The Circumference

By David R. Jones

The circumference of the Sigillum is divided into 40 equal segments (of 9° divisions 360/40=9) containing either letters and numbers or letters alone. The letters and numbers are used in a simple algorithm for drawing out divine names from the circumference which will be dealt with in due course. It is presumed that the reader has read through at least Mysteriorum Liber Secundus prior to reading this analysis.

Thrones: From and in the 40 Chambers are three sets of spiritual creatures.

  1. 40 angels are individually associated with the Chambers themselves, their letters and numbers.
  2. 7 (plus 2 or 3 hidden) names are drawn by the arithmetical algorithm from the Circumference.
  3. The 7 Alphanumeric Seals located within the semicircles that result from the inscription of the Septagon within the Circumference.

The Alignment of the Circumference to the Celestial Sphere

These divisions can also be seen to mark the divisions of the celestial sphere and to have intrinsic meaning of their own.

The orientation of the Sigillum is upright on the Holy Table facing east. The 4T located in the first division of the Sigillum's Circumference is therefore oriented toward this eastern position.

This 4T is correlated to the T with 4 flames above it that is the seal of the Eastern Watchtower by Dee is his marginalia to the the Spirit Actions of 25 June 1584: “Vide 1582. 20 Martii. lib. 2” that is to say “See 1582, 20 March, Liber Secundus.1 (whose king is Bataiva/Bataivh). It has been demonstrated elsewhere that the King of the Eastern Watchtower has a dual yet harmonious attribution to Aquarius embracing both the astronomical aspect related to the fixed and ancient Babylonian Royal Star Fomalhaut and to the midpoint of the zodiacal sign of Aquarius corresponding to the midpoint between Winter Solstice and the Vernal Equinox, known in the ancient Celtic calendar as Imbolc (also Brigit’s day and Candlemas). Both correspondences are quite ancient and have been associated with the Cherub Man in Ezekiel and in particular the Apocalypse of St. John. It is notable that of all the Watchtowers only the location this (i.e. the Bataiva/Bataivh)* table remains unchanged through the various angelic rearrangements of the order and location of the tables.2

If this alignment is consistent then other hypotheses regarding attribution can be drawn and tested against the indications given in the Spirit Actions.

Astronomical Alignment

If a Heptagram (that is the basic figure of the Sigillum) in centered on Polaris and a line is drawn from Fomalhaut through it topmost point (here indicated the beginning of the 4T division) and through Polaris, it will bisect both the angle that joins the base points of the Heptagram and the constellation of Leo. This angle not only fully encloses the constellation of Leo but its extension also encompasses the entire sign of Leo, though the two only correspond in part due the phenomena of precession.3

Spirit Action of 20 March 1582 this angle in the Sigillum contains the line DEIMO30A from the 4th company of pillars.4 That the arc of the Circumference in which the angle of DEIMO30A is inscribed corresponds to Leo in both astrological and astronomical definitions is confirmed by the description of that line Vivo in sicut LEO in media illorum, that is “I live as a Lion in their midst.”

This does not in and of itself resolve whether the course of the zodiac proceeds in a clockwise or counter clockwise direction. But the next following line, from the 5th company of pillars I26MEGCBE says: “Serpens sum, et devoraui serpentem,” and Michael replies: “Et bonus et malis serpens Domine.” That is to say “I am a Serpent and I devoured a serpent,” and “And you are a serpent to good and evil, Lord.” Similarly an arc cut into the Celestial Sphere by the angle that encloses this line encompasses both the tail of Hydra the evil water snake - enemy of Apollo and the head of Serpens the good healing snake of Asklepios.

This would indicate that the Circumference aligns to the Celestial Sphere in natural order though the order of the constellations is clockwise around the figure; different than one would read in an astrological chart, but exactly how they are laid out on an astronomical planisphere and the necessary perspective when viewing the motions of and on the ecliptic from the Northern Hemisphere.5

This ordering is confirmed again by the next line or the 6th company of pillars ILAOI218VN from which a voice declares: “Ignis sum penetrates” - “I am a penetrating fire.” This would harmonize appropriately with Sagittarius, which is both constellation ally and astrologically in the arc described by the extension of the angle which contains this line.

Astrological Alignment

As stated above the 4T indicates a directional alignment to the Eastern or Air Watchtower and its King Bataiva/Bataivh. The first of these names is associated not with the fixed stars and constellation of Aquarius but with the corresponding Zodiacal signs, particularly it’s midpoint at 15° Aquarius. If this position is adopted as the point marker dividing the 6ω from the 4T at the top of the Sigillum then the 40 divisions are necessarily attributed as follows:

