Associated with each Sephirah of the Tree of Life is:
1. a Godname, which functions in Atziluth, the Archetypal World, and embodies the abstract essence of that Sephirah;
2. an Archangel, which functions in Beriah, the World of Creation;
3. an Order of Angels, which functions in Yetzirah, the Formative World, and
4. a Mundane Chakra, which exists in Assiyah, the World of Action. In an astrological context, it is the astronomical body that has been traditionally thought to manifest the quality of a given Sephirah.
The Hebrew name of a Sephirah manifesting in each of the four Kabbalistic Worlds is equivalent to a number that is the sum of the number values of its letters. In one or two cases where the number is a multiple of 10, the values have to be further contracted to these multiples. For example, the final mem in the Godname Elohim is usually counted by Kabbalists as 40 (the number of mem) instead of 600, so that its gematria value is 86, not 646. However, the true number of Elohim is 50, not 86, because the number 40 should be further contracted to 4: 4 + 0 = 4. This is a fact unrecognized by most Kabbalists because they have no independent way of confirming whether the traditional gematria number values of Godnames, etc are actually correctly calculated by simply adding their letter values! Sacred geometry — the domain of the Divine Names par excellence — provides such a check. Hence, in the one or two cases where the number listed in this table is not that given in reference works on Kabbalistic gematria, e.g., Godwin's Cabalistic Encyclopedia, it means not that the author has made an error of adding but that, prompted by sacred geometrical considerations, he has taken into account the necessity of contraction, so that the true gematria number value of a few Godnames is not merely the sum of their letter values, as these works assume. Such considerations are not ad hoc but motivated by the fact that Godname numbers have a simple, geometrical basis, as illustrated on pages 25-34, so that consistency with this necessitates the contraction of the value 40 of the final mem in Elohim to 4. A few other differences in the table arise because the author follows traditional, Jewish Kabbalah, not Hermetic societies of the West, such as the Order of the Golden Dawn, which inspired source books like Godwin's Cabalistic Encyclopedia.

Whenever the number values of the 10 Sephiroth in the four Worlds appear in the discussion of sacred geometries, they will be written in bold.