While the period of the reign of the 10 Babylonian antediluvian kings is given as 432,000 years,* the duration of the postdiluvian Kali-yug is also given as 432,000, while the four ages or the divine Maha-yug, yield in their totality 4,320,000 years. Why should they, if fanciful and "extravagant," give the identical figures, when neither the Aryans nor the Babylonians have surely borrowed anything from each other ! We invite the attention of our occultists to the three figures given- 4 standing for the perfect square, 3 for the triad (the seven universal and the seven individual principles), and 2 the symbol of our illusionary world, a figure ignored and rejected by Pythagoras. Five Years Theosophy. HPB.

Every figure must be 7x (7 to the power of x); x varying according to the nature of the cycle in the subjective or real world; and every figure or number relating to, or representing all the different cycles from the greatest to the smallest -- in the objective or unreal world -- must necessarily be multiples of seven. SD1 36.

JC: All cycles not divided into the general average by the occultist are seen as septenary in division and also may be further multiplied as septenates, and this we are told by the Tibetan Master. Karma plays a part in all this obviously so. The ray periods given in AKSD reveal the living numeric rate governing the periods, these periods are not always plain to see or calculate in races and sub races, due to the obscure process of ray activity which lives out manifestation or pralaya in septenate an infinite number of multiples of the ray numeral which will obscure the numeric rate or value. But the ray number or sacred numeral is ever functioning and active. Regarding the average divisions summing a kalpa or grand period of 4,320,000,000 years it is interesting that the division is reached using the 432 numerical sequence and for no small reason. It is itself based on the 7 or compound number because, 4+3=7 which geometrically represent the Square and Triad, together with the symbol of duality the 2. Cipher 2 prefixes the sacred double cipher 25 which is appointed to our fourth order solar system and prefixes the 4th ray.

7x49= 343 and we know that this numbers the groups of constellations as calculated by the adepts. Multiples as used by the adepts, are the 7x7=49 divine mathematics and 7x49=343 multiple. HPB indicates that regarding the outer form and cyclic calculations such multiples of seven are always used in this our fourth order solar system. This should be considered and read in conjunction with Cyclic Will and Law of the Chohan Hilarion and the work of DK as well as HPB. The great white brotherhood under the Will of Sanat Kumara work precisely with the cyclic 49 year sweep of solar and ashramic inspiration and sharing manifesting in the 7x7=49 yearly group festival of ashramic decision and opportunity. The number seven is not only the number of man but also the universal multiple and number of universal division controlling ordered group expression under the law of affinity and karma upon the 49 sub-planes of the cosmic physical plane. 7x7=49 in one respect is the number of the group soul and may be multiplied or divided therein. Therefore we are shown a basic hierarchal building block, the basic cycle of 49 and how it is determined and worked with and stepped down as the divine impulse of the WILL registered and contacted by Sanat Kumara and the Chohans every 49 years as the universal impulse of cosmic and solar sharing of universal Will, under cyclic law.

Regarding 7x7 = 49 logoi, we find, as HPB indicates, that "classes of Rishis" appear "seven and seven" equalling forty nine entities. This should be considered by students regarding all "classes" of logoi or Rishis. Individual constellations of x 7 stars known as 'systemic wheels,' are divided into 343 groups accordingly by degree of Order and Magnitude which is a formula of 49 x 7 as used by the Adepts, or otherwise 7 to the 3rd power. The formula of 10 to the 3rd power is of great moment incidentally and has been considered as the formula for the turning of the 3rd key AKSDP "1,000 is the number ten to the third power, and therefore the number 7,000 is also symbolical.SD1 36" and fits the ray periods and suggestions given by DK and HPB. We might ask, as maths is an exact science, can this tell us anything? 7 to the 3rd power reveals to us the truth that the Rishis or great solar logi appear 7 x 7 = 49 forming seven constellations of seven stars each thus occultly a group multiple to the 3rd power of 7 according to "class" or "magnitude" of the group of Rishis concerned. HPB gives us a hint of a formula being 7 to the power of x, x being the unknown quantity according to the nature or type of the cycle in the subjective or real world.

