A TRANSLATION OF THEOREMS 1-17 OF JOHN DEE'S MONAS HIEROGLYPHICA
by Nancy Turner and Teresa Burnes
Since the writers of the accompanying article on the Hieroglyphic Monad worked from this translation, it seems appropriate to include it here. This is part of a much larger work in progress forthcoming from Waning Moon Press, which includes translations of the long dedicatory preface to Maximillian, the letter to printer William Silvius, and the remaining theorems. Thank you to Darlene for providing the color frontispiece, and Alan Moore for the line drawings and help in deciphering the handwritten Greek within the Latin Monas Hieroglyphica.
We encourage those seriously studying Dee’s Hieroglyphic Monad to attempt their own translation, or if that is not possible, to at least closely compare the different versions available. One soon finds that much of Dee’s word play in Latin loses its resonance when translated, and by taking the most logical English equivalent — say, circle for Circulus—many of the multiple levels of meaning start to fade. Where Dee's words seem most confusing or mix languages, one almost always finds a nod to the Hermetic tradition, as in the oddly rendered Stilbon perfecting Mercury on the frontispiece scroll. We’ve noted these things when possible, but that is no substitute for making the exploration on one’s own. Similarly, in working through one’s own translation, one is left to ponder why Dee has chosen to capitalize certain words, oddly space others, arrange the text around graphics in a particular way, and insert accents which don’t always follow usual typography rules. We’ve commented on this to a very limited degree, and noted where he’s switched from Latin to Greek, but again these comments are no substitute for one’s own study and exploration. One might also want to look closely at Dee’s Propaedeumata Aphoristica, whose frontispiece displays the same Monad glyph, suggesting it is at least in part structured around the same concepts.
We followed this translation process: Dr. Turner, who has studied more of classical and medieval Latin but less of Dee and Hermeticism, occasionally consulted the 1964 C. H. Josten translation which has become the default favorite of critics writing in English, and the 1982 translation to modern German by Agnes Klein, while making her own, literal-as-possible translation of the Latin text. I then compared her English translation to Josten’s and to J.W. Hamilton-Jones’s oft-reprinted and oft-criticized 1946 translation available on the web and recently reprinted with a new introduction, consulted the commentaries by all three, and looked for further commentary and analysis of Dee’s Greek references to place them within the most appropriate Hermetic current. As you can see from a comparison of three of the shortest theorems (three which also seem unusually straightforward compared to the rest of the work), even these differ from translator to translator. We also consulted the 1925 French translation by Grillot de Grivy, but in less detail due to our own language limitations. Then, based on the new insights I gained from Turner’s translation and our theorem-by-theorem discussion about which of several possible English words would be closest equivalent to Dee’s Latin or Greek, I wrote the endnotes you see here and the bibliography.
As one moves further through the Monas, the differences in translation become much harder to navigate and both of the previous English translators seem to make errors or omissions, though Josten makes many fewer than Hamilton-Jones. Hamilton-Jones, while easier to read, seems to work mainly by paraphrase, clearly has preconceived ideas about what he is translating, and provides no notes on why he has chosen particular words or what the originals were, though he does offer a commentary that refers the reader to other alchemical writers expressing similar ideas. Josten, on the other hand, scrupulously tries to keep to a literal translation and provides the Latin side-by-side with his English translation and notes, but often loses the beauty (and occasionally the meaning) of the language in his wordiness. Their translation errors show that neither man completely understood the work he was translating, though Josten is much more honest in saying so.
Both C. H. Josten and Agnes Klein include valuable notes on why they have translated a particular passage a certain way, and we have reproduced some of those here.
The Hieroglyphic Monad
Cabalistically, and Anagogically Explained
One who does not understand should be silent or learn.
[Words on the scroll around the monad, with other markings:]
Mercury becomes parent and the king of all planets when perfected by stable, pointed Stilbon, 
May God give thee of the dew of heaven, and of the fat places of the earth, Gen. 27
Printed by Willem Silvius, Royal Typographer, Antwerp, 1564.
By means of the straight line and the circle, the first and simplest production and representation of things was made in the light, as were non-existent things and those that are hidden behind the veil of Nature.
The circle without a straight line cannot be artificially created, nor a straight line without a point. Consequently, everything, properly, began from the point and the monad. And whatever is strived for by the periphery of the circle, no matter how big it is, can in no way succeed without the ministry of the central point., 
Therefore the middle point, which we see in the center of the HIEROGLYPHIC MONAD, represents the EARTH, around which the SUN, the MOON and the other Planets complete their paths. And in this movement, since the SUN assumes the supreme dignity, we depict it (because of its excellence) by means of a complete circle with a visible center.
Although the semi-circle of the moon is above the Sun, as it were, and comes first, nevertheless the Moon regards the SUN as lord and king; the Moon even seems to rejoice over the sun’s form and vicinity, since the Moon, in one way, emulates the size of the Sun’s radius (or so it appears to the ordinary person) and in another way the moon constantly turns its light toward the Sun. And finally, the Moon so desires to be filled by the SUN’S rays, that it, so to speak, transforms into the Sun and disappears completely from the sky, until it appears again after a few days in the form of a little horn, exactly as we have depicted it.
And most definitely by bringing the lunar semi-circle to the solar completion, one day is made out of morning and evening. Thus this would be the first day on which the LIGHT of the Philosophers was made.
Here we see the SUN and the MOON supported by a rectilinear cross. It can reasonably, and appropriately enough, hieroglyphically signify a TERNARY as well as a QUATERNARY. It represents a TERNARY through the two straight lines and the point common to them both, a uniting point, as it were. It represents a QUATERNARY from the 4 straight lines, including 4 right angles, each one being repeated twice (for this purpose). (And thus an OCTAD, very secretly, presents itself, in a way in which I doubt our predecessors, the Magi, ever observed, and which you will note with great attentiveness). The magical TERNARY of the first fathers and wise ones arose from the BODY, the SPIRIT, and the SOUL, through which we here have the first SEPTENARY manifested, [arising] to be sure, from the two straight lines AND a common point, and from the 4 straight lines that are separated BY one point.
The elements that are removed from their natural seats and whose homogeneous parts are scattered, will teach experimenters that the elements naturally return to their places by means of straight lines. Thus it will not be absurd [to say] that the secret of the FOUR ELEMENTS (into which all elementary things can in the end be dissolved) is affirmed by means of 4 straight lines that expand from a single and indivisible point into 4 opposite directions. Here you will carefully note what the Geometers teach: a LINE is produced from the FLOWING OF A POINT. And using this same principle, we point out that this is also the case in our mechanical magic, because the lines indicating our elements are produced by the continuous fall of DROPS (which are like physical points) [moving] as though they are FLOWING.
Moreover, the cabalistic expansion of the QUATERNARY, according to the customary way of counting (when we say one, two, three, four) produces the DENARY. As Pythagoras used to say, “1, 2, 3, and 4 make ten.” It is not by chance then that the rectilinear CROSS (that is, the twenty-first letter of the Roman alphabet), which was considered to have been created from 4 straight lines, was chosen by the most ancient of the Latin philosophers to represent the Denary. It was decided that its location in the alphabet was to be where the TERNARY, multiplying its strength by the SEPTENARY, situates the letter.
One will also see that this coincides very well with the SUN and MOON of our MONAD, since through the magic of the same 4 elements a very exact SEPARATION is made in their lines, and therefore by means of the circumference of their lines (for according to the rules of Geometry, regardless of how large the given lines are, a circle can be drawn) a CONJUNCTION of the circle was made in the SOLAR complement. So one cannot fail to see how well the proportion of the DENARY of the cross serves the SUN and MOON of our MONAD.
The sign of the zodiacal Aries, which is very well known to everyone, has, according to the custom of astronomers, this (rather sharp-edged and pointed) form: . And it is well known that from this place in the heavens, it manifests the beginning of the fiery triplicity. For this reason, we have added the astronomical sign of Aries in order to signify, that (in the practical use of this MONAD), the ministry of fire is required. And thus we have briefly completed one hieroglyphic consideration of our MONAD, which we want to express in a singular hieroglyphic construction as follows:
THE MOON AND SUN OF OUR MONAD DESIRE THEIR ELEMENTS, IN WHICH THE DENARIAN PROPORTION WILL RULE, TO BE SEPARATED, AND THIS IS TO BE DONE WITH THE MINISTRY OF FIRE.
The mystical sign of Aries, which is formed out of two semi-circles connected at a common point, stands very fittingly at the place of the equinoctial Nykthemerons. The time of twenty-four hours, in the mode of the equinox, denotes our most secret Proportions. I say “our” with reference to the Earth.
The oldest wise ones, the Magi, have passed down to us the hieroglyphic signs of the five planets, all of which have been constructed from the signs for the MOON and the SUN, along with the hieroglyphic sign of the elements and of Aries, as for example you see fashioned here.
It will not be difficult to explain each of these figures hieroglyphically [using] our previously established foundations. First of all, we’ll speak paraphrastically about those [signs] that contain characteristics of the Moon, then we’ll speak about those [signs] that contain solar characteristics. When our LUNAR nature first revolved around our Earth by means of the science of the elements, it was mystically called SATURN. And from the same occasion it also received the name JUPITER and maintained a more secret shape. And [the oldest wise ones] denoted the Moon more obscurely after the third time it [revolved] by means of the elements. This they usually call MERCURY. You see how LUNAR it is. Some wise ones want to say that Mercury is produced by the FOURTH Revolution. This will not, however, be in contradiction to our secret proposition. In this way, the purest magical spirit will carry out the work of the whitening instead of the Moon, and by means of its spiritual virtue, with us ALONE, and as in an ordinary, natural day, it would speak hieroglyphically without words, introducing and IMPRINTING into the very pure and simple Earth, which is prepared by us, those 4 geogamic figures, or in their place, that other figure.
Is not the mystical character of MARS formed out of the hieroglyph for SUN and ARIES, along with the intervention of the elements (to some extent)? And VENUS, I ask—isn’t it formed by a fuller unfolding of the SUN and the Elements? Thus these planets look at the revolution of the SUN and its work of reviving with fire, in whose progress that other Mercury-- -- who is in reality the uterine twin of the first one [the Mercury of lunar character] is finally apparent. In the same way that the lunar and solar magic of the elements is completed, this hieroglyphic messenger speaks very clearly to us; we want to more attentively fix our eyes on him and listen to him. (BY THE WILL OF GOD) he is that most famous MERCURY of the Philosophers, MICROCOSM, and ADAM. Indeed, some very clever people used to put the SUN itself in his place and rank. This we cannot achieve in our present age, unless we put in charge of this work made of coral-gold a certain SOUL who has been separated from his BODY by means of the Pyrognomic Art.
THE PRINCIPLE MONADIC ANATOMY OF THE ENTIRE REALM OF ASTRONOMIA INFERIOR
This act, however, is difficult to carry out and is also very dangerous because of the fire and the sulphuric vapor that arise from it. But one thing is certain: this SOUL will be able to achieve wonders, no doubt tying with indissolvable bands LUCIFER and even the FIRE BEING to the disc of the MOON—or at least of MERCURY—and in the third place (as they want it)—(in order to complete our SEPTERNARY number)—showing us the SUN of the PHILOSOPHERS. You see how exactly and openly the ANATOMY of our HIEROGLYPHIC MONAD corresponds to the SACRED MYSTERIES signified in both of these theorems [12 and 13].
It has already been clearly confirmed that this whole Master Work depends upon the SUN and MOON, which is something the thrice-great HERMES once taught us when he asserted that the SUN is its father and the MOON its mother. We know with no doubt that it is nourished in the LEMNIAN EARTH by LUNAR and SOLAR rays which exert a singular influence around it.