1. 4 T 16°♒-24°♒
2. 9 G 25°♒-3°♓
3. 7 n 4°♓ -12°♓
4. t 9 13°♓-21°♓
5. 22 h 22°♓-30°♓
6. n 1°♈ -9°♈
7. 6 m 10°♈-18°♈
8. 22 o 19°♈-27°♈
9. 20 a 28°♈-6°♉
10.14 n 7°♉ -15°♉
11.6 a 16°♉-24°♉
12.h 25°♉-3°♊
13.o 18 4°♊ -12°♊
14.26 1 13°♊-21°♊
15.l 30 22°♊-30°♊
16.n 1°♋ -9°♋
17.l 8 10°♋-18°♋
18.7 G 19°♋-27°♋
19.13 r 28°♋-6°♌
20.H 12 7°♌ -15°♌
21.go 16°♌-24°♌
22.y 15 25°♌-3°♍
23.t 11 4°♍ -12°♍
24.o 8 13°♍-21°♍
25.e 21 22°♍-30°♍
26.10 b 1°♎ -9°♎
27.11 A 10°♎-18°♎
28.15 I 19°♎-27°♎
29.8 a 28°♎-6°♏
30.r 16 7°♏ -15°♏
31.n 16°♏-24°♏
32.6 A 25°♏-3°♐
33.O 10 4°♐ -12°♐
34.5 G 13°♐-21°♐
35.h 14 22°♐-30°♐
36.o 17 1°♑ -9°♑
37.s (5)10°♑-18°♑
38.a 5 19°♑-27°♑
39.a 24 28°♑-6°♒
40.6 ω 7°♒ -15°♒

Δ “All the Companies of these 40, stood together and five together, and so in eight Companies; each, of five.”

The 40 Divisions

These are notable and interesting divisions to which some cabalistic analysis will be applied in due course. They bear a definite resemblance to the more traditional system of decans being but one degree less in dimension. The art and science of decans was quite popular in Dee's era and the works of Giordano Bruno are particularly commended to study, but this formula of division is much older than the 16th century, and medieval and ancient works on the subject are worthy of serious consideration.

The divisions of the Sigillum though, prove a bit more utilitarian in that unlike the decanate system none of the eightfold seasonal and mid seasonal dates falls with the body of any of the 9° segments. Each falls elegantly upon the actual dividing lines themselves and not as they would within the midst of a decan as the midpoints would in the more traditional method of subdivision. As Dee says they were divided into 8 Companies, each in this way marking the a seasonal ingress or mid season feast. The principles of this method of analysis and the other methods of analysis used herein can be studied in Dee’s Propaedeumata Aphoristica.

The Great Serpent

Three Fathers and their descendants
And seven planets and their hosts,
and the twelve diagonal boundaries

A proof of this
true witnesses to the Universe, Year, Soul
and a rule of twelve,

and seven and three:

He set them in the Teli, the Cycle and the Heart.

Sepher Yetzirah 6:1

It is both interesting and significant that the total of the numbers given in the segments of the Circumference of the Sigillum is 440.


This is the value of the Hebrew word תלי (Teli or Theli) which is given in 777 as meaning The Great Dragon or “curls,” In the Idra Rabba Qadisha or Greater Holy Assembly of the Zohar.

Teli is an obscure non biblical Hebrew term that appears in the Sepher Yetzirah and from there in subsequent Qabalistic texts. It my be studied in this context and in greater detail in these texts particularly the above mentioned, as well as in the Bahir. Areyeh Kaplan’s analysis in his commentary to his translation of the Sepher Yetzirah is without peer and the student is ardently recommended to begin his study of the matter therein.

It is useful though to give a synopsis of some of his ideas therein and how they relate to underlying principles of the Sigillum. Since the meaning of Teli is oblique the rabbis have variously interpreted it as pole, pole serpent, curls, or hangings. As the pole and pole serpent, the curls are seen as the coils of the Great Serpent in a kind poetic punning common to Hebrew poetic forms. These coils will be clearly seen in the explication of the names that are drawn from the Circumference. Often identified as Leviathan, but what Kaplan calls the “overseer and director of all the other stars.”

It is from the Teli that that stars and signs are said to “hang,” and it is pictured as both surrounding and supporting the constellations and their contents. Compare this to the hanging of the baskets whose description follows after the details of the Circumference have been brought to a close. Kaplan asserts that the Jewish calendric astronomers see it as resolving, in a dual aspect (twin serpents) the obliquity between the ecliptic and the equator, a problem addressed above in the relationship between the astronomical and the astrological attributions [though as noted above the underlying issue here is actually precession.], but as Kaplan notes problems related to both the nodes of the Moon (the so-called Head and Tail of the Dragon) and to the seasons.

The function of the Teli is so similar to that of the Circumference that it seems unlikely that the numerical values given are coincidental, especially given the rather tortuous explanation regarding the 37th division where the “s” is said of Michael to be “Est numerous in numero,” i.e. “It is a number in a number,” to wit Dee replies “I understand it to be a letter, and the number 5 also,” confirmed by Michael’s “So it is.”

1. T&FR 173

2. This dual relationship is directly related to the two-fold name of the King and his function as conveyer of Knowledge and Judgement in Human Affairs respectively, the solar or astrological aspect being knowledge and the stellar or astronomical aspect being judgement.

3. Note there is the problem of precession, which affects all direct astrological to astronomical problems. If they are kept separate they present little real problem to the magician, but the serious student is advised to compare values for a 1582 epoch, by taking the difference between it and the present date, dividing the result by 72 and shifting the astrological values that many degrees counter to the annual motion of the Sun.

4. Peterson 130

5. It seems likely that Dee’s Paradoxical Compass was also laid out in this manner.

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