The key to understanding all the many and varied kinds of cycles is yet to be known but must be the key mentioned by DK which unlocks all the mathematical cycles. He explains that there are many cycles of great entities which "can be extended into septenates and into an infinity of multiples of seven." However, HPB says that the multiple of seven used for divine calculations has for the purpose of ordinary calculations no sense or meaning. We must therefore take into account the following from HPB. ""The Three, the One, the Four, the One, the Five" (in their totality -- twice seven) represent 31415 -- the numerical hierarchy of the Dhyan-Chohans of various orders, and of the inner or circumscribed world.".

This number accounts to the mathematical value of Pi the ratio of the diameter to the circumference of a circle as 1 to 3.1415, and here were are given an exact description of its origin. It represents the sacred 7 as the twice seven or 2x7=14 or the occult swastika containing the 31415 or astronomical Pi otherwise understood as the number of the circle or inner circumscribed world from which the divine logos manifests and in so doing makes possible all divine creation and all Elohim or orders of Dhyan Chohans. The 1 or line diameter originating from the point within the circle which has neither limit or boundaries and is the parabrahmic cause of the circle or circumference which together making the decad or perfect 10 is the sum of all the Kosmos. The first un manifested Logos is simultaneous and one with the diametrical line drawn across the diameter of the Circle.

These create with endless possibility "a Decad with the primordial Triangle which originated it" along with the septenary of the rays thus making the perfect Ten with all numbers contained therein. Therefore the Line, the Triangle, the Pentacle, the second Line and the Cube or 13514 when bisected by the numberless central point or synthetic logos creates simultaneously the diameter or feminine principle becomes the sacred manifestation or creation of the divine numberless one composing the self moving sacred ciphers thus the self moving action or motion becomes 31415, or a triangle, a line, a cube, the second line, and a pentacle manifesting or descending as the chronologers or keepers of seasons and cycles, the divine septenate the7 ray lords or great breaths before concealed in Sarvatma yet emanating from and subject to the great un manifest 1st logos as the triad, the line, the quaternary, the line and the five pointed star of Mahatic energy, manas/man. Thus do the geometrical self moving figures 13514 or 1,3,5,1,4 or 2x7=14, become the numerical or mathematical 3.1415 the compound of which is 7.

"The sparks mean the Rays as well to the lower intelligence as to the human sparks or Monads. It relates to the circle and the digits, and is equivalent to saying that the figures 31415 as given on pages 90 and 91, are all subject to the circumference and diameter of the circle". Collected Writings X 398/9. HPB.

JC: Taking the formula given in the Secret Doctrine for LIGHT which is John A Parker' true or perfect calculation of Pi in accordance with the occult doctrine as being 20612 to 6561which gives an accurate ratio of Pi as being 3.1415942691662856271909769852157 exactly, as the numerical value and formula of the divine logos, Alohim or God. At the beginning of each new cycle of 4,320,000 years the Seven great breaths initiate each new cycle by giving impetus to it. We do know that the numbers, 4, 3, 2 and 1 are embraced in the Yugas and therefore in all larger average time periods. These numbers equal the sum of 10 or the perfect ONE/NAUGHT or the line/diameter and the circle/circumference. 3+4+3= 10 which is the sacred Decad or universal number of 7 to the 3rd power upon which all is built and is the symbol of the ten sacred numerals which governs the zodiac of ten and issues forth as the ten sacred numerals of the seven rays 1+5+9+2+5+3+ 5+1+5+7 = (43) = 7 the compound number reducing to the 4+3=7 of the seven great ray breaths.