Consequently, we suggest to philosophers that they examine the labors of the SUN and the MOON around the earth; for instance, in what way the moon, while the SOLAR radiance is focused upon Aries, receives a new dignity of light in the nearest sign (namely Taurus) and is EXALTED above its innate powers. The old ones explained this proximity of the LUMINARIES (the most notable of all) by creating a certain mystical character with the distinguished name of TAURUS. This is very well known, in fact, to be the EXALTATION of the MOON and has been handed down all the way from the first age of the Human Race (among the teachings of the astronomers). Yet only those understand the mystery, who have become the absolute high-priests of the mysteries. For a similar reason, TAURUS is said to be the HOUSE of VENUS: indeed the house of pure and fertile conjugal love, since “Nature rejoices in Nature,” as the great Ostanes concealed in his most secret mysteries.
[We suggest to philosophers that they examine] by what means the SUN, having experienced some eclipses of its light, receives the strength of MARS, and also by what means in this same house (namely of our Aries) [the SUN] is said, as it were, to be triumphant in its EXALTATION. Our MONAD demonstrates most clearly and perfectly these most secret mysteries by means of the hieroglyphic figure of TAURUS which is depicted here, and by means of [the hieroglyphic figure] of MARS, which we presented in theorems 12 and 13, which the SUN moving towards ARIES reveals. So from the present theory, another cabalistic anatomy of our MONAD shows itself, which is a true and artful description: THE EXALTATIONS OF THE MOON AND THE SUN ARE SUPPORTED BY THE SCIENCE OF THE ELEMENTS.
I suggest there are two things to be especially noted here: one, that the hieroglyphic symbol of Taurus exactly represents to us the dipthong  of the Greeks, which is always the genitive singular ending of the first declension. Two, that by the proper turning (of the two signs), the letter ALPHA appears to us in two ways: either with the circle and semicircle merely touching, or (as here) with them mutually intersecting.
At this point in the discussion of our proposition we must philosophize a little concerning the CROSS. Although our CROSS is composed of two straight lines (as we said), and the lines are of equal length, they do not divide each other into equal lengths. But in the mystical arrangement of our cross we wanted to have both equal and unequal parts, to affirm that in the power of two lines divided in this manner is hidden also (because they are equal in size) the virtue of an equilateral CROSS. For, a certain JUSTICE of NATURE very generally requires that a CROSS is to be drawn with equal straight lines, and in the dividing of the lines cross-ways [that is, in the form of an ‘X’] its lines ought to be equal to begin with. According to this norm of justice concerning an equilateral CROSS (for example, the twenty-first letter of the Latin alphabet [=X]), we will propose, after careful consideration, the following: if a straight line is produced that crosses diagonally anywhere through the common point of a rectilinear, rectangular, and equilateral CROSS with oppositely positioned angles, then the parts of the Cross are entirely the same and equal on both sides of this diagonally-crossing straight line. Their forms are the same as the letter of the Latins that is accepted to be the FIFTH vowel [=V], and was most commonly used among the most ancient philosophers of the Latins to denote the number FIVE. And I think this was by no means done by them illogically, since it takes the shape of half of the number ten. From this form, which has been divided into two parts (as a result of the hypothetical division of the Cross), both [parts] of which represent the number FIVE (although one [part] is upright and the other is upside down), we point out that it portrays a multiplication of the squaring of a square root (which amazingly falls upon a CIRCULAR NUMBER, namely, FIVE). From this it definitely is not irrational that TWENTY and FIVE are produced (for that letter [i.e. V] is number twenty [in the Latin alphabet] and is the fifth vowel). Now we will consider another aspect of this equilateral CROSS, an aspect which is the same as that of our MONADIC CROSS. We suggest a that similar division of the cross into two parts be made (as was done above), from which another letter of the Latin alphabet is revealed which is [also] a doubled figure—one is upright, the other upside down and backwards, which (from the most ancient custom of the Latins) has been used to represent the number FIFTY.
This, it seems to me, is first established: that this is indeed a sign of the QUINARY, essentially derived from our DENARY of the Cross; and that from this position, the Cross, as the greatest of all mysteries, is the most perfect/complete hieroglyphic sign.
Thus the power of the DENARY, EMBRACING its QUINARY virtue, congratulates the NUMBER FIFTY on its offspring. OH MY GOD, HOW GREAT ARE THESE MYSTERIES? And even the name of that letter, EL, seems to refer to this denarian virtue of the Cross, since it is placed in the middle between the first letter of the alphabet and the Denary of the Cross [i.e. the letter X], and is tenth in order from either one. And since we have now pointed out that there are two complete parts in the CROSS (considering now only their numerical meaning), it is very clear that the number ONE HUNDRED arises from them. But if they [i.e. the two letters L] are multiplied with each other by the law of squares, they will produce for us the number Two Thousand Five Hundred. If this SQUARE is compared to the square of the previously mentioned circular number and is then applied to it, the CENTARY is restored again. Thus, when this CROSS displays itself in the context of the power of its DENARY, it can be recognized as the number ONE HUNDRED. And since this character of the CROSS is of but one kind, so it also represents unity. Here therefore (besides this other very worthy and distinguished thing) we have learned from these theories of the CROSS to count and to proceed in this fashion: One, Ten, One Hundred. We are thus raised up by the DENARY proportion of the CROSS.
As is evident from the sixth theorem, FOUR right angles can be considered to be in our CROSS, and the preceding theorem teaches that the sign of the QUINARY can be attributed to each one of them, the right angles of course being arranged in one way, but maintaining another position. The same theorem explains the production of the hieroglyphic symbols of the number FIFTY. Thus, it is very clear that the CROSS generally denotes the DENARY; and that in the order of the Latin alphabet, it is the twenty-first letter (whence it was the case that the wise ones called the Mecubalists signified the number twenty-one with the same letter); and finally, it can be considered very simply to be seen as one sign, no matter what kind of, and how much, other power it has. From all of these things together, we see it can be concluded by means of a very good cabalistic explanation that our CROSS can signify to initiates, in a remarkably shortened way, the number TWO-HUNDRED-FIFTY-TWO. Namely, FOUR times FIVE, FOUR times FIFTY; TEN; TWENTY ONE; and ONE, add up to TWO-HUNDRED-FIFTY-TWO; which number we can deduce in still two other ways from our previous [statements]. Thus we recommend to cabalistic Tyrians that they scrutinize this same [number], studying it in such a brief space, concluding the varied, skillful production of this Master Number to be worthy of the consideration of philosophers. I will not conceal from you here another memorable initiator to the mysteries. Our CROSS having suffered itself to be divided into two different letters, and as earlier we considered/analyzed their [i.e. the letters’] numerical virtue in a certain way, we will now compare in turn THEIR VERBAL POWER WITH THAT CROSS, because from this may be born LUX (LIGHT), a WORD we perceive with the highest admiration, finally and masterfully (through the harmony and agreement of the TERNARY in the unity of the word).
 Burns and Moore, this issue.
 For a comparison of this frontispiece to those from two different versions of Dee’s Propaedeumata Aphoristica, Ibid.
 These sources are referred to throughout these notes and in the bibliography.
 See Appendix.
 At his worst, Hamilton-Jones is glib to the point of being quite irritating. For instance, while both Josten and Hamilton-Jones make what we see as errors in Theorem XV, Hamilton-Jones’s only comments to the reader are that “we revert to astrology and receive a lesson based on the Monad, which explains why the Moon is said to be exalted in Taurus and the Sun exalted in Aries (p. 62),” as if he knows what this lesson is but chooses not to tell us. Yet his mistranslation, and consistent non-discussion of multiple meanings throughout the work, suggest otherwise.
 The entire frontispiece
needs to be “read” as an alchemical emblem, though that explanation is
beyond the scope of this commentary. Note fire (ignis) and air (aër),
the two active elements, on top of the two pillars.
 Of the frontispiece numbers 1, 2, 3, and 4 on one side, and 1 and 4 on the other, Josten adds: “They may be there to indicate a connection between Dee’s monad and the Pythagorean tetraktys; but their being placed at irregular intervals, and apparently against certain letters or syllables of the inscription, suggests rather that some sort of cryptogram is intended” (p. 113 n. 1).
 This line, the ten-fold blessing of Isaac to his duplicitous son Jacob, continues: “and plenty of corn and wine.” Also, note that Dee’s citation is to all of Genesis 27 (the rivalry between Rebekah’s twin sons Jacob and Esau), not only this line.
 While we tend to think of “circle” as a straightforward geometric term, in Dee’s time it was not. First of all, it enters English from Greek by way of Old and Middle English, where in all three cases it can mean anything from “ring” to “crown” to “heavenly sphere” and in Old and Middle English is mainly used to describe concepts in astronomy such as the sphere in which different heavenly bodies were supposed to move. Thus the term suggests not only the perfectly round plane figure we know from Euclidean geometry, but how that figure transforms into a variety of moving, multi-dimensional sacred concepts.
 Both the Hamilton-Jones and Josten translations omit translating Lucem as light, a significant omission since this references Genesis 1:3, “Fiat lux” (“Let there be light), and its myriad of esoteric resonances. Most obviously, this theorem combined with Theorem II suggests that the light which creates the line and circle emanates from a single point.
 Klein stresses we should look at Monad as equaling one, or a unity (p. 63, see also p.118 n. 88). Dee himself gives us its translation into English, in his introduction to Billingsley’s translation of Euclid: “Note the worde, Unit, to express the Greke Monas, & not Unitie: as we haue all, commonly, till now, used” (See Dee’s preface n. 2; also, see Josten p. 91), and later English usages are directly influenced by Dee’s translation. Latin Monas comes directly from ancient Greek , (pronounced monas) meaning a unity, singularity, or point. We have only Latin and Arabic sources for the “Emerald Tablet ,” but note that after the famous maxim “That which is above is like that which is below, to generate the miracles of the one thing” comes: “and as all things have been derived from that one, so all things are born from that one thing by adoption” (Bridges p. 436). The only logical Greek word for this “one” is , monas.
 The idea of all things in nature emanating from one “point” connects easily to cabalistic thought just as the notion of what is within—a spark of consciousness—supporting what is without echoes the frequent Hermetic maxim and the associations with Stilbon on the frontispiece (see n. 10 above).
 Neither Klein nor Hamilton Jones seem to see the point in the drawing and only provide the reader with the circle and line. Josten does not reproduce figures since the Latin text with Dee’s original figures appears side-by-side with his English translation. We think this graphic is a more accurate reproduction of the Latin original. (See comparison in Appendix)
 Where Dee has written a word in all capitals, we have usually done so as well. When he has capitalized the first letter only, we have used our own judgment about whether or not to do so in this translation. Suffice to say he is not following usual Latin rules for capitalization.
 Many writers have seized upon this Theorem as evidence that Dee believed the planets and Sun all revolve around the earth, while forgetting that modern astrologers (who presumably learned in school that the earth revolves around the Sun) do the same thing when they draw up astrological charts, and, like Dee, believe they have more accurate charts if they have an exact location on Earth. The “Earth” denotes the point from which the other phenomena are observed and upon which the forces act.
 Though this could be translated simply as “highest rank,” we’ve used “supreme dignity” to keep the astrological overtone.
 Cf. Genesis 1:5.
 This light, to Dee, is the essential element of alchemy. The capitalized LVX in the Latin original of Theorem V also implicitly refers us to the LVX analysis in Theorem XVII.
 Hamilton-Jones translates this as a “copulative point,” which we think forces a particular tantric understanding more than would be apparent to readers of the original Latin. If not, then his choosing an awkward cognate is just poor translating.
