Chapter XI
Plato said in regard to the Elements of the Universe: “God fashioned them by form and number.” We have had something to say about Form but have touched very little upon Number. It will be well for use to make a few observations in the light of the Forms we have reconstructed.
I shall have little to say in regard to the Numbers attributed to the ordinary Qabalistic Plan of the Sephiroth, these having been dealt with in “Q.B.L.” and elsewhere. It is merely necessary to recapitulate as follows:
The simple twodimensional figure consists of 10 Sephiroth; 10 being the sum of the numbers from 1 to 4. This importance of this lies in the Fourfold Nature of the Ineffable Name which is the Formula of the whole System. There are 22 (2 + 2 = 4) connecting links or Paths. These consist of 3 + 7 + 12, and correspond to the Elements, Planets, and Signs of the Zodiac. In all we have 32, called, in relation to this System, the 32 Paths of Wisdom, representing the whole figure. One of the special virtues of this number is that it represents the coalescence of Macroprosopus and Microprosopus in the Divine Name AHIHVH, and thus shows the connection between Kether—The Highest Crown—and the Nine lower Sephiroth, which emanated from it. When we allow this simple figure to expand in one direction, as previously explained, we find, since Malkuth remains One and the same throughout, that the Second Tree contains 19 Sephiroth, which is a prime number, reduces by addition to 10. Likewise the Third Tree consists of 28 Sephiroth, a Perfect Number which again reduces to the original 10 and therefore to 1 or Unity. The Fourth Tree contains 37 Sephiroth, another prime number reducing to 10. The Fifth gives 46 which reduces to 10, while the Sixth represents 55 which not only does this but is the Sum of the Numbers from 1 to 10. And since the number of the Sephiroth will be increased by 9 at every progression, their total, at each step, will always reduce to 10 by addition.
The 22 Paths of the first figure will increase by 20’s to 42, 62, and so on, since two of these—Beth and Daleth—retain their own nature indefinitely.
Thus the progressions of the whole Tree will be from the original 32 to 61 and so on; 29 being added each time.
We may now consider the outstanding features of the figure when shown expanding in Six directions as the Snowflake. Since Netzach and Hod now combine we have in all 49 Sephiroth in the unprogressed figure. This, it may be remarked, is a distinctly Venusian Number (that of the Intelligence of Venus) and the Square of Seven. It reduces to 13, the number of Unity and Love. The number of Paths in this figure is 126 (a number attributed to two important Names of God) and this, added to 49, gives 175 as the total number of Sephiroth and Paths. This, it may be remarked, is the Number of the Spirit of Venus. It represents the sum of the numbers from 1 to 49 divided by 7, and it again reduces to 13 by addition.
When we consider the progressions of this Sixfold Figure we find the Sephiroth increase by 48 each time, Malkuth remaining single. This is of interest because 48 is the numeration of KVKB, the Sphere of Mercury, and we find the particular feature of this Sixfold plan is that the Spheres of Venus and Mercury are forever united. I have always considered this word Kokab to be in some way connected with the words Khu and Khabs; Khu being the Magickal entity of man, and Khabs meaning a Star. Considering this arrangement is as a Sixfold Star and the uniting of the Paths and Spheres of Venus and Mercury as Love under Will, this will be interesting to Students of the New Aeon.
The number of Sephiroth in the Second progression is therefore 49 + 48 = 97. This is another prime number and that of the Archangel of Netzach. It has many other correspondences, one of which is “An architect.” The next progression gives us 145 which, according to the old arrangement, corresponds to the 13 Paths of the Beard of Microprosopus. But the Fourth progression produces 193, another prime number of particular importance since it is the Number of Sephiroth in the unprogressed but complete threedimensional solid which forms the Dodecahedron. 193 also reduces to 13, which, it may be remarked, is the number of Sephiroth in the single prismatic solid.
The 126 Paths of the sixfold plan progress by adding 120 each time (since the Paths of Venus and Mercury are combined) and this is a very important Number to the Rosicrucian, and on account of its representing the God ON. Other interesting numbers can be traced out by the Student who possesses a copy of the Sepher Sephiroth. The whole figure progresses by the addition of 168 (the additional 48 Sephiroth and 120 Paths) and this is a very important number, being that of the Parentes Superni.