The white lodge of our 4th order scheme meets 4 times in conclave every century with the most important being the first quarter or first 25 years. The 100 year sounding of the OM by Sanat Kumara is done at that time. In our first Ray Monad 4th order scheme this timing is of importance with the 4 posing huge significance. We of course must correlate the 4th fundamental in with this, the [1+5+9+2+5+3+5+1+5+7 = (43) = 7]. It is Man the quaternary and the divine triad or 4+3=7. This formula contains the rates of periodic ray manifestation as understood and worked with by the great white lodge and as exactly given by DK and presents us with a huge field of study into the occult mysteries and plan of the hierarchical masters. In considering Pi we are told that 3+1+4+1+5= 14 = 7 as the compound number. 14 = seven universal and seven individual principles of the 7 rays.

31415 = 311,040,000,000,000 years through exchange (or "permutation") of numerical elements of this set. This may be extended into septenates, for instance Constellations of x 7 stars divided into groups of 343 is a formula of 49 x 7 or otherwise 7 to the 3rd power.

To be then extended into septenates and into an infinity of multiples of seven:

01 Circle+Diam > 10 Sacred Numbers 7 rays

13514 > Pi = 1 : 3.1415927 = 14 > 1+5+9+2+5+3+5+1+5+7 = (43) = 7

It is the number 1 and number 7 as indicated by H.P.B. which begins in the esoteric calculations with the first manifested principle or number one if we count from above or the alpha number, and then the seventh when counting from below, or from the lowest Principle or omega number. HPB said "1,000 is the number ten to the third power, and therefore the number 7,000 is also symbolical." The numerical values attributable to rays 1 to 7 begin with 1 to the third power equalling 1000 or the alpha number. 7 is symbolical and equates within the formula equalling 7000 or the omega, and therfore encompasses the beginning and the end. Five other rays are calculated using the same formulaic process by S.D.P. as follows:

I. 10 x (1) = (10) x 10 = (100) x 10 = (1,000

II. 10 x (5) = (50) x 10 = (500) x 10 = (5,000)

III. 10 x (9) = (90) x 10 = (900) x 10 = (9,000)

IV. 10 x (2.5) = (25) x 10 = (250) x 10 = (2,500)

V. 10 x (3.5) = (35) x 10 = (350) x 10 = (3,500)

VI. 10 x (1.5) = (15) x 10 = (150) x 10 = (1,500)

VII 10 x (7) = (70) x 10 = (700) x 10 = (7,000).

[1+5+9+2+5+3+5+1+5+7 = (43) = 7] 3rd key AKSD, SDP.

JC. Key to the Hebrew-Egyptian Mystery in the Source of Measures: J. Ralston Skinner. An expounding on key points.

The numbers 3 and 4, in their blending of 7, as those of 5, 6, 9, and 10, are the very corner-stone of Occult Cosmogonies. J. Ralston Skinner. Source of Measures. The Secret doctrine. HP Blavatsky.

Three gravitating bodies of equal magnitude revolving together, their relative motion shall be 4/3 or 1.3333333333333333333333333333333 of primary circumference of circle. The Parker form of area of square 6561:5153 area of inscribed circle or 5153x4 = 20612. 20612 to 6561 is 31415 to one [3.14159] or otherwise, Alhim, God or Light.

His general form for calculating of time periods using his "problem of three revolving bodies" with factors 4 and 3 in the formula is:

20612 x 4/3 = 27,482.666666666666666666666666667 x 4/3 = 36,643.555555555555555555555555556.

We will clearly see a further mention of the 4 and 3 as being highly important with regard to the calculation of time periods, with 3 being the "numerical integral relation" of such just as the triad is the natural originator of all plane shapes. 3. expressing the value of the circle to the square and cube with the difference expressed at the sixth decimal point. The 4 and 3 are numerical factors and key to the computation of cycles and incidentally of architectural construction. We should here recall that numbers are colour and sound and in ancient times it was the use of these that enabled the priest kings and adepts to construct the pyramids according to the mathematical formulas derived from and based upon 20612 to 6561with the latter being the area of the square, and together as a Pi value in its original and occult form decipher the "Quadrature of the Circle". The construction of the great pyramid was a monument to this ratio and its fractions and uses such as the sacred cubic and is the "source of measures" and the mathematical/geometrical source by which deity constructs and geometricises. The circle is the primary shape of all shapes occultly understood and contains or circumscribes the triangle and the cube. They are opposites yet hold a numerical and integral relation to each other as well as one geometrical. DK tells us that the sacred planets are composed of triangles whereas the Sun is formed of interlaced circles and the non sacred planets are of squares. This makes complete sense does it not? The law of separation through motion bisects the square into two triangles to create the sacred "star of life" or planet thus ending the "rule of the square".