 Here, Dee at first seems disingenuous. Of course Platonists and Pythagoreans were familiar with the octad and considered it a prophetic number. One of the earliest known usages of the word “Monad” in English by someone other than Dee, Sandys’ translation of the Sibylline Oracle in 1615 (as cited by the Oxford English Dictionary) uses language which echoed Dee’s: “Eight monads, decads eight, eight hecatons Declare his name [sc. = 888] .” Rather than simple disingenuity, Dee’s understanding of the Octad, part of the “most secret” teaching alluded to in Theorems XII and XV, is something Dee thinks the Magi may have known but not observed first-hand, such as a celestial event.
 Throughout, Dee’s “you” is plural.
 Note that here FOUR is spelled out and later in the same theorem written as a numeral. We’ve followed the original in spelling out, or not spelling out, numbers.
 The Latin FLUXU implies a beautiful wordplay impossible to translate into English: the points of the line correspond to drops of water in a river.
 X. The Roman alphabet Dee refers to had 22 letters--A B C D E F G H I K L M N O P Q R S T V X Y-- making X the 21st letter, or 3 times 7. See Klein p. 121.
 Dee’s repeated reference to the “SUN and MOON” alludes to the Emerald Tablet ’s famous maxim that the Sun is Father and Moon is Mother of all things, and connects it with the “Denary” (likely the ten Sephiroth). Thus this observation in the 9th theorem connects to the 9th Sephira, Yesod.
 Though we’ve followed Hamilton-Jones and Josten in translating this as “zodiacal,” it is of note that Dee’s Latin word—Dodecatemorii instead of the much more usual zodiacus—may refer the readers to works on geometric solids, especially the discussion of the dodecahedron in Plato’s Timaeus and instructions on its construction in Euclid’s Elements. See the original in the Appendix.
 In parentheses here, Dee has “quasi Acioaedes, Acuminataque,” which we have translated as “a rather sharp-edged and pointy form.” The references here at first seem puzzling, as Acioaedes, is neither a known Latin word nor name, as it and Acuminatat might superficially appear (the capitalization of the first letter of each word would seem logical if they are names, as it appears on first read, but not if they are adjectives, as the word meanings indicate.) Josten notes that Acioaedes is “apparently a word of Dee’s invention whose meaning remains uncertain; it may be a misprint for Acioeides, as the word appears in the edition of the Monas reprinted in Theatrim Chemicum, Strassburg, 1659, p. 194. The translation given [by Josten, who translates it as “dagger-like”] would then seem almost justified, though the “o” joining the root of acies to -aides (Greek word) cannot be accounted for” (p. 161). Acuminatat, from which comes English acumen, can imply sharpness of thought. Thus the odd wording here, like ACUMINE on the frontispiece, suggests both a sharp flashing object and sharpness of thought or inspiration, and may refer us to the staff of Hermes Trismegistus.
 As Dee draws it, the
form at first seems not pointy at all. But note that the middle point
where the semi-circles join are, in most glyphs, the arrow of Mars.
 Aequinoctialis Nycthemerae loco. Josten reminds us this refers “to the place of the Sun at the date of the vernal equinox, which is the beginning of Aries” (p. 161 n. 42). Klein points out (p. 122 n. 97) that the unusual word Nykthemerons, which means “day plus night” [and may imply “the day when day and night are equal”] may come from the Nucthemeron of Apollonius of Tyana, a version of which was found in Amsterdam in 1721 and translated by Eliphas Levi as an appendix to his 1856 book Rituel. It appears in English as an appendix to Waite’s translation of several works of Levi, Transcendental Magic, pp. 507-509. One wonders if Dee had access to similar works.
 Aequinoctii modo distributum. Josten: “Dee is referring to a division, of the celestial equator into twenty-four equal hours, as opposed to one into unequal hours such as results from a division (into twelve equal hours each) of the periods from sunrise to sunset and from sunset to sunrise at times of the year other than the equinoxes. In the sixteenth century both systems were used side by side; their readings coincided entirely only at the times of the equinoxes, when day and night are of equal length and the twenty-four hours, therefore, equal by either system” (p. 161 n. 43).
 Notice that this theorem refers to measurements of a day and a year, suggesting that the “secret Proportions” being denoted are numbers used to measure multiple temporal cycles: a day, a year, and perhaps others.
 See note 16 above.
 Note that this can’t refer to the literal Sun, Moon, Saturn, and Earth as we conceive them. We have had the Earth (or a point of consciousness on the Earth) as the frame of reference; now “our” frame of first creation has a “LUNAR” reference. Looking for this ordering in classical references on wandering stars only leads to more confusion: Saturn and Jupiter are the first two spheres, but then the reference seems to fall apart. The reader is asked to make a transformation in the terminologies used here to be able to go further and contemplate how this lunar nature might be mystically called Saturn. Cabalists might note that Binah, and at times all Three Supernals, is often referred to as Saturn, and the reflection of the Sphere of Saturn referred to the path from Yesod (Sphere of the Moon) to Malkuth (Matter/Earth).
 This refers to the symbol for Jupiter in the first column.
 One assumes this connects to the “secret proportion” mentioned in Theorem XI, and alludes to some sort of oral teaching. Note that we may have an indirect reference to the Four Ages if we let the obscure third revolution associated with the Moon and Mercury become another reference to Tiphareth: Saturn (Lead), Jupiter (Tin), Moon/Mercury/Hermes/Tiphareth (Gold), Moon (Silver); similarly, we may have a reference to the Four Elements by looking at the common associations of Saturn (Earth), Jupiter (Fire), Mercury (Air), and the Moon (Water).
 I.e. Hermes/Mercury.
 Dee presents this word in Greek. Josten translates it as “albification,” likely because of the reference to physical alchemy; we’ve used “whitening” to keep the echo of “whitening” as reflected light, especially the proportion of solar light upon an element on the Earth’s surface. However, as usual, many of the Greek resonances do not translate, such as the faculty of “seeing white,” or the allusion in Greek to a “white god” or “white goddess,” Leukothea, a poetic way of referring to the sea-goddess Ino. Note that here and twice again in Theorem 13, Dee places a Greek word next to or near Latin Opus, or work, perhaps suggesting the “Greek”/Hermetic origins of the Great Work.
 Geogamicas, another word likely invented by Dee. Almost certainly the roots are from the Greek geo, meaning “earth” in compounds like geography, geology, or geometry, and the adjective gamic, meaning something having a sexual character or relating to marriage. Josten, in his complete translation, refers this to an earlier comment in Dee’s letter to King Maximilian, which proceeds the beginning of the Monas text: “One may infer from the explanation of Gamaaea given earlier in the text (see p. 135 n. 45) that these figures were meant to convey the idea of, or even to promote, the marriage of the innermost terrestrial body of the monad to lunar influences” (p. 163). Josten translates that earlier section to the King as “I know well (O King) that you will not shrink away in horror if I dare proffer this magic parable in your royal presence. This our hieroglyphic monad possesses, hidden away in its innermost centre, a terrestrial body. It [sc. the monad] teaches without words, by what divine force that [terrestrial body] should be actuated. When it has been actuated, it [sc. the terrestrial centre of the monad] is to be united (in a perpetual marriage) to a generative influence which is lunar and solar, even if previously, in heaven or elsewhere, they [sc. the lunar and solar influences] were widely separated from that [terrestrial] body [at the centre of the monad.] When this Gamaaea has (by God’s will) been concluded. . .the monad can no longer be fed and watered on its native soil, until the fourth, great, and truly metaphysical revolution be completed” (p. 135). Gamaaea is translated by Schumaker as “talismans” when he encounters the same word in Dee’s Propaedeumata Aphoristica Theorem XXVI, which begins “The stars and celestial powers are like seals whose characters are imprinted differently by reasons of differences in elemental matter” (p. 135). The closest modern English word is cameo, and its Renaissance English equivalents—gamahe, gamaieu—echo medieval rather than classical Latin.
 The fifth figure, which results from the first four.
 Mars in the graphic accompanying Theorem XII, which includes the cross of the elements.
 Josten, who translates this as “uterine brother,” says: “i.e. the Mercurius philosophorum, emerging at this stage, is the uterine brother of ‘the first’ Mercury (of lunar character) mentioned in Theorem XII” (p. 165 n. 48). Astrologically Mercury rules Gemini, the Twins.
 Mercury/Hermes/Thoth now transforms to Adam Kadmon, who encompasses all the Sephiroth but the Three Supernals and Malkuth, and is in Hermetic cabala often referred to Tiphareth and a “sacrificed god” such as Jesus, Mithras, or Osiris. See Burns and Moore.
 Refers to the common association of the Microprosopus/Son to Tiphareth and the Sun. Dee believes this is incorrect. It may also allude to a syncretization where Hermes rather than Apollo is associated with Tiphareth.
 Here Dee gives us: Operi . Josten notes that the closest known Greek word, , means “gold-coral” and is used to refer to several different metals (p. 165 n. 50). Dee’s “misspelling” may refer us also to Greek korallion, which means coral, especially red coral. Thus this alludes to both the “Golden work” and “red earth” of the alchemists and the idea of the “Great Work” creating matter, something like an exoskeleton (like that of coral) extruded from within. [Thank you to two pseudonymous posters to the “AlchemistRoyalAdvisorDrJohn Dee” e-group (http://groups.yahoo.com/group/AlchemistRoyalAdvisorDrJohnDee/) for their discussion of this material.] Finally, Klein connects the idea of “coral-gold” to I.N.R.I., initials traditionally above Jesus on the cross, if one takes the story of the crucifixion as a cosmic alchemical allegory (pp. 123-124 n 101).
 Latin anima; in physical alchemy this word is used to refer to the vapors emitted during the firing of the prima material. Latin anima is often associated with Greek psyche, the primary substance and source of life and consciousness to the early Greek philosophers.
 Pyronomica, another of Dee’s invented words. Note pyr-, one of many Latin roots for “fire,” comes into Latin from Greek and implies a funeral pyre. Dee’s Greek earlier in this theorem contains this same root. Pyr alludes to the place, Pyra, on Mount Aetna, where Hercules, after completing his twelve labors, asks to be burned alive while the deities of Mount Olympus look on. Additionally, the Greek word for wheat or grain sounds similar, leading linguists to argue about whether the Latin word for pyramid comes from Egyptian or from the ancient Greek for a funeral pyre, granary, or echoes all three. One of the first uses of pyramid in English is in Billingsley’s 1570 translation of Euclid, for which Dee wrote the introduction. Pyr is joined to –nomica, alluding to the Greek gnomon, the part of ancient sun-dials which cast a shadow to indicate the time of day, and to other indicators such as a carpenter’s square. In Billingsley’s translation of Euclid, we also find one of the first uses of this word in English: here Gnomon refers to the part of a parallelogram remaining after a similar parallelogram is removed from one of its corners. Pythagoreans, meanwhile, also use the term to refer to odd numbers.
 Josten: “Astronomia inferior is the science of the metals as produced by the influence of the seven planets; therefore, alchemy” (p. 165 n. 52). Since this differs so much from the most logical English translation, we’ve chosen to leave these words in Latin.
 Luciferum, “the light-bringer,” associated in some traditions with Hermes and with the Olympic spirit Ophiel (see Bridges). Josten’s translation of Luciferum as “Venus” makes no sense, because in the tradition that equates Lucifer/Hermes/Mercury, Lucifer marries Diana/Venus/Aphrodite.
 Pyroenta, literally “Fire Being.” See notes 50-52 above. The “flash” of Hermetic energy animating matter likely also equates to the marriage of the Son Zauir Anpin to Malkah the Queen/Kalah the Bride, both referred to the Sephira Malkuth.