We may now engage in a brief consideration of the Solid Figure. The first simple form contains 13 Sephiroth, which number gives it the Seal of Unity. This solid also contains 13 parts which produces the angles representing the Paths. Thus it represents 26, the Number of the Ineffable Name.
When this solid is extended in 20 directions (20 is the full numeration of IVD, the first letter of the Name spelled in full) 193 Sephiroth are produced. These added to the 260 (13 X 20) parts give 453, a number reducing to 12 which is the number of pentagonal faces on the 20pointed dodecahedron. But, which is perhaps of greater interest, this number 453 is that of NPSh ChIH, the Animal Soul in its fullness; i.e., including the Creative Entity or Chiah. The importance of this will be plain when we remember that the total number of Sephiroth and Paths in the Whole Solid is—as has been shown in Chapter VII  775 and this, added to the 260 parts or sectional solids, gives 1035, which is the sum of the numbers from 1 to 45. Now 45 being the numeration of ADM (Adam) indicates that we have once more shown the Qabalistic ADAM in all his Spiritual and Animal fullness and that he once again contains the sum of all his parts.
Also the 20 points and 12 faces of the dodecahedron equal 32, the original number of the Paths of Wisdom.
One other point seems worthy of notice in this connection. The SepherYetzirah makes a very strong feature of TEN Sephiroth (ten and not nine, ten and not eleven), and it may be assumed that we have departed entirely from this fundamental conception.
But it is also true that the ancient Qabalists considered the Three Veils of the Negative—AIN, AIN SUPH, AIN SUPH AUR—as depending back from Kether; thus, although these are unmanifest, the whole scheme was based on 13. It may be further remarked that there are Seven Sephiroth below the Supernal Triad and the Three unmanifest Ideas above, so that we have, as it were, 7 + 3 = 10, 10 + 3 = 13; the 10 standing midway between the 7 and the 13.
Now it has been pointed out that the progressions of the single Tree are made by the addition of nines, so that each number produced reduces to 10 when we add the digits. In this case, then, the essence of the original basis remains. Nor is this basis lost when we consider the Sixfold twodimensional figure, the Single Prismatic solid, and the Twentyfold solid and their progressions, although it is more deeply concealed in these instances.
All these start from a basis of 13. The Single solid has 13 Sephiroth and increases by the addition of 12 at each progression. Thus the series is 13, 25, 37, 49, 61, 73, 85, etc. If we reduce these by addition (leaving the first as it stands) we obtain 13, 7, 10, 13, 7, 10, 13, etc. Now this is the series we noticed above in regard to the original Tree—the 10 Sephiroth with three Veils above the Supernal Triad and 7 Spheres below it. And this series recurs with every three progressions, so that since 7 + 10 + 13 = 30, the average is still, in essence, 10 throughout. And when we consider the Sixfold Plan we start with 49 which reduces to 13, and progress by adding 48. Now 48 being 4 times 12 we find we are running in a series which coincides at certain definite points with the previous one, and the same peculiar rule is noticed in regard to our reductions of digits. Thus, 49, 97, 145, 193, 241, 289, 337, etc., etc., reduce to 13, 7, 10, 13, 7, 10, 13, etc. as before.
The same is true of the complete solid. We begin with 193 which reduces to 13, and progress by adding 192; which in this case is 4 times 48. Therefor we find the same underlying law if we consider 193, 385, 577, 769, 961, 1153, 1345, etc., with the exception of the one instance of 769, which reduces to 22 (the number of paths) on its way to its final reduction to 4 without first forming 13 as in all the other cases. And we of course find that every fourth progression of one series coincides with the number produced by one of the others. Thus the fourth progression of the Prism gives us 49 which is the basic number of the Star. The fourth progression of the Star gives us 193, the basic number of the complete solid, and so on. In fact every progression of the Star will give a number which is that of some progression of the Simple Solid, and every progression of the Complex Solid a number equal to some progression of both the Star and the Simple Solid, and the numbers common to all will always reduce to 13 (or 4).