Therfore, the relative motion of "three gravitating bodies of equal magnitude, revolving together, their relative motion shall be as four to three, or one and one third of one primary circumference", [see 'source of measures, J. Ralston Skinner]. Where forces, distances and velocities of gravitating bodies are disproportionate or unequal, their relative magnitude and relative motion remains always in exact proportion to the "standard of measure" of 4/3 under the law of attraction and repulsion, Einstein 's law of relativity and as expressed also by time as speed and distance of orbital motion and path. This numerical form of Parkers stands as 6561 : 5153 x4= 20612 and "none other." This is of course in accordance with the mathematical laws of nature and deity as Ralston makes clear. I am eager to point out that the equation includes the indication of time periods relating to the computation of orbital cycles for one. The formula factor of 4/3 in some form should hold good for the calculating or figuring of much greater time cycles as HPB also indicates as she invites our attention to "4 standing for the perfect square, 3 for the triad" as 432,000 yields 4,320,000 years with the 4 the 3 and the 1 composing, even if invisibly, all other time periods as is stated in the Secret Doctrine. Let us for a moment note in AKSDP the ten sacred ciphers of the seven rays equate to 43 and compound to 7. 1+5+9+2+5+3+5+1+5+7 = (43) = 7. I find this point of great moment and highly indicative of the afore discussed "standard of measures". There is no doubt in my mind that ten sacred ciphers sum the standard of measure as is used by occult numerology in nature and under mathematical law. In other words the 3rd astrological key to the seven ray periods and cycles is formed on the same basis of the geometrical and numerical 4 and the 3, the key measure which is discussed and demonstrated by Helena Blavatsky, Dwhial Kule, John A Parker, J. Ralston Skinner and others.

"1st ray: 10 x 1 = 10 x 10 = 100 x 10 = 1000"*

1000 x 4/3 = 1333.3333333333333333333333333333

x 4/3 = 1777.7777777777777777777777777778

According to esoteric numerology DK suggests ten year cycles of development with seven of learning and three of application. Here we will see that the 1, 10, 100, or 1000 year cycles follow an outgoing period of 7 and a ingoing period of 3 relative to the length of the cycle. This is unique to ray 1 and using here the formula of 1000 x the key factors of twice 4/3 as a key measure we can see how it reveals in this instance the numerical cycle unique to it. This compounds the fact that all rays ciphers are substantiated by and multiply to 43. We can clearly see the 1-7 and the 1-3 outgoing and ingoing cycles. Of course, the whole 3rd key rests on the formula of HPB of the 1st ray being "10 to the 3rd power" which in itself holds significance to 1 and 3 for the 7.

"Cycles of Ray 1

Sacred Cipher 1

Outgoing period: 70 years duration

Comprised of 7 sub-ray periods of 10 years each.

Ougoing Peak reached: 70 years

Ingoing Period: 30 years duration." *AKSDP.

"2nd ray: 10 x 5 = 50 x 10 = 500 x 10 = 5000"*

5000 x 4/3 = 6666.6666666666666666666666666667

x 4/3 = 8888.8888888888888888888888888889

First I would like to remark that 8 is the number of the Christ force, the Bodhisattva and it is of no mere chance that it recurs here as a factor of the sacred number 5 of the 2nd ray. In this 2nd ray system it stands to govern all spiral-cyclic motions and incidentally rules our second ray hierarchy and the soul or Christ consciousness. The 6 is the 2nd ray driven into materialism and form and is the number of Space the great entity and symbolises the Christ line of idealism though of a material nature. 8+6= (14) = 5. There are 31 recurring eights making the 3-1-8 or gnostic value of Christ. DK states, "number 8 inaugurates ever a new cycle, following after the number 7." This is verified in the formula for the 2nd ray of love/wisdom, with the sacred prefix "5".