 Lucifer/Hermes/Tiphareth “the Son” uniting with the Yesod “the Moon” to create the Kingdom, another familiar cabalistic transformation. The “Fire Being” is perfectly conceived in Yesod from energy emitted from Tiphareth, and so tied to both Sephiroth.
 Another transformation of Mercury, now as the Cadeuceus of Hermes projected on the Tree of Life as the three Hebrew mother letters (Mem-Water, Aleph-Air, Shin-Fire) one on top of the other, as described more than 300 year later in, among other places, the Golden Dawn Knowledge lectures (Regardie p. 68.) Note the parallel in Dee’s 18th Aphorism in Propaedeumata Aphoristica, which makes a similar reference. Finally, one can also project the Cadeuceus onto the Tree as a glyph that encompasses all seven of the lower Sephiroth, thus as the union of Adam Kadmon and Malkah the Queen/Kalah the Bride creating life.
 As noted above, the final transformation of Mercury, as the Cadeuceus of Hermes, encompasses the seven lower Sephiroth. Perhaps Dee’s “third place” alludes to the Three Supernals, which with the Cadeuceus yields the whole Tree, the “Sun of the Philosophers.”
 The creation of the Philosopher’s Stone in terms of at least three understandings: how time and space are structured geometrically from a fundamental unity, and how that knowledge allows the alchemists to animate matter.
 Hermes Trismegistus, another reference to the Emerald Tablet .
 An echo of the famous third and fourth lines of the Emerald Tablet : “The sun is its father, the moon its mother. Wind has carried it in its belly and the earth is its nurse” (Bridges p. 436). Klein (pp. 124 n. 103) notes that these lines have as their subject the prima materia.
 Josten: “Terra Lemnia, an allusion either to Vulcan, the god of fire, who is sometimes styled Lemnius, or to rubisca Lemnia, i.e. a kind of red chalk, or terra sigillata” (p. 167 n. 55). Thus, Dee alludes to the “red earth” animated by the alchemists. Klein suggests that the terra lemnia in its allusion to the Isle of Lemnos, is an indication of the Androgyne as the product of the marriage of Sun and Moon.
 Labores implies exertion or effort and so suggests the astrological understanding in note 19; it likely also alludes to the twelve “labors” of Hercules, which in turn are often associated with the zodiac and especially associated with the signs Aries and Scorpio, both traditionally ruled by Mars.
 In Latin, Aries, the first of the twelve signs of the zodiac, and “ram” are the same word, both associated with Ares, the Greek God of War renamed Mars by the Romans. While the vernal equinox today falls in Pisces, during Roman times (approximately one zodiacal age ago, when the constellations and signs as designated by Hipparchus all matched up) the vernal equinox and the constellation Aries fell in the sign of Aries. Astrologers still consider that the vernal equinox falls upon the first point of Aries. By far the most known occurrences of Aries in classical Latin occur in Vitruvius’ De Architectura, where it most obviously refers to the "battering ram” used in warfare. But here Dee uses the feminine ablative (Ariete) of a word that is usually masculine.
 In Latin Tauri, or Taurus, the second of the twelve signs of the zodiac, and “bull” are the same word. “The Bull” is also the second of the zodiacal constellations and includes the Pleiades (“Seven Sisters”) and the Hyades. Note that Dee does not put this tauri in all capitals as he does the next one (see note 61).
 Josten (p. 167 n. 56) notes: “Taurus [the sign] is in astrology the so-called exaltation of the Moon. While the Moon remained in that sign, her beneficial influence was supposed to be enhanced.”
 Dee’s capitalized LUMINARIUM clearly has multiple meanings, as it can refer to anything that emanates real or metaphoric light, from celestial bodies to people of wisdom.
 TAURI, here and later in the theorem, suddenly is placed in all capitals, first as a name, nomine, then as a hieroglyph, Tauri “Hieroglyphica” (a term used elsewhere to describe the Monad, the union of the Sun and Moon, and the Cross, but not astrological signs). Thus the Hieroglyphic Taurus seems to refer to something different. As a glyph, it is part of the symbol for Mercury, a conjunction of the symbols for Sun and moon, and a reference to many glyphs for Pan, Herne, Cerrunnos, or the “Horned God” of many pre-Christian pantheons. Also, in the notation following this theorem, Dee says it looks like the Greek letter Alpha [if you place the glyph on its side].
 Dee’s DOMUM most obviously suggests “house,” and as Josten notes (p. 167 n. 57): “The houses, or domiciles, of planets enhance their beneficial effects to an even stronger degree than their exaltations.” The house of Taurus is ruled by Venus. Yet domum can also suggest a school of thought or particular metaphysical line of teaching, and that meaning seems more appropriate to the knowledge of the “absolute high priests of the mysteries.” One may note that the zodiacal Age of Taurus, which would have been at its height about 5,000 years ago and during which the constellation now called Aries fell in the sign now called Taurus, was the age of the cults of the Great Goddess throughout Europe and Mesopotamia, and the rise of Old Kingdom dynasties in ancient Egypt.
 VENERIS, translated most simple as Venus, carries several obvious puns in Latin, as veneris is the generative form of Venus; an inflected form of the verbs venio, to come, and venor, to hunt or chase; puns on veneror, worthy of respect or veneration; and part of mons veneris, or the “mound of Venus,” the pubic area of a women. Given the pun between mons and monad, we may be certain this latter meaning is among those Dee intended, and suggests wisdom attained through sacred sexual union; indeed the “union of Sun and Moon” referred to throughout must on one level refer to the hieros gamos.
 Josten and Hamilton-Jones both translate this as “chaste,” which seems rather forced in this context.
 Written in Greek, . Josten: “Cf. M. Berthelot, Collection des ansiens alchimistes grecs, vol. i (2nd part), Paris, 1887, pp. 43, 57, where [Pseudo-] Democritus and Synesius attribute this saying, which Dee quotes incompletely, to Ostanes” (p. 167 n. 58) The complete saying, “Nature rejoices in nature, nature rules over nature, and nature is the triumph of nature” can be found in the story of how Democritus, “a thrice-wise man,” was initiated into the Egyptian mysteries of Memphis by the Persian Magus Ostanes, (Berthelot, p. 57) and nods as much to this Greek alchemical tradition as to the particular quote. A similar speech occurs in the Turba Philosophorum (Klein p. 124 n. 105). A similar speech appears elsewhere as that of the angel Amnael to Isis: Nature takes pleasure in Nature; Nature triumphs over Nature, Nature rules Nature. A human begets a human, the lion begets the lions, the dogs beget the dogs, grain begets grain: learn this from the farmer Achab. What is begotten against nature is a monster incapable of life. The Adepts teach this: only gold brings forth gold again at the harvest. This is the revealed mystery. (Goldschmidt pp. 1961-1962, translation Turner)”.
 Ostanes is also sometimes spelled Osthanes, and in some sources said to be Persian and in other Alexandrian. An Arabic alchemical treatise titled Kitab al-Fusul al-ithnay ‘ashar fi 'ilm al-hajar al-mukarram (The Book of the Twelve Chapters on the Honourable Stone) is attributed to him, but is as far as we know unavailable in translation into English, French, or German.
 The “Philosophis proponimus Considerando” of the theorem’s very first line seems echoed in this second paragraph.
 The sun is exalted in Aries, as the Moon is in Taurus.
 Gignitiuam, another word Dee has invented.
 Josten comments on Dee’s Latin Gignitiuam thus: “There is almost certainly a play here on the word Gignitiuam for which normally the word Genetivam would have been used. Dee regarded it probably as significant that the genetive ending or belongs to the casas genetivus, i.e. a case having reference to generation, and that he wished to draw attention to this fact by using the unusual word, gignitivus, apparently invented by him, which, as genetivus, might be translated ‘generative’” (p. 169 n. 61).
 If the circle and semicircle intersect, the area of intersection is the shape of a vesica pisces, which was considered a holy figure by Pythagoreans among others. While it would not be an exact vesica in Pythagorean terms, because we don't have two complete circles where the center of one lies on the circumference of the other, it is the exact shape of a vesica.
 Latin propositum, which can mean general theme, principle, design, or purpose and in logic is the first premise of an argument. Its English cognate, in Dee’s day, meant not only something proposed for discussion but a parable, riddle, or problem to be solved, and is used throughout the translation of Euclid’s Elements for which Dee wrote the preface.
 As usual with capitalized words, Dee plays on multiple meanings. CRUCE – the masculine ablative singular of CRUX, and CRUX in the next sentence – refer to a gallows, frame or tree on which something was crucified; a medieval Latin derivative, crucibulum, becomes English “crucible.” In England of Dee’s time, a– cross was often appended as a place identifier to cross-roads or places where a cross monument stood (market-cross, St. John’s-cross, etc.) The crux of the matter is also the central problem which it vexes one to solve; presumably this is why Dee “must philosophize” at this point.
 Much of what follows is, on one level, right out of Euclid’s Elements. A line, for instance, is defined as “breadthless length,” (definition one in Euclid), whose ends are points (definition two). No end-points have been given for these lines, and without the point they cannot divide themselves.
 See Elements Book X, especially the propositions concerning unequal straight lines. Book X depends on the discussion of ratio and proportion in Book V.
 Dee describes a cross as composed of right angles, likely again directing a reader to Euclid’s discussion of right angles in Elements.
 NATURÆ. Perhaps for the readers who missed the “Nature takes pleasure in nature” reference in the previous theorem because they didn’t read ancient Greek, Dee now gives the word in Latin. Latin naturæ, and the words etymologically derived from it in French and then English, has little to do with our current sense of nature as “countryside” and refers instead to a constellation of ideas ranging from an active order-establishing force in the universe to elemental characteristics or properties that define objects, to some one or thing’s consistency with that order, to the organs of generation and what they generate, including menstrual blood or semen.
 This seems to invite the reader to visualize the lines as three axes passing through the same point. Two lines which exist at right angles to one another, according to Elements Book XI, are in the same plane. That plane then becomes the Euclidean “plane of reference” and the other line runs through it. As soon as one proposes characteristics about the third line running through the point, one has described a way that points lying outside of the plane exert influence on the plane of reference, an idea Dee develops in Propaedeumata aphoristica Theorem XXXIII to describe how a ray emanating from a celestial body might effect another convex surface: “a right cone, radiant and sensible, surrounds every sensible ray which emanates toward any external point from the body of any star and makes equal angles everywhere with the convex surface of the same star. The axis of the cone is the ray; the vertex is the external point. The base, finally, is that luminous portion of the convex surface of the same star which is nearest to the said vertex and is bounded by the circumference of a circle described by the end of a straight line drawn from the said vertex to the star and which barely touches the star” (p. 137 in the Shumaker translation.) If one takes the point where all three lines intersect as a vertex, and projects conic sections from the point using the third line as an axis, we might have, according to Dee’s understanding of ancient Greek works on Conics, a geometric model for how a point emanates light. If we have two equal cones emanating from the same point with the same axis and try to describe how a plane might intersect them, we get seven possibilities, one of which looks like a cross. From the possible plane of reference described in Theorem XVI, we have only three geometric possibilities: a point, a line, or a cross. See further discussion in Burns and Moore. Thank you to James Swenson for his succinct explanation of how Euclid envisioned conic sections.
 Here, one might note that Book V of Euclid’s Elements, on the foundation of ratio and proportion, does not depend on any of the concepts in the previous books except that of the unit or monas. Books XI through XIII, on solid geometry, depend on the ratio and proportions in Book V, as does Book X (see note 80).
 Josten (p. 171 n. 63): “Five and six were considered to be numbers ‘returning to themselves”, and were called circular, inasmuch as the last digits of. all their powers are five or six, respectively. See Petrus Bongus, Mysticae Numerorum Significatonis Liber, Bergarno, 1585, vol. i, pp. 182—183. Cf. Theonis Smyrnaei Philosophi Platonici Expositio Rerum Mathematicarum ad legendum Platonem utilium, ed. E. Hiller, Leipzig, 1878, p. 38, line x6, top. 39, line 9.