A word now in regard to the proportion of the various parts of our figures. We found in constructing the first simple plan of the Sephiroth and Paths that the proportion of the Diameter of the Sephiroth to the Width of the Paths was very important, especially in regard to the Progressions.
I noticed recently that in his footnotes to the new edition of Eliphas Levi’s Transcendental Magic, Mr. A. E. Waite makes the following remarks, evidently with the intention of discrediting Levi: “In the Tree of Life KETHER, the Supreme Crown, abides above CHOKMAH and BINAH, forming with these the Supernal Triad, below which are CHESED and GEBURAH. It must be said further that the Tree comprises three triangles, beneath which is MALKUTH. There is nocircle, as Levi suggests, except in the accidental sense that the names and titles of each Sephira are inscribed within this figure.”
Without some idea of a Circle or Sphere, if only to represent the Absolute or the Universe, one can hardly conceive of any Qabalistic Scheme at all; and that all the Qabalists have merely used the Sephiroth as convenient receptacles for names and inscriptions while giving to the Paths any semblance of reality, seems to me rather puerile.
However, since the very Points representing the Centers of the Sephiroth in any properly proportioned “Tree” are produced by the original generating circles, we may leave aside Mr. Waite’s remarks and consider the matter as if the Sephiroth were Circles and the Paths Lines.
In the construction of the Tree we commence with 4 generating circles. These may be of any desired size, but by their means we obtain the Centers of the Ten Sephiroth.
The logical diameter of each Sephiroth will be found to be onefourth of that of the generating circles. This makes the length of the short Paths—such as Aleph—exactly equal to the diameter of each Sephiroth.
Next, in order to discover the logical width of the Paths we should examine the structure of the Tree where the five Paths from above unite in Tiphereth and the three proceed from below that sphere. It will be noticed that the natural division of the circle will be into 12, as this will make all the Paths the same width and leave a space equal to the width of one path between the lower ones. Thus the width of each Path should be onehalf the radius of the Sephira. (The greatest possible width without the Paths conflicting with one another above Tiphereth.)
When it comes to the progression of the Trees we shall then find that the third will produce Sephiroth equal in diameter to the original generating circles, while the width of the Paths of the third progression will be exactly that of the diameter of the Sephiroth of the first Tree.
A glance at the Colored Plate will show how exactly all the details fit in if this plan is adopted; even in the case of the fourfold division of Malkuth the progressed Paths exactly coincide with the diagonals. (See Plate A.)
It should be remembered, however, that all our measurements are made from center to center of the Sephiroth.
As a further check on the correctness of the size of the Sephiroth we find that a Vesica constructed upon the Path from the center of Chesed to that of Geburah, having a length from Kether to Yesod, will exactly touch the circumferences of Chokmah, Binah, Netzach, and Hod.
Our final summary will deal with the proportions of the whole figure as based on those of the Vesica Piscis. We have shown the importance of 15 to 26 (the proportions of the Vesica) in relation to the sacred Names IH and IHVH. The Student may consider for himself such further proportions in this series as 30 to 52, 60 to 104, 120 to 208, 240 to 416. The last of these is of peculiar interest for 240 is NTzNIM, Prima Germina, and 416 is HRHVR, meaning Thought or Meditation. Again the next proportion, 480 to 932, is important. 480 is LILITh and 932 is OTz HDOTh TVB VRO, The Tree of Knowledge of Good and Evil. This is surely a valuable correspondence worthy of study.
But there is another set of proportions in connection with the Vesica, viz.: 30 to 52. 30 is the Letter of Libra—Balance; 52 is the numeration of ABA VAMA (Father and Mother), AIMA (The Supernal Mother—fertilized), and of BN (The Son: Assiah’s “Secret Nature”). The correspondence between these and Balance is an interesting one.
Further we may use 52 to 90, for 90 is SVD HVVG, The Mystery of Sex. This, as applied to ABA VAMA, AIMA, or BN leads to ideas suitable for the highest “meditation” about which we should be “very silent.” (Strangely enough, as I wrote this I noticed another correspondence, for ZMH, Meditation, adds to 52, and DOMM, Very Silent, adds to 90. I shall therefore take this as a hint and pass on.)