"Cycles of Ray 2

Sacred Cipher 5

Racial ray period: 500 years

Peak emergence: 250 years

Ingoing cycle: 250 years" *AKSDP.

"3rd ray: 10 x 9 = 90 x 10 = 900 x 10 = 9000"*

9000 x 4/3 = 12000

x 4/3 = 16000

We have here simply 1+2= 3 of the ray of active intelligence or 3x3=9 along with the 1+6= 7. 9 is the number of initiation of which the 3rd is the first major hierarchical one. 6 is the number of form. Note the 45 of outgoing and ingoing equals the sacred 9. 6+2= 8 +1 = 9. 20612 is the Mahatic LIGHT of the third logos of intelligent activity.

"Cycles of Ray 3

Sacred Cipher 9

Period: 900 years
Outgoing peak: 450 years.

Ingoing cycle: 450 years." *AKSDP.

"4th ray: 10 x 2.5 = 25 x 10 = 250 x 10 = 2500"*

2500 x 4/3 = 3333.3333333333333333333333333333

x 4/3 = 4444.4444444444444444444444444444

We have represented the most occult of symbols being the tau or cross as the 4 crossed by the 3 indicating the source of measures and 4+3=7. The cube within the circle unfolded becomes the cross with the circle at the head. Man is thus "welded to the cross in ancient use" as 133/355 and 6561/20612 as the triad and the quaternary crucified on the cross of matter and qualified and conditioned by the 4th ray of harmony through conflict which incidentally is associated with the seventh or violet ray. The 4th ray is placed mid way at the cross point between 1 and 7 yet containing the 7. It symbolises the occult factors of 4 and 3 understood as a source measure or factor numbers in calculating the esoteric and abstract quadrature of the circle or harmony through conflict and ultimately the Pi value of 20612 to 6561 or LIGHT and indeed gives "man" an astronomical value be it human or logos. Zodiacal cycles based on 2,500, 25,000 and 250,000 years are prefixed by the sacred dual ciphers 25 for this fourth order system with the equatorial rotation of the Sun per 25 days, all of which factor the ten sacred numbers of the seven rays 1+5+9+2+5+3+5+1+5+7 = (43) = 7.

"Cycles of Ray 4

Sacred Cipher 25
Period: 250 years
Outgoing peak: 125 years." *AKSDP.

The constant pi, denoted p, is Greek for perimeter and defined as the ratio of a circles circumference divided by its diameter indicating the occult 1 or ONE self moving from the circle or numberless naught becoming the 3 or triad and the compound 7 or seven. The circumscribed ring pass not issues forth seven ray energy in circular, spiral cyclic motion. Pi is an infinite decimal and has an infinite number of recurring digits unlike other formulas, never repeating any pattern and indicating the infinity and multi dimensionality of the great geometrician the Kosmic Logos. JC.

1585. Adriaen Anthoniaz [Peter Metius] (1527 - 1607) (France) 355/113 (3.141459292...). Rediscovered this Chinese value, also known to the Japanease, when he was obliged to seek a still more accurate value than 3 1/7 to disprove of Van der Eycke. He proved that Pi lay between 377/106 from which he concluded that the true fractional value would be obtained by taking the mean of the numerators and the mean of the denominators of these fractions, which gave 355/113. The "rediscovery" was perhaps a lucky guess. The value was published in 1625 by his son. Pi. A Source Book. By Lennart Berggren, Jonathan M. Borwein, Peter B. Borwein.

JC: The Area or Circumference of a circle. [Parker the perfect calculation, Metius the imperfect one].