 Possibly an allusion to Elements Book X, which depends on Book V, and in part concerns irrational lines.
 In Roman numerals L + L = C
 Dee seems to be rediscovering this great mystery as he tells his reader.
 L written phonetically as “EL” but also certainly the Hebrew El, , (aleph lamed), a name of God, and a suffix on most of the angelic names used in Dee’s system of magic (Michael, Gabriel, Uriel, Raphael, Anael). In this context “denarian” also refers us back to the ten sephira of the cabalistic Tree. If we have visualized the cross as two cones sharing an axis and focus, one might see each cone two-dimensionally as an “L.” In the conics of Apollonius of Perga as translated into Latin then English, “l,” referring to the latus rectum, is part of a fascinating geometric transformation that describes a parabola. Interestingly enough, one of the first uses in English of “parabola” to describe conic sections was in 1579 by Dee’s student Thomas Digges (OED).
 Here Dee is saying the letter L is exactly in the middle of the alphabetic sequence that runs from A to X. But while Dee is correct in saying that the letter L is exactly in the middle between A and X, it is actually eleventh in order from both A and X. His addition only works if you let L be zero, and count out in both directions with the adjacent numbers being 1, 2, and so on to 10.
 Because we are more accustomed to expressing these ideas algebraically, we might be more likely to say: “If this SQUARE number is divided by the square number of the previously mentioned circular number, we once again get the CENTARY.” In other words, if 502 (2500) is divided by 52 (25,) we get 100, which is 102. But Dee’s language would make sense to a Euclidean, as the concept of squares in Book II of Elements is expressed this way and never uses numerals. Almost all ancient Greek mathematical works rely heavily on analogia, which can mean both proportion and analogy. In this sense most of Elements Book V are analogias, and the numbers are not only numerals in the algebraic sense, though we may understand them that way. As Fried notes, “in Greek mathematics, proportion was not only a vital manipulatory tool but also a means of making [or evoking] images.” The two squares and circle in this line may also allude to two of the most famous ancient mathematical problems, the doubling of the cube and the squaring of the circle. The first, the so-called Delian problem, has an analogous problem in two dimensions (the doubling of the square) that is easy to solve. The most well-known solution to the Delian problem, by Archytas, involved using conic sections.
 Unicus. See note 30.
 Unum. See note 30.
 Another sign for the cross is X.
 Josten and Hamilton-Jones both omit “sign.” The simplest “sign” for five is V.
 One of the few usages of “quinari” in a similar form comes in Book 8, Chapter 6, Section 4 of Vitruvius’ De Architectura, where we are told of three ways of conducting water. For the third way, via lead pipes, we’re told that lead pipes that are “fives” should weigh sixty (LX) pounds.
 In other words, L. By reprising past theorems, Dee gives the sign LVX backwards.
 A Reprise of his earlier reference to the DENARY as the cabalistic Tree and the Pythagorean Decad.
 Mecubalist comes from Hebrew Mekubalim, and is one of several terms used to refer to a learned sage of the Cabala.
 Josten (p. 173 n. 70): “No example of this symbolism has been found. Professor G. Scholem, of the Hebrew University, Jerusalem, kindly informed me that there appears to be no caballistic explanation for Dee’s statement.” If as preeminent an expert on cabalistic symbolism within Judaism as Scholem sees no connection, perhaps its safe to assume that this is because Dee is referring to Hermetic, rather than Judiac, cabala, which almost always associates a cross with the sixth Sephira Tiphareth. His term “Mecubalist” also suggests a cube. Noting that Tiphareth is the six Sephira and that there are six faces on a cube, one might observe that 1 + 2 + 3 + 4 + 5 + 6 = 21. See note 100.
 By the end of Theorem XXIII, after three very long theorems which contain geometric and Hermetic explanations and diagrams which none has explained in print, Dee will equate 252 with the philosopher’s stone. Josten points out that 252 = 22 + 23 +24 +25 +26 +27 (p. 175 n. 71). It is also the product of the three types of letters in the Hebrew alphabet: three mothers, seven doubles, and 12 simples, 3 x 7 x 12 = 252. Thus Dee equates the Philosopher’s Stone to the entire Hebrew alphabet, which to a cabalist is the entire represented powers of creation. For further discussion, see Burns and Moore.
 Dee does not tell us what these two ways are. One may assume this is part of the oral teaching. Modern esotericists, noting the analysis of the keyword INRI/LVX transformation, might want to try this exercise in gematria on their own before jumping to the adjoining article. Since Dee by his capitals is as usual suggesting concepts as well as numbers, one might also want to mentally reprise what these concepts, on the most elementary level, might be. He is treating the 252, the Cross, LVX, and the Monad itself as a very packed symbol comprised of the concepts and glyphs represented by these numbers.
 Tyronibus, another word of Dee’s invention. Josten translates it as “beginner,” which makes grammatical sense (tiro + ibus) if one assumes Dee “misspells” tiro. But we’ve found no other case of inexplicable misspelling, and it makes no sense for beginners in cabala to study a teaching Dee equates with the philosopher’s stone. We suggest that the spelling is intentionally distorted to nod at several different meanings of Tyr. It is perhaps a reference to the ancient Phoenician city of Tyre/Tyros, whose name means “rock” and which was the legendary birthplace of Europa and Elissa (Dido). Tyre was reknowned for its purple dye; hence the Tyrian dye referred to repeatedly in the Turba Philosophorum; Tyr can be a poetic term for Theban (since Cadmus, the founder of Thebes and Grandfather of Dionysis, was from Tyre.) Týr is also the Old Norse God whom Latin writers identify with Mars and from whence comes our “Tuesday.” In Old Norse, his name meant simply “God,” Týr also was a Viking name for Polaris, the North Star; the rune Tyr is an arrow pointed upwards. Finally, Tyronibus could be a pun on Tyr + omnibus (for all, or that rock, Tyr, which contains all).
 Here Dee uses the term Mystagogus for “initiator to the mysteries.” In classical Latin a Mystagogus is a priest who initiates people in sacred mysteries, from ancient Greek , a person who gave instruction to candidates for initiation into the Eleusian or other mysteries.
 “ILLARUM VERBALEM VIM, CUM IPSA CRUCE, CONFEREMUS, quod inde Oriatur LUX” This phrase loses its clever word-play when LUX is translated directly to English as “light.” LUX (LVX in Dee’s Latin) as the “sign” of the “CROSS” has been built up as a signifier for Dee’s entire teaching to this point, and saying LVX or what it represents lets light be made is a clear allusion to the Fiat Lux in Genesis 1:3.
The Hieroglyphic Monad of
by Teresa Burns and J. Alan Moore
John Dee’s Hieroglyphic Monad remains one of the most enigmatic works in the history of western Hermeticism. The best introduction still is C.H. Josten’s, which declares unequivocally that it is a work of alchemy, suggests many possible contexts, but adds that the “specific message which Dee tries to convey by his symbol of the Monad, and by his treatise thereon, is lost. His explanations are sometimes explicitly addresses to a mystae and initiati whose secrets we do not possess.”
Composed by Dee in 12 days, the Monad was clearly accompanied by an oral teaching, and in his later writing Dee reminds the Court of his providing part of that instruction to Queen Elizabeth and perhaps, King Maximilian. Dee himself called the Monad a magic parable, and for many years there was certainly a group of initiates that understood it well. Frances Yates has argued that the “more secret philosophy” behind the Rosicrucian manifestos “was the philosophy of John Dee, as summed up in his Monas Hieroglyphica.” The Chymical Wedding of 1616, which Adam Mclean has noted is structured as an “elaborate Hermetic allegory” of inner transformation, displays the Monad glyph prominently next to the first poem; Jacob Boehem’s 1625 Clavis and Ananasius Kirscher’s 1650 Obeliscus Pamphlicus also show this glyph and exhibit ideas strongly influenced by Dee’s work. The American alchemist and first governor of Connecticut, John Winthrop, used the Monad symbol as a bookmark, as did his son and grandson.
By the time 20th century scholars became interested in the Hieroglyphic Monad, those who understood the work seemed to have died with its secrets. The author of the first scholarly biography of Dee, Peter French, suggested that a major concern of Dee’s magical parable was the “Gnostic ascent to the One. . . The process of man’s spiritual transformation is therefore the deepest subject of this work, rather than the mundane alchemical quest for gold.” Yet like C.H. Josten before him, and a series of commentators since, French felt that, “Dee wrote within an oral and secretive alchemical tradition that has probably been permanently lost.”
Has it been? As the community of scholars and esotericists studying the Monad starts to overlap more each year, perhaps we have enough old information coming to light that we can resurrect this hidden teaching. Certainly at least part of the oral teaching has been hiding in plain site, within the very stream of the western mystery tradition that the Hieroglyphic Monad gave birth to.
We think that teaching can be recovered simply by looking at what contexts Dee wrote in and where parts of those contexts survive. Let us make the not-so-radical assumption that the work encodes many different levels of information at once, and describes many processes at once, and one of those is the process of initiation. Therefore the more one wants to understand the other processes, the more the student must actively participate in that initiatory process and discover the magical correspondences. Today, we have enough other works available to “rediscover,” on our own, what likely were two of the core oral teachings that accompanied the Hieroglyphic Monad: precessional astronomy and tantric gnosis.
In fact, we contend that the process of carrying through a study of this work through to the point where a true understanding begins to enfold is in itself an initiatory process. Just as Renaissance actors used an elaborate three-dimensional mnemonic system to remember their lines, the student of the Monad needs to build up an at least three-dimensional, moving system of correspondences and how those correspondences transform into others, to start to understand the work.
Our goal in this commentary is to assist you on your own journey of discovery and apotheosis. This isn’t a cook-book guide. It’s a series of suggestions about how Monad might unpack through Theorem XVII, the Theorem which reprises the Sign of the Adept and so stands at the gate to most complex understanding of the Mysteries.
One of the secrets of that art known as physical alchemy known to the true initiate is that the Great Work cannot be achieved by physical, external, or mental means alone, but requires that in parallel to the physical processes of the alchemist’s laboratory and mental gyrations of the student’s mind a holistic inner alchemical transformation takes place within the entirety of the alchemist himself or herself. It is through the catalyst of inner transformation that the external process can be fulfilled. Thus also it could be said that the truest understanding of that which this work holds in potential or the truest understanding which lies latent with this corpus cannot blossom without similar inner transformative process in the mind and psyche of the student. The process by which this structure is built through the theorems presented, when accompanied by the proper focus and laid upon a firm, well-prepared foundation, is in itself an alchemical process in which the passages are contemplated and an understanding begins to dawn in the mind of the initiate.
Because of this, to read the Hieroglyphic Monad and not understand at first is to be expected; yet to read it with the wrong contexts is to invite misreading, confusion or the conclusion that the glyph really means nothing at all. For John Dee, to whom mathematics, magic, and divine cosmology were inextricably intertwined, any set of complex symbolic teachings would have to start with the same axioms and they would need to build consistently through all three fields. If we, as readers, start with different axioms, the transformation his work tries to trigger will never take place. For instance, if one searches through Dee’s lines and circles knowing nothing about geometry—or perhaps worse, thinking one knows, but superimposing a modern conception of math and numbers onto the ancient Greek perception, his geometry will make no sense, and one might simply conclude Dee didn’t understand numbers.