The next proportion 90 to 156 is of even deeper significance for here we find the relation between “The Mystery of Sex” (90) and BABALON (156) The Victorious Queen. (See XXX Aethyrs: Liber CDXVIII). And the very next progression 156 to 260 gives us a relation between BABALON (156) and I.N.R.I. (270). Enough has been said to indicate to the Adept that a study of these proportions is well worth while.
But, so far we have been dealing with the actual proportions of the Vesica, and we have not mentioned those of the complete Tree of Life itself. Those of the Vesica being as 26 to 45 we see the proportions of the Tree must be 26 to 60, or, since we can divide by 2, we may put them at 13 to 30. Here we enter upon the consideration of our basic number 13 (Unity and Love) in right relation with “Balance.” For “Equilibrium is the Basis of the Work.”
We again obtain an interesting series of proportions, 13 to 30, 26 to 60, 52 to 120, 104 to 240, 208 to 480, 416 to 960, etc., but these will again be left to the consideration of the Student for we have yet to deal with a greater Mystery.
If 13 to 30 is the exact width and height of the twodimensional figure of the Tree of Life, what will be the proportions that will give us the correct angle of the Supernal Triad in order to change this to a Solid? The present angle is 120 degrees, the interior angle of the Hexagon; what proportion will give us the interior angle of the Solid Pentagon by which Kether, Chokmah, and Binah take their places each touching the circumscribing SPHERE?
This final revelation, only made to us on May 30th, 1925, yet necessary to the completion of our treatise, has come as the Seal of the Supreme upon our Work. It is not possible to enter into the proper consideration of the importance of this discovery in relation to the Magical lifework of the Author and to the Mysteries of the New Aeon. For the present, therefore, we simply state this proportion to be as THIRTEEN is to THIRTYONE.
13 to 31 gives the exact angle of 108 degrees necessary to the building up of our solid, the additional part being used to raise the Point of Kether to the Pinnacle of the Solid.
But let us examine the progressions of this proportion as before. We obtain: 13 to 31, 26 to 62, 52 to 124, 104 to 248 and 208 to 496. This last, be it noted, is the Fifth progression.
Now let us remember that the Fifth Progression of Malkuth as an expanding Sphere is the one which First embraces the Kether of the First Tree (and the Dodecahedron formed by the Tiphereths of the Second Tree). How many Sephiroth shall we find in the Complete Solid at the Fifth Progression? 193 + 192 + 192 + 192 + 192 = 961. Therefore when the Sephiroth have increased to 961 in the Solid, Malkuth will have expanded to the First Kether. 961 happens to be 31 X 31, or the Square of 31, and it reduces to 13.
But what of our Proportion of 208 to 496, the Fifth progression of the proportions of 13 to 31? Not only is 208, the width of our Tree, equal to the length of a Pure Vesica whose breadth is 120 (our original Kether angle), but our other proportion 496 is a Perfect Number, the Sum of the Numbers from One to ThirtyOne, and the Numeration of MLKVTh—Malkuth. AL, it must be remembered, is the Highest Kether Name of God  31  which being read in reverse is LA, Not, and thus forms the true formula of the transition from the unmanifest to the manifest. Let us never forget that the True Kether—Hadit is forever concealed in the Center of Malkuth, and that of this it has been written in Liber AL vel Legis:
I am NOT (La = 31) extended (1 + 2 + 3 . . . 31 = 496) and Khabs (a Star) is the Name of my House. In concluding this section we may remark that the 76th progression of the Single Solid, and the 19th progression of the Star, show 913 Sephiroth, 913 is BRAShITh, Berashith, “In the Beginning”—the First Word of Genesis. The 80th progression of the Single Solid, the 20th of the Star, and the 5th of the Complete Solid, all give 961 (13 x 31), and in case you should forget this, all you have to do is to stand in The Kingdom, Malkuth (496), and LOOK UP. You will then see Yesod (9) and above that Tiphereth (6) and—by the Grace of God—Kether (1). So mote it be.