The kabbala is a "whole series of developments based upon the use of geometrical elements; giving expression in numerical values, founded on integral values of the circle" (one of the seven keys hitherto known but to the Initiates), discovered by Peter Metius* in the 16th century, and re-discovered by the late John A. Parker.† Moreover, that the system from whence all these developments were derived "was anciently considered to be one resting in nature (or God), as the basis or law of the exertions practically of creative design"; and that it also underlies the Biblical structures, being found in the measurements given for Solomon's temple, the ark of the Covenant, Noah's Ark, etc., etc.,—in all the symbolical myths, in short, of the Bible.

And what are the figures, the measure in which the sacred Cubit is derived from the esoteric Quadrature, which the Initiates know to have been contained in the Tetraktis of Pythagoras? Why, it is the universal primordial symbol. The figures found in the Ansated Cross of Egypt, as (I maintain) in the Indian Swastika, "the sacred sign" which embellishes the thousand heads of Œesha, the Serpent-cycle of eternity, on which rests Vishnu, the deity in Infinitude; and which also may be pointed out in the threefold (treta) fire of Puraravas, the first fire in the present Manvantara, out of the forty-nine (7 x 7) mystic fires. It may be absent from many of the Hindu books, but the Vishnu and other Puranas teem with this symbol and figure under every possible form, which I mean to prove in the SECRET DOCTRINE. The author of the Source of Measures

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* [Probably Adriaan A. Metius is meant here. Vide Bio-Bibliogr. Index under METIUS.—Compiler.]
† Of Newark, in his work The Quadrature of the Circle, his "problem of the three revolving bodies" (New York: John Wiley and Son, 1851). Collected Writings VII 293. HPB.

Nevertheless, what the learned author has discovered and proved mathematically, is wonderful enough, and sufficient to make our claim good: namely, that the figures and 3+4= 7, are at the very basis, and are the soul of cosmogony and the evolution of mankind.
To whosoever desires to display this process by way of symbol, says the author speaking of the ansated cross, the Tau of the Egyptians and the Christian cross—

 . . . it would be by the figure of the cube unfolded, in connection with the circle, whose measure is taken off onto the edges of the cube. (The cube unfolded becomes, in superficial display, a cross proper, or of the tau form, and the attachment of the circle to this last gives the ansated cross of the Egyptians, with its obvious meaning of the origin of measures.)* Because, also, this kind of measure was made to coordinate with the idea of the origin of human life, it was secondarily made to assume the type of the pudenda hermaphrodite, and, in fact,

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* And, by adding to the cross proper + the symbol of the four cardinal points and infinity at the same time, thus , the arms pointing above, below, and right, and left, making six in the circle—the Archaic sign of the Yomas—it would make of it the Swastika, the "sacred sign" used by the order of "Ishmael masons," which they call the Universal Hermetic Cross, and do not understand its real wisdom, nor know its origin. [H.P.B.] Collected Writings VII 294. HPB.

To quote our friend and much respected brother for the last time, since he says that. . . . . our [Aryan] philosophers have associated seven occult powers with the seven principles [in men and in the kosmos] or entities above-mentioned. These seven occult powers in the microcosm correspond with, or are the counterparts of, the occult powers in the macrocosm. . . .*

—quite an esoteric sentence—it does seem almost a pity, that words pronounced in an extempore lecture, though such an able one, should have been published without revision.
H. P. BLAVATSKY. Collected Writings VII 300.

Circular measures taken off on to the edges of a cube. Cube unfolded is in display a cross of the tau form, or Egyptian form, or of the Christian cross form. Circle attached to the first, gives the ansated cross of the Egyptians. Numbers 3+4 =7, and 6+1 =7, days in the circle of the week, as 7 lights of the sun. So also, as the week of seven lights give origin to the month and year, so it is the time marker of birth, The cross form being shown, then by the connected use of the form 113 : 355, the symbol is completed by the attachment of a man to the cross. Keys to the Hebrew and Egyptian Mysteries in the Source of Measures. Extracts. J. Ralston Skinner. 1894.

"The Three, the One, the Four, the One, the Five" (in their totality -- twice seven) represent 31415 -- the numerical hierarchy of the Dhyan-Chohans of various orders, and of the inner or circumscribed world.** When placed on the boundary of the great circle of "Pass not" (see Stanza V.), called also the Dhyanipasa, the "rope of the Angels," the "rope" that hedges off the phenomenal from the noumenal Kosmos, (not falling within the range of our present objective consciousness); this number, when not enlarged by permutation and expansion, is ever 31415 anagrammatically and Kabalistically, being both the number of the circle and the mystic Svastica, the twice seven once more; for whatever way the two sets of figures are counted, when added separately, one figure after another, whether crossways, from right or from left, they will always yield fourteen. Mathematically they represent the well-known calculation, namely, that the ratio of the diameter to the circumference of a circle is as 1 to 3.1415, or the value of the (pi), as this ratio is called -- the symbol being always used in

[[Vol. 1, Page]] 91 THE IMMACULATE CONCEPTIONS.

mathematical formulae to express it.

This set of figures must have the same meaning, since the 1 : 314,159, and then again 1 : 3 : 1,415,927 are worked out in the secret calculations to express the various cycles and ages of the "first born," or 311,040,000,000,000 with fractions, and yield the same 13,415 by a process we are not concerned with at present. And it may be shown that Mr. Ralston Skinner, author of The Source of Measures, reads the Hebrew word Alhim in the same number values, by omitting, as said, the ciphers and by permutation -- 13,514: since [[hebrew]] (a) is 1 : [[hebrew]] (l) is 3 (or 30); [[hebrew]] (h) is 5; [[hebrew]] (i) 1 for 10; and [[hebrew]] (m) is 4 (40), and anagrammatically -- 31,415 as explained by him.

Thus, while in the metaphysical world, the circle with the one central Point in it has no number, and is called Anupadaka (parentless and numberless) -- viz., it can fall under no calculation, -- in the manifested world the mundane Egg or

Circle is circumscribed within the groups called the Line, the Triangle, the Pentacle, the second Line and the Cube (or 13514); and

when the Point having generated a Line, thus becomes a diameter which stands for the androgynous Logos, then the figures become 31415, or a triangle, a line, a cube, the second line, and a pentacle. SD1 91.

JC: 13514 becomes 31415 upon generation of the diameter or Kosmic logos in generation, action or manifestation. This ratio of the diameter to the circumference of a circle is as 1 to 3.14159, which becomes, using this formula loosely understood upon ratio and division, 311,040,000,000,000 years, or a 100 year age of brahma.

31415 = 311,040 through exchange (or "permuting") elements of this set. To vaguely understand this formula for the computation of cycles we need to comprehend that In the general sense permutations are sequences where each element or number occurs at most once, but that not all elements, in this case numbers, of any given set or periodic cycle needs to be used by omitting as necessary any given numeral or replacing with a nought in the sequence, as I deduce or decipher it, albeit without cracking the actual Law of Cycles, a given set or cyclic period may be calculated. All that may be alluded to is that the Law of Cycles, at least in some part, is based upon combinatorics or permutations. In mathematics a cycle is a permutation and there is no reason to exclude the thought that in the case of occult cycles there are combined with this the use of septenate multiples also, as HPB and DK indicate with x defining a formula or power, which as HPB states, varies [SD1 36] according to the cycle involved. Thus in order to define the cycle or its length one needs to understand which power applies to which cycle as well as how the process of permutations operates as possibly combined with this. Crucially though, Master DK tells us that these periods as given in the Secret Doctrine by HPB only "strike the general average" and so those permutation may well only be used for striking such periodic averages whilst the true and occult method lies entirely with the extension of septenates [to the power of x] for the subjective and real world with infinite multiples of seven. Thus only the initiated are given to understand or comprehend the true cycles as DK and HPB indicate. Therefore the true comprehension comes through the knowledge of septenary cycles and their periods of duration. This is a loose definition of the law of cycles as I understand it in some small part.

JPC.

7/8/08.