While we may discuss mathematical concepts in this guide, we want to do so within the western mystery tradition. If one knows nothing about that tradition -- and many who have written on Dee have at best only a very superficial grasp of it -- reading the Hieroglyphic Monad through Theorem XVII would be akin to reading through the Golden Dawn Outer Order rituals or worse, the cipher manuscript they came from,  and wondering why they make no sense. They do make sense if a person has the right context; they don’t if one doesn’t.
Theorem XVII and the Analysis of the Key Word
To give an extended example of this, let’s look at one place where we are certain part of Dee’s teaching has been transmitted, in the Golden Dawn’s analysis of the keyword, an encapsulated ritual utilized in the 5=6 initiation, the consecration of the Vault of the Adepti, and in many shorter Adept-level rituals. Most notably, the INRI/LVX transformation is part of what symbolically opens the Vault of Christian Rosenkreutz. It has as its only known source the Hieroglyphic Monad, yet many who are familiar with or participate in these ceremonies seem unaware of this connection. Perhaps this is because one must understand the Monad through Theorem XVII to really understand the keyword analysis, and the few who study it in that much detail often lack the right contexts.
For the Adepti, we’ll start this commentary at Theorem XVII, then circle back to the frontispiece and opening theorems.
If one compares Theorem XVII and the Analysis of the Keyword, there at first seems little similarity:
As is evident from the sixth theorem, FOUR right angles can be considered to be in our CROSS, and the preceding theorem teaches that the sign of the QUINARY can be attributed to each one of them, the right angles of course being arranged in one way, but maintaining another position. The same theorem explains the production of the hieroglyphic symbols of the number FIFTY. Thus, it is very clear that the CROSS generally denotes the DENARY; and that in the order of the Latin alphabet, it is the twenty-first letter (whence it was the case that the wise ones called the Mecubalists signified the number twenty-one with the same letter); and finally, it can be considered very simply to be seen as one sign, no matter what kind of, and how much, other power it has. From all of these things together, we see it can be concluded by means of a very good cabbalistic explanation that our CROSS can signify to initiates, in a remarkably shortened way, the number TWO-HUNDRED-FIFTY-TWO. Namely, FOUR times FIVE, FOUR times FIFTY; TEN; TWENTY ONE; and ONE, add up to TWO-HUNDRED-FIFTY-TWO; which number we can deduce in still two other ways from our previous [statements]. Thus we recommend to cabbalistic Tyrians that they scrutinize this same [number], studying it in such a brief space, concluding the varied, skillful production of this Master Number to be worthy of the consideration of philosophers. I will not conceal from you here another memorable initiator to the mysteries. Our CROSS having suffered itself to be divided into two different letters, and as earlier we considered their [i.e. the letters’] numerical virtue in a certain way, we will now compare in turn THEIR VERBAL POWER WITH THAT CROSS, because from this may be born LUX (LIGHT), a WORD we perceive with the highest admiration, finally and magisterially (through the harmony and agreement of the TERNARY in the unity of the word).
From the Golden Dawn Adeptus Minor Ritual
If one looks closer, and knows from earlier in the Monad that the “Cross” is X, the Quinary is Roman Numeral V, and Fifty in Roman numerals is L, we see Dee giving the LVX sign backwards. Signing it backwards, just as an English or Latin writer would think of Hebrew as written “backwards,” or right-to-left, suggests a particular context. His use of the word “Mecubalist,” from Hebrew Mekubalim, suggests an even more particular context within Jewish mystical thought, just as his use of “Tyrian” near the end suggests a multitude of classical literary, Norse pagan, and Gnostic Christian contexts. Those contexts, in different ways, suggest a four letter word turned into three; also, Theorem XIII (noting that 13 can become 1 + 3 or 4), as we’ll see later, could be interpreted as INRI. For a student of Dee’s, those meanings would already be part of the set of correspondences built up before getting to XVII, where INRI becomes LVX.
LVX, of course, is how the
Latin word lux, or light, was spelled during the Renaissance. INRI is
traditionally looked at as the initials of the Latin phrase placed by
the Romans at the head of the cross on which Jesus was crucified, and
stands for “Iesus Nazarenus Rex Iudaeorum,” or "Jesus of
Nazareth, King of the Jews". Regardie points out that medieval
alchemists suggested it meant “Igne Nitrum Renovatur Integra,” or
“The whole of Nature is renewed by Fire,” and indeed that could
stand as a brief statement of one of the meanings of the entire Monad:
the Sun and Moon as understood by previous theorems, plus the Cross of
the Elements, are renewed by Fire as symbolized by the glyph of Aries.
On the most basic level, the letters LVX are all parts of the cross:
Dee equates light, and the LVX keyword as sign of the Adept, with the number 252, which by the end of Theorem XXIII of the Monad he will have equated with the philosopher’s stone, and with the sign of the Cross. He attributes the Cross to the “DENARY,” suggesting both the Pythagorean tetractys and the ten Sephiroth of the Tree of Life, and cryptically explains that this should be clear because the cross (X) is the 21st letter of the Latin alphabet. Some of the best Dee scholars and Judaic cabbalists have puzzled over this, but the answer is clear if one understands Hermetic cabbala and geometry implied in previous theorems: INRI transforming to LVX would take place at the sixth Sephirah, Tiphareth, and if one takes the Sephiroth usually referred to Tiphareth (Yesod through Chesed) plus the “non-Sephirah” Da’at and connects them, one draws a hexagram or hexagon with Tiphareth in the middle. Similarly if one folds these into a cube, it has six faces. Noting the importance of all of these sixes, we observe: 1 + 2 + 3 + 4 + 5 + 6 = 21.
If one has built upon these geometries enough to see a 5:6 proportion developed throughout the preceding theorems, in particular in how the Pythagorean decad and Cabbalistic ten Sephiroth transform into systems based on twelve  (5:6 :: 10:12) one suspects 5=6 and the rank of an Adept carries additional significance that modern-day Adepts may have lost. The six-faced cube, incidentally, is one of five regular Platonic solids.
INRI turns into 252, and therefore the Cross, in yet another way, through a combination of Pythagorean mysticism and gematria. The gematria of I + N + R + I, yod nun resh yod, 10 + 50 + 200 + 10 yields 270, a rather significant precessional number. But if we remember that to the Pythagoreans, the Decad (10) was simply a higher form of the Monad, and we collapse this higher form into one unit, we have 1 + 50 + 200 + 1 = 252.
What else of the number 252? What are the two other things we should be able to “deduce” from his “previous statements”? Perhaps, as Josten noted, that 22 + 23 + 24 + 25 +26 + 27 = 252. Secondly, it is the product of the three types of letters in the Hebrew alphabet: three mothers, seven doubles, and 12 simples, 3 x 7 x 12 = 252. Thus Dee equates the 252, the Light of the Cross, and the Philosopher’s Stone to the entire Hebrew alphabet, which of course to a Cabbalist signifies the entire represented powers of creation.
Then, Dee says “I will not conceal from you here another memorable initiator to the mysteries,” yet he seems to conceal it after all, telling is only that “Our CROSS having suffered itself to be divided into two different letters, and as earlier we considered their [i.e. the letters’] numerical virtue in a certain way numerical virtue in a certain way, we will now compare in turn THEIR VERBAL POWER WITH THAT CROSS, because from this may be born LUX (LIGHT), a WORD we perceive with the highest admiration, finally and masterfully (through the harmony and agreement of the TERNARY in the unity of the word).”
If the Adepti manipulate sections of the cross as we did with LVX, they may find two Hebrew letters whose sound, when put in the context of a particular stream of Greek alchemy, becomes I A O.
Making the Key Word Meaningful
While playing with letter and number combinations can be a lot of fun, it won’t feel profound unless one understands the myriad of correspondences that are supposed to be built into it. Thus we offer this guide to looking at the frontispiece and first sixteen theorems.
While many of us fall into the habit of thinking we know much more now than those in days past, its crucial to understand that Dee’s hypothetical 15th century student would have had a much broader frame of reference, in terms of languages and allusions to classical literary and mathematical texts, than we have now. Dee himself had by far the largest library in England, and a study of what books he was collecting just prior to writing the Monad leads to interesting speculations. We know he also was copying manuscripts he never recorded in his library lists, perhaps because the works themselves would have been too heretical.  We know he was fascinated by caballistic correspondences: though his only work on cabbala, Cabalae Hebraicae Compendiosa Tabella, has been lost, its title suggests it was something along the lines of Aleister Crowley and Allen Bennet’s “Sepher Sephiroth.” If something in the Hieroglyphic Monad seems like an allusion it probably is; if you see caballistic correspondences beyond the obvious, you’re certainly not imagining them.
As you study the Hieroglyphic Monad, you’ll notice that while the theorems in one sense build logically one to the next, in another way many of them ask the reader to cycle back through the whole group. Piece by piece, they build a structure which superficially has its representation in the glyph of the monad, but the body of knowledge represented by this work and indeed by the glyph itself is not to be understood by superficial information alone. As the glyph which embodies the core of the instruction to be had in this work is assembled piece by piece, so too is the inner teaching, the deeper mystery, which is to be found within this work, assembled in the mind of the initiate.
This guide will attempt to take you through in an accelerated form a few layers of the learning cycle which culminates in the keyword LVX. To attempt to fully unpack the wisdom available is far beyond the purview of this article and indeed were one to be thorough, it would fill volumes. Therefore in this article we will attempt to investigate but a few layers out of the many, and to help the reader to begin his or her own journey of discovery and transformation. In particular, we want to suggest the “building blocks” in the first ten theorems, and point to places in those which follow where one might be able to discern the references to the ancient Eleusianian or Samothracian mysteries, and references to precessional astrology.
Study the frontispiece, and
note in particular the contexts Dee sets up in it. The Monad
appears in an egg between two pillars. Before jumping to the egg in
Theorem XVIII, just notice what is most obvious visually: it is the
“middle” between two pillars.
The odd statement on the garland suggests we must play with language as much as geometries (especially since Dee, in his letter to King Maximillian, asserts that Latin, Greek, and Hebrew alphabets each have significant geometries.)  The best way to render this line in English, “Mercury becomes parent and the king of all planets when perfected by stable, pointed Stilbon,” helps most students’ understanding not at all unless the associations of Mercury and Stilbon are explored.
The odd language use suggests several contexts. As the notes in the accompanying translation point out, Dee writes “” in Greek, which must be transliterated to Roman letters to read Stilbon, “shining one,” the god of the wandering star Hermaon or Mercury. Yet, as the translators comment, “it also makes us think of Latin stilus, which can refer to a stake, staff, or pale, a pointed implement used for writing or for style in speaking. . . [r]ecall that Tehuti/Thoth is often shown with a writing implement, and becomes the Greek Hermes/Mercury. Thus Dee’s odd language nods to the Emerald Tablet of Hermes Trismegistus as a governing context for the work.” It also suggests a transformation between Mercury and the Sun which won’t become clear until much later, because the usual “unperfected” understanding would be that the Sun, not Mercury, is “Father” or “King.”
While we don’t plan to refer to each note of the accompanying translation in this guide, we hope the brief analysis above does suggest to the reader one of the most important ways in to understanding the Monas: word-play. Dee was writing to someone who read not only Latin but Hebrew and ancient Greek, and further, was familiar with particular texts in those languages that have come to influence the core teachings of the western mystery tradition. The best way to explore Dee’s language play is to attempt one’s own translation, but if that isn’t possible, the student has many resources available to at least explore word etymologies and which classical writers make frequent use of his terms.
In Dee’s letter to Maximilliam, he refers to the Monad symbol as “my London Seal of Hermes,” again suggesting the context of the Emerald Tablet . Further, he expects his reader to know that the word monad, Latin monas from Greek , (pronounced monas) means a unity, singularity, or point. This is likely the “one” in the Emerald Tablet  and certainly the basic unit (often directly translated as “monad”) in Pythagorean, Platonic, and Euclidean thought. The fundamental unit in Euclid’s Elements is the monad, and Euclid devotes all of Book VII to exploring its meaning. Dee, of course, wrote the preface to the first English translation of Elements, so one should become familiar with that work, in its ancient rather than modern context. Geometric images, to Euclideans and Pythagoreans, were sacred images and manipulating them was a way to evoke the divine in one’s own mind.
The numbers 1, 2, 3 4; then 1 and 4, on the frontispiece likely both suggest the Pythagorean tetractys, which will be referred to indirectly in many theorems.
The bottom line of a tetractys add up to 10, 1+2+3+4=10, just as there are ten points; the top point, 10 or the Decad, is simply a higher order Monad. The irregular spacing of these numbers on the frontispiece has made some suspect a cryptogram,  if so, we’d suggest that the cryptogram is simply “LVX” written in yet another way. Note that both the ten points of tetractys and the sum of its first line make 10, X; 1 and 4, as 1 + 4 = 5, to V, and both together (10 x 5) to 50, or L. We have LVX again, backwards.
At the bottom of the frontispiece, we find a quote from Genesis, part of the ten-fold blessing of Isaac to his duplicitous son Jacob. Thus yet another context is suggested; knowing Dee’s other interests, we might be much more successful looking for Gnostic or caballistic explanations of passages in Genesis rather than mainstream Christian ones.
Many have noticed that the Monas glyph appears on both versions of Dee’s Propaedeumata aphoristica. Dee wrote the first version as part of a letter to Gerard Mercator in 1558; his revised edition was published in London in 1567. It is available in an excellent English translation by Wayne Shumaker which includes, from a history of science rather than Hermetic perspective, analyses of Dee as a mathematician, and the aphorisms as understood through the lenses of applied mathematics, physics, geocentric astronomy, and astrology. We hope someday someone who understands the Monad through the lens of Hermeticism well enough to explicate all 24 theorems will have the time to back through these 120 aphorisms and add to Shumaker’s commentary.
Theorems I-III and I-X
Given the contexts set up on the frontispiece, we might expect to find references to the Pythagorean tetractys, especially since one explanation of that sacred figure is that the first row represents zero dimensions (a point); the second, one dimension (a line segment running from the first point to the second), the third, two dimensions (a plane, defined by a triangle or three points and sharing the same shape as the tetractys in 2D); and the fourth, three dimensions (a tetrahedron, defined by four points and sharing the same shape as the tetractys in 3D). We might also expect to find references to the cabbalistic Tree of ten Sephiroth; we might expect references to Genesis, and we would certainly expect references to the Emerald Tablet .
To fully comprehend the ideas in this group of theorems, and indeed the whole Monas, one must constantly cycle back through, so that later understandings also change how one understands what is read before. Theorem I, therefore, starts with what we are able to see: a line and a circle, or the first two dimensions and how they create the third. We don’t “see” a point, so we can’t start with it.
Here Dee introduces the idea of a point, and in doing so invites us to cycle back through Theorem I. He equates it to a point of light, or a spark of consciousness. If we think of many of his theorems as energy transformations, here we also have the idea of energy that has been localized, and is no longer a stream or ray, and he would find support in the modern notion that the tiniest quantum particles are energy that is vibrating in one place and not streaming in motion.
Macrocosmically, the monad, the beginning point for manifestation, is light localized to a point. It takes on dimensionality by becoming a stream, or an infinite flow of points, thus giving us a line (first dimension). An infinite flow of lines give us a plane, or the second dimension. The circle, the most “perfect” figure in plane geometry, can’t be defined without either. So far, Dee’s explication could be straight out of Euclid, though one may cycle back for other interpretations later on.
Now the two-dimensional “circle’ becomes a sphere, and so the Earth. Dee’s “light” alludes to the fiat lux of Genesis and thus the creation of all things from light. One might want to further explore the different meanings of “circle” and “sphere” to ancient writers, for they carry layers of significance lost in our modern notion of these as “only” geometric objects. At the very least, “circle” and “sphere” both involve movement and an unending, usually sacred, cycle.
Because this theorem says that this middle point can also represent the earth, Dee is making the point or monad the top of the tetractys or decad, and further suggesting that the “Earth,” composed of the monad/decad, is referred to the tenth Sephirah, Malkuth.
As he is introducing the idea of the Sun, Moon, and other Planets completing their paths around the earth, Dee seems to be suggesting a geocentric view of the universe, and indeed, many very good writers have assumed, from this Theorem and XVIII, that this was his view. They neglect to note what should be obvious to Hermeticists: that if “I” am the spark of consciousness, that spark will be the center. Similarly, those of us who study astrology today do not think the Sun revolves around the Earth, but we know we have more accurate charts when we know the exact location on Earth to draw the chart from. “Earth,” or a point on Earth, is the frame of reference, the point from which other phenomena are observed and upon which other forces act.
It is very important to keep this idea in mind when working through the later Theorems, especially if you try to project these concepts onto the Tree of Life, or that Tree onto a Sphere. You are not attempting a diagram of the solar system; you are attempting a diagram of how consciousness comes into manifestation.
It his later theorems and in the Propaedeumata aphoristica, Dee will want us to understand that cosmic forces influence us in the same proportions that they stand in relation to us, that we can observe from our central “point.” We do not observe from the point of reference of the Sun, but from wherever we are on earth. We are analyzing our own being and consciousness from the geometries we reflect from our vantage point on Earth.
Finally, note that here and in most places Dee capitalizes SUN and MOON, which throughout also refer to the marriage of Sun and Moon in the Emerald Tablet .
This theorem starts to test our ability to visualize the Monad in three dimensions and rotate it around so it is viewed from different perspectives. The moon would “appear” to be superior from the point of the observer: it is placed there not because it is superior, but because it looks that way from Earth. It “appears to the ordinary person” that the Moon emulates the size of the Sun because the Full Moon looks the same size as the Sun.
Yet the face, or semi-sphere, always reflects the light of the Sun—it does not generate light.
The next lines, that the Moon desires to be impregnated by the Sun, should be cycled back to when one has a greater understanding of what “Sun” and “Moon” may mean in the Emerald Tablet , but on the most simple level we have a description of the phases of the Moon: saying it desires to be impregnated (in appearance) by the light of the Sun means it wants to become full and look like the Sun.
Of note, the Moon in Dee’s Monad looks like Diana’s Bow, the first phase of the Moon after it has conjuncted the Sun and disappeared (the New Moon), then reappeared as a tiny sliver in the sky.
Note that this Theorem, V, refers to light, the essential element of alchemy. The capitalized “LVX” for “light” in the Latin original of Theorem V also implicitly refers us to the LVX analysis in Theorem XVII, or begins an idea that the later Theorem completes.
Five also refers us to Venus and the Pentagram, which is formed in the sky if one watches solar conjunctions of Venus and the Sun from the Earth.
Finally, by equating the creation of the first day and night with the “LVX” of the philosophers, Dee implies that alchemy involves the measurement of time and space, and so introduces the idea of precessional astronomy. Cabbalists and fundamentalists have argued about the meaning of the Hebrew word for “day,” the former arguing that that this word meant not our current conception of day, but a unit measurement of time: a day, week, era, age. Following this interpretation, we should look at numbers in terms of spatial and temporal unit measures.
As V refers to the Pentagram and Venus, VI will refer to the Hexagram and Mercury, as the pattern of conjunctions between Mercury and the Sun, viewed from earth, form a Hexagram.
In certain ways the first ten Theorems can be referred to the Sephiroth and their places on the Tree,  but notice this isn’t apparent until VI, which would correspond to the sixth Sephirah, Tiphareth. This is important because it again suggests our frame of reference.
Tiphareth represents the highest level of manifestation that we can perceive from our own consciousness. The light of Kether reaches us through Tiphareth, which is why it is often referred to the Sun. We can’t see the center of the galaxy, but we can see the Sun, even though all the power that the Sun wields comes from the center of the galaxy. We can understand what we can’t see, but first have to understand what we can see. So in one sense Theorem I starts with what we can see, but in another, Theorems I-V are all the abstractions you have to set things up until you get to what you can really see. So we know that the “Sun” and “Moon” in first 5 theorems will likely be concepts we’ll later return to, with new definitions.
For instance, we know the “one thing” or monad of the Emerald Tablet has the Sun as its Father and Moon as its mother; or is the product of the marriage of the Sun and Moon. This Theorem, referring as it does to the Sun and the Moon and a uniting point, suggests at least one type of union at Tiphareth.
In this context, the reference to “body, mind, and soul,” directs us to the nephesch, ruach and neschamah, the three parts of the soul to cabbalists. One is invited to meditate further upon what, beyond 3 + 4 = 7, Dee means when he tells us that the septenary manifests from the ternary and quaternary. Remember that “seven” was the usual count of both planets and alchemical metals.
Dee’s comment about the octad won’t make sense until one has built a structure beyond Theorem XVII, but his suggestion, in the context of precessional astronomy, may be that the ancient Magi had never observed something in the sky, even though they may have calculated it.
At first this Theorem seems like a reprise of what has come before. The four lines and the language of “flowing” might remind us of the four rivers of Eden in their esoteric or cabbalistic context. But very subtly, Dee is returning to the idea of the pentagram: by displacing the central point from the cross, we now have five. This central point, recall, was the point of origin from which the line and plane was formed, and in effect governs the four elements as Dee has equated them to the lines. Because all four elements flow out of the original creative light, and because the displaced central point gives us the fifth point, we can infer a pentagram with the crowning point of Spirit, which then governs the four elements.
We have another reference to the tetractys in theorem 8, whose number refers us also to the octad or octave. The Pythagoreans had both a tetractys of addition, which Dee refers to directly by again noting a connection to the denary (1+2+3+4=10), and a more complex tetractys of multiplication, whereon the fourth level, referred to the third dimension, contains the first two cubic number: 2 x 2 x 2 and 3 x 3 x 3. The first of these, 23, equals 8.
X, the 21st (3 x 7) letter of the Roman alphabet, gives us another of the letters in our keyword.
The double reference to the SUN and MOON return us to the Emerald Tablet and the one, or monad, having the Sun as its father and Moon as its mother. Dee suggests we see the “Sun” and “Moon” both as circles which conjunct the cross; if we expand from two dimensions to three, we have two spheres.
Nine also refers us to the ninth Sephirah, Yesod, associated with generation, and the synthesis of the influences of all the other Sephiroth. It constitutes the “foundation,” or formative blueprint, for the manifest world in Malkuth. Note that Theorems 6, 9, and 10 refer directly to Sephiroth as usually numbered, which the other theorems in 1-10 do not, perhaps because the 6th, 9th, and 10th Sephiroth are on the Middle Pillar.
If we start to conceptualize a three-dimensional Great Tree from the information presented thus far, we have two spheres, the Sun and the Moon, with the axis of the Middle Pillar running through their central points, conjuncting the cross.
This theorem sets up the 10:12 or 5:6 ratio explicitly in the first line, by using the odd Latin Dodecatemorii instead of the more usual zodiacus. It likely refers us to works on the geometric solid dodecahedron as well as the zodiac; thus time and space measures continue to coincide and the unit numbers significant to one are significant to the other. This word and number play invites us to consider how spatial and temporal units of twelve divide and govern our understanding of the 10th Sephirah, Malkuth, the manifest Kingdom.
Within this manifestation, fire is the penetrating, fructifying, purifying force. Dee’s wordplay further equates fire with Hermes  and the symbol for Aries, the first sign of the zodiac. Dee makes it clear he is using the sign for Aries, rather than “Aries” itself, in any of its many references.
From this point on, our guide can only be as clear as your understanding of the first ten theorems. Wherever Dee’s meaning is not clear, we again suggest looking at his wordplay, cycling back through the earlier theorems, and trying to visualize in three dimensions what he is talking about.
When Dee speaks of “the time of 24 hours, in the mode of the equinox,” he again suggests numbers that are temporal unit measures and so alludes to the precession of the equinoxes. The “most secret proportions” of “our” earth are these precessional numbers. Note also that the Monad has 24 Theorems.
Eleven also refers to the “non-Sephirah,” Da’at or Knowledge. Sometimes Da’at is numbered only when Kether is not, suggesting it is the faculty by which we experience gnosis of all we can’t see, and that mystical state by which an individual experiences the unity of all of the Sephiroth.
From this point of Gnosis, one can now conceptualize a Great Tree whose “axis” runs from Kether to Malkuth, and whose proportions are precessional numbers. At Malkuth, it must intersect with the Cross of the Elements, which again divides time and space in terms of precessional numbers: four directions, four seasons; and so on.
In this Theorem and the one which follows, Dee’s language use and literary allusion become particularly dense.  He creates a Latin word where he can find none that express his meaning, and here and below, drops in a word from ancient Greek next to the Latin Opus, or work, possibly suggesting the origins of his ideas in Greek alchemy.
Dee provides glyphs of the planets and says they are all made from parts of the glyphs for Sun and Moon. Remembering our 10:12 proportion, and that Theorem X discussed mainly measures of 12, we might want to refer Theorem XII back to 10 and see what happens. If we have Great Tree of ten Sephiroth with the “Sun” and “Moon” as two spheres on the Middle Pillar, then all of the other planets, lying as they do “off” of the main axis, only exist as polarities or aspects of these energies.
His order of planets in this section has puzzled many, and should be returned to after one understands Theorem XVIII. They seem to correspond to the Four Elements, but only if we associate the fourth revolution with water; and could connect to the Four Ages of Lead, Tin, Gold, and Silver, but only if we somehow make the Moon and Mercury refer to Tiphareth or the Sun. The word “revolution” suggests temporal measurements, and indeed if one returns to these glyphs after further study, one may find that each corresponds to a type of temporal age, and the fifth figure--the synthesis of the preceding four—shows them combined into one zodiacal age.
If one considers the attributions of planets on the Middle Pillar, the progression from Saturn to the Moon is clearer. Saturn is usually referred to Binah, but can refer to all of the Three Supernals since it is the furthest “wandering star” we can see. Saturn/Binah’s reflection is to the Moon/Yesod, and what is “imprinted” in Yesod manifests in Malkuth, the physical world or Earth.
Here we also have “Mercury”/Hermes, the “pure magical spirit,” performing the “whitening,” one of the steps of physical alchemy, upon a zodiacal age, suggesting that external alchemy involves the transformation of time as well as space.
Dee’s language use in this theorem is so complex, and his transformations between concepts so packed, that a reader really should go to the Latin text to fully appreciate and understand it. As in the last theorem, he plays on multiple meanings of gnosis and gnomon, and adds a play on multiple meanings of pyr, fire, whose English cognates range from a funeral “pyre” to a “pyr”amid. The idea of “fire” expressed through the theorem is thus always alluding to a death and rebirth, hence the association of this theorem to INRI.
Dee suggests that the Great Work is harder to do in this age than before, and seems to refer to the process of physical alchemy: the “soul” separated from the “body” on one level refers to the vapors given off as a substance is purified. But that interpretation alone won’t help us through the next paragraph. “SOUL” in this Theorem has two opposing meanings—the dross that needs to be burned off, and the gate to the inner mysteries.
Dee associates Lucifer, the “Light-bringer,” with Hermes/Mercury, the Microcosm, and the reborn Adam Kadmon. Seamlessly woven in as allusion to the witches Sabbath,  and thus perhaps the marriage of Lucifer and Diana, this Theorem suggests that for the INRI transformation to occur, the marriage of the Sun and Moon either transform or become analogous to the marriage of Lucifer/Hermes/Mercury to his sister Diana/Venus/the Moon.
What are we to make of this? How can Venus and the Moon refer to each other? Part of the solution lies outside of Theorems 1-17 of the Monas, in Dee’s idea of the Age of Venus and its Olympic Spirit Anael as Ruler of the Age.  If we assume that this was part of the oral teaching concerning precessional astronomy, “Venus” governs the Moon, and indeed the whole Middle Pillar, during the “Age of Venus.”
We can more easily explain how Lucifer/Mercury/Hermes has, by means of this “SOUL,” been tied to the “MOON.” Consider that the “SOUL” (Latin anima) as vapors exuded during physical alchemy makes less sense that the more overtly sexual understanding we might draw from the Old Religion or Greek magical papyri. Soul, or anima, corresponds to ancient Greek psyche, which usually means mind, soul, or spirits of the dead, but in several passages of the magical papyri studied by Hans Betz, Betz concludes it means “the female pudendem; i.e. a synonym for physis,” and where it is translated as “soul,” it is frequently in an erotic context and suggests a double entendre on the other meaning,  just as “Fire-Being” in this same Theorem suggests a phallus.
If one is not familiar with Dee’s use of Olympic spirits, one might consider a common modern projection of the Venus glyphs onto the Tree, as a symbol encompassing all ten Sephiroth, representing the “Isis of Nature,”  and wonder if there is any connection back to this Theorem of Dee’s. If one sees in this brother-sister marriage an allusion to the legend of Isis and Osiris, one might see the outlines of how INRI stands for Isis Naturae Regina Ineffabalis,” or “Isis the Ineffable Queen of Nature.”
Finally, if returns to the usual reference of INRI, considers the Biblical crucifixion allegorically, and remembers Jesus’s words -- “I am thirsty” -- one might meditate upon two additional ideas: vinegar (as that given to Jesus on the Cross) as a solvent,  and needing water as an allegory for needing the Hebrew mother letter mem (water), or its several correspondences.
Dee concludes: “You see how exactly and openly the ANATOMY of our HIEROGLYPHIC MONAD corresponds to the SACRED MYSTERIES signified in both of these theorems (12 and 13).” We suggest that the sacred mysteries are precessional astronomy (in 12) and tantric gnosis (in 13).
Consider this theorem a reprise of the Emerald Tablet , with its allusion to the “red earth” animated by the alchemists, as a suggestion on how these two mysteries become one and the same. One might also explore the multiple allusions made by the phrase “terra lemnia.” 
This Theorem opens with an allusion to the labors of Hercules, and indeed one can spend many days connecting the labors to different alchemical ideas. It also stacks multiple meanings of ram/Aries and bull/Taurus, since the word for the animal, constellation, and zodiacal sign are the same in Latin.  One should review the astrological meanings, and note that because of the precession of the equinoxes, the constellations and signs of the zodiac no longer match up; the vernal equinox is still called the first point in Aries though it falls in Pisces. Approximately one zodiacal age ago, in Roman times, they did match.
We suggest one look at this Theorem as another fusion of the mysteries presented in Theorems XII and XIII, which XV explicitly refers to.
Dee refers to the “hieroglyph” of Taurus in almost the same language as the Monad, and by studying the allusions and wordplay, one suspects it has little to do with the sign or constellation Taurus, and much to do with the mystery cults, or “houses,” which flourished during the Age of Taurus, approximately 5,000 years ago. This was the last age of the Great Goddess cultures in Europe and Mesopotamia, and the rise of the Old Kingdom in Egypt.
His wordplay reinforces the
idea, including writing “Venus” in the genetive form, veneris,
which carries several obvious puns in Latin: on veneror, worthy
of respect or veneration, and as part of mons veneris, or the
“mound of Venus.” Given the pun between mons and monad, we
may be certain this latter meaning is among those Dee intended, and suggests
wisdom attained through sacred sexual union; indeed the “union of Sun
and Moon” referred to throughout must on one level refer to the
hieros gamos. Further, the Taurus glyph, which looks like
some of the line drawings of Cerrunos, Herne, and other Horned Gods of
the Old Religion, is drawn with the circles slightly overlapping and so
suggests one of the most sacred symbols to the Pythagoreans, the
In this story, it appears Isis learns the secret of alchemy through ecstatic union with the divine, and, having become divine, passes that knowledge on to her son Horus. In the fragment, she is called not Queen nor Goddess but “Prophetess,” having become an oracle of the divine.
To make sure the reader hasn’t missed his generative point, Dee puns on it yet again in the note at the end.
When Dee tells us we must stop and philosophize a bit concerning the Cross, he puns on “crux,” and means he will talk a bit about the central point of the matter. What follows seems like a long discussion of how to cut up the cross into different angles and make it correspond to different letters, but if one looks closely, most of this section comes right out of Euclid’s Elements and will parallel similar ideas expressed in more detail in Dee’s Propaedeumata aphoristica. In particular, he is telling us how to geometrically structure the ideas he has presented in previous XV Theorems. As Turner and Burns discuss in more detail in the notes to the accompanying translation, Dee invites us to visualize the cross in terms of conic sections.
First Dee asks us to picture a diagonal passing through a rectilinear cross; basically, a third line running through the point where these two intersect. His references to “V” and light also suggest the shape of a cone, if one imagine this in three dimensions. Then he tells us five (V) is a circular number, alluding to the circle as one of the four conic sections. If one makes the diagonal an axis for two cones sharing the same vertex, or point, and let that point be the intersection of the lines of the cross, we now have two cones and a plane. The plane can intersect the cones in one of seven ways, and makes one of seven figures: a circle, an ellipse, a parabola, a hyperbola, a point, a line, or a cross:
If the plane is running through the vertex, as Dee describes, then we can have only a point, line, or cross.
It is very important for the student to work through these images and draw them for herself, if one really intends to study the Monad in the context intended. If we use Euclidean geometry, the diagonal must be at a right angle, but we know Dee also had copies of the work of Apollonius of Perga, and his understanding of conics in Propaedeumata aphoristica show he was extremely well-versed in these ideas.
We also now have an image that Dee will use to express how a point of light, as the vertex of a cone, exerts influence. In his Propaedeumata aphoristica, particularly Theorems XXX through XLV, Dee will describe the properties of luminous cones, their axes, bases, and vertices, and strength upon the Earth at various distances, as a way of explaining how different celestial objects exert force upon the Earth. Recall that both versions of this work had the Monad glyph on their frontispiece, and Dee refers to these 120 aphorisms in his letter to Maximillian which accompanies the Hieroglyphic Monad.
The reference to “EL,” incidentally, is not only to the letter L or the Hebrew godname, but to an “l” in conics as defined in the Conica of Apollonius of Perga Book I, Proposition 11. The “l,” Latinized as latus rectum, is used in a particularly fascinating geometric transformation by which one derives a parabola from the conic section of an ellipse, and refers to a chord running perpendicular to the transverse axis and running through the foci. If such a notion seems absurd, consider how Dee likely influenced the first Latin translation of Conica.
As one studies these ideas more, their connection to the ancient mysteries will start to take shape. For instance, one might study Appolinius of Perga’s references to the treatment of conic sections on the ancient Isle of Samos, study the geography of the Oros Fengari (Mt. Moon), and be surprised at the connections one can make.
Finally, one may also want to research any of the Renaissance contexts that viewed 1000 (103) as a perfect number. It was a common enough idea that it even lent mystical support to Elizabeth I’s regency, as her mother, Anne Bolyn, was Queen for 1000 days. Certainly, the end of this Theorem may be one of the reasons Elizabeth was so taken with Dee’s Hieroglyphic Monad.
How to Progress Past Theorem XVII
Now we return again to where we began, the Theorem that gives the LVX Sign of the Adept and the number, 252, which Dee refