurately examined the weights and the equal counterpoise of the hammers, he returned home, and fixed one stake diagonally to the walls, lest if there were many, a certain difference should arise from this circumstance, or in short, lest the peculiar nature of each of the stakes should cause a suspicion of mutation.

Afterwards, from this stake he suspended four chords consisting of the same materials, and of the same magnitude and thickness, and likewise equally twisted. To the extremity of each chord also he tied a weight. And when he had so contrived, that the chords were perfectly equal to each other in length, he afterwards alternately struck two chords at once, and found the before-mentioned symphonies, viz. a different symphony in a different combination. For he discovered that the chord which was stretched by the greatest weight, produced, when compared with that which was stretched by the smallest, the symphony diapason. But the former of these weights was twelve pounds, and the latter six. And, therefore, being in a duple ratio, it exhibited the consonance diapason; which the weights themselves rendered apparent.

But again, he found that the chord from which the greatest weight was suspended compared with that from which the weight next to the smallest depended, and which weight was eight pounds, produced the symphony diapente. Hence he discovered that this symphony is in a sesquialter ratio, in which ratio also the weights were to each other. And he found that the chord which was stretched by the greatest weight, produced, when compared with that which was next to it in weight, and was nine pounds, the symphony diatessaron, analogously to the weights. This ratio, therefore, he discovered to be sesquitertian; but that of the chord from which a weight of nine pounds was suspended, to the chord which had the smallest weight [or six pounds,] to be sesquialter.

For 9 is to 6 in a sesquialter ratio. In like manner, the chord next to that from which the smallest weight depended, was to that which had the smallest weight, in a sesquitertian ratio, [for it was the ratio of 8 to 6,] but to the chord which had the greatest weight, in a sesquialter ratio [for such is the ratio of 12 to 8.] Hence, that which is between the diapente and the diatessaron, and by which the diapente exceeds the diatessaron, is proved to be in an epogdoan ratio, or that of 9 to 8. But either way it may be proved that the diapason is a system consisting of the diapente in conjunction with the diatessaron, just as the duple ratio consists of the sesquialter and sesquitertian, as for instance, 12, 8, and 6; or conversely, of the diatessaron and the diapente, as in the duple ratio of the sesquitertian and sesquialter ratios, as for instance 12, 9, and 6.

After this manner, therefore, and in this order, having conformed both his hand and his hearing to the suspended weights, and having established according to them the ratio of the habitudes, he transferred by an easy artifice the common suspension of the chords from the diagonal stake to the limen of the instrument, which he called chordotonon . But he produced by the aid of pegs a tension of the chords analogous to that effected by the weights.

(4) Thou'lt see how of necessity must pass This on one side, when that upon the other, If thine intelligence right clearly heed." "Truly, my Master," said I, "never yet Saw I so clearly as I now discern, There where my wit appeared incompetent, That the mid-circle of supernal motion, Which in some art is the Equator called, And aye remains between the Sun and Winter, For reason which thou sayest, departeth hence Tow'rds the Septentrion, what time the Hebrews Beheld it tow'rds the region of the heat. But, if it pleaseth thee, I fain would learn How far we have to go; for the hill rises Higher than eyes of mine have power to rise." And he to me: "This mount is such, that ever At the beginning down below 'tis tiresome, And aye the more one climbs, the less it hurts. Therefore, when it shall seem so pleasant to thee, That going up shall be to thee as easy As going down the current in a boat, Then at this pathway's ending thou wilt be; There to repose thy panting breath expect; No more I answer; and this I know for true."

(12) It follows that we must allow contrariety to Quantity: whenever we speak of great and small, our notions acknowledge this contrariety by evolving opposite images, as also when we refer to many and few; indeed, "few" and "many" call for similar treatment to "small" and "great."

"Many," predicated of the inhabitants of a house, does duty for "more": "few" people are said to be in the theatre instead of "less."

"Many," again, necessarily involves a large numerical plurality. This plurality can scarcely be a relative; it is simply an expansion of number, its contrary being a contraction.

The same applies to the continuous , the notion of which entails prolongation to a distant point.

Quantity, then, appears whenever there is a progression from the unit or the point: if either progression comes to a rapid halt, we have respectively "few" and "small"; if it goes forward and does not quickly cease, "many" and "great."

What, we may be asked, is the limit of this progression? What, we retort, is the limit of beauty, or of heat? Whatever limit you impose, there is always a "hotter"; yet "hotter" is accounted a relative, "hot" a pure quality.

In sum, just as there is a Reason-Principle of Beauty, so there must be a Reason-Principle of greatness, participation in which makes a thing great, as the Principle of beauty makes it beautiful.

To judge from these instances, there is contrariety in Quantity. Place we may neglect as not strictly coming under the category of Quantity; if it were admitted, "above" could only be a contrary if there were something in the universe which was "below": as referring to the partial, the terms "above" and "below" are used in a purely relative sense, and must go with "right" and "left" into the category of Relation.

Syllable and discourse are only indirectly quantities or substrates of Quantity; it is voice that is quantitative: but voice is a kind of Motion; it must accordingly in any case be referred to Motion, as must activity also.

(42) In case the opposite of a thing is not known to us, because it has not as yet been discovered by or made known to us, nevertheless in such case we are fully justified in ascribing to the unknown opposite the qualities and characteristics diametrically opposed to the known opposite. The rule is this: "Whatever is affirmed of one of a pair of opposites must be denied to the other"; and " whatever is denied to the one, must be affirmed of the other." So true and infallible is this rule that it may be applied and employed as the basis of logical reasoning from the known to the unknown, for the purpose of discovering the latter.