Editor’s Note.— This text forms the first subsection of Section III of the surviving “Würzburg Manuscript,” an early draft of The Secret Doctrine prepared by H. P. Blavatsky principally during 1885–1886, before the work was extensively reorganized into the form published in 1888. It belongs to the historical and occult material that originally formed part of the projected introductory volume and was later largely reassigned to the projected third volume.
“Mathematics and Geometry—the Keys to the Universal Problems” was first published from the manuscript in The Theosophist, March 1933, pp. 625–627, as part of C. Jinarajadasa’s serial publication of the Würzburg material. Much of its subsequently revised material was later included by Boris de Zirkoff in H. P. Blavatsky: Collected Writings, vol. XIV, in the corresponding discussion of occult systems of numbers, alphabets, and geometrical symbolism. The complete surviving Würzburg section was published in The Secret Doctrine Würzburg Manuscript (Eastern School Press, 2014), pp. 53–56.
The present text was later revised and substantially expanded into Section X of the posthumous 1897 Secret Doctrine, Volume III, pp. 98–104. Its original sequence and even its division from the following subsection were largely preserved, though several passages were omitted and a considerable body of new material on Gematria, Temura, arithmancy, numerical symbolism, and initiatory language was inserted into the later version. The Würzburg text therefore preserves a particularly clear early form of a section that subsequently developed without being fundamentally rearranged.
I. Mathematics and Geometry—the keys to the Universal Problems
The transcendental Methods of calculation—as well explained in Cornelius Agrippa—are very difficult to practise. Its most perfect exposition, however, is found in the Chaldean Book of Numbers1 and the great Hermetic or Chaldean Kabala cannot be thoroughly understood without becoming an M.A. in this science. Pythagoras was not its inventor as some believe. Thousands of years before his day it was known to the Sages of Aryavarta, whence it was brought by the Samian mystic and philosopher, not as a Speculation but as a demonstrated science. “The numerals of Pythagoras” says Porphyry, “were hieroglyphical symbols, by means whereof he explained all ideas concerning the nature of all things.” (“De vite Pythag.”)
The fundamental geometrical figure of the Kabala—that figure which tradition and the esoteric doctrines tell us was given by the Deity itself to Moses on Mount Sinai2 contains in its grandiose, because simple combination, the key to the universal problem. This figure contains in itself all the others. For those who are able to master it, there is no need to exercise imagination. No earthly microscope can be compared with the keenness of the spiritual perception.
The symbolism of numbers and their mathematical interrelations are also at the foundation of mental magic so to say, of divination and correct perception in clairvoyance. Systems differ but the idea is everywhere the same. As Kenneth R. H. MacKenzie IX° says in his Royal Masonic Cyclopœdia: “One system adopts unity, another trinity, a third, quinquinity; again we have sexagons, heptagons, novems, duodecimals, and so on, until the mind is lost in the survey of the materials alone of a science of numbers. Numbers also are related to proper proportion, and as one scale or the other is adopted in a system, so the proportion varies; and with the devarication we obtain dissimilar forms of architecture . . . . It is impossible to deny the multiplication table, or to assert that the three angles of any triangle do not comprise the rectangles.” Although beings are infinite in numbers, however (as Leibnitz says) it does not follow that their systems should at once receive all the perfection of which they are capable. “For if so,” he adds,—“the hypothesis of the rectangle would be demonstrated, for the hypothesis of equal perfection is that of the rectangle.”
The Eastern or Oriental Numerical alphabet3 is like the Chaldean, the Hebrew and the Hermetic alphabets the world over, plus—the full and complete significance given of every letter in its relation to spiritual as well as terrestrial things. And, as there are only 22 letters in the Hebrew alphabet and 10 fundamental numbers and in the Sanskrit or Devanagari 35 consonants and 14 vowels, making altogether 49 simple letters (or 7×7) the margins of speculation, or we should say knowledge are vaster in proportion. Every letter has its equivalents in other languages and its equivalent in a figure or figures of the calculation table, as also its numerous significations, the latter depending upon the special idiosyncrasies and characteristics of the person, object or subject to be studied. As the Hindus claim to have received their Devanâger [devanāgarī] characters or alphabet from Sarasvati, the inventress of Sanskrit, “the language of the Devas” or gods4—so most of the ancient nations claimed the same privilege for the origin of their letters. The Hebrews called kabalistically theirs the “Alphabet of the Angels” which was communicated by the Angels to the Patriarchs, as the Deva-nagari was by the Devas to the Rishis. The Chaldeans found their letters traced in the heavens by the “yet unsettled stars” and comets—says the Book of Numbers; and the Phoenicians, showed a sacred alphabet formed by the twistings of the sacred Serpents. The most ancient is certainly that of the Secret Doctrine, in which the oldest work on the Evolution of Cosmos and planets is traced, and the Netar-Khari (Hieratic) alphabet and “Secret Speech” of the Egyptians.
However it may be, this kind of interpretation of the hidden sense of apocalyptic writings is one of the keys given out in the Zohar and is its most sacred lore. St. Hieronyus assures us that it was known to the school of the Prophets and taught therein which is very likely. Molitor, the learned Hebraist in his work on tradition says that “the two and twenty letters of the Hebrew alphabet were regarded as an emanation, or the visible expression of the divine forces inherent in the ineffable name.” Those letters find their equivalent in, and are replaced by numbers; for instance: the 12th letter and the 6th of the alphabet yield 18—in a name; the other letters of that name are added being always exchanged for that figure that corresponds to the alphabetical letter; then all these figures are subjected to an algebraic process that transforms them again into letters; after which the latter yield to the enquirer “the most hidden secrets of divine Permanency (eternity in its immutability) in Futurity (Chaldean Book of Numbers).”
1. We are not aware that a copy of this ancient work is embraced in the catalogue of any European library; but it is one of the “Books of Hermes,” and it is referred to, and quotations are made from it in the works of a number of ancient and mediæval philosophical authors. Among these authorities are Arnoldo di Villanova’s “Rosarium Philosoph;” Francesco Arnolphim’s “Lucensis opus de lapide”; Hermes Trismegistus’ “Tractatus de transmutatione metallorum,” “Tabula smaragdina,” and above all in the treatise of Raymond Lulli, “Ab angelis opus divinum de quinta essentia.”
2. Exodus, XXV, 40.
3. The so-called “Magic Squares” (the Oriental Square, Zchal), and the Pythagorean Triangle are well known. “A magic square is a series of numbers (in two squares) and an equal number of cells constituting a square figure, the enumeration of all whose columns, vertically, horizontally, and diagonally will give the same sum . . . These magic squares, which almost run to infinity, have attracted the attention of the thoughtful and learned in all ages . . . The Oriental Square, named after the planet Saturn Zohal, the sum of the digits being equal to 45 (1+2+3+4+5+6+7+8+9) being the exact corresponding value of the letters in the word Zohal, in Arabic. The table (a square divided into nine cells) is the Talmud real method, making fifteen each way, being the numerical value of YAH, a form of the Tetragrammaton. Cornelius Agrippa has given all these squares.” (Royal Masonic Cyclopœdia.)
4. The Secret Doctrine teaches otherwise. We shall explain further on. It is one of the few things permitted to be given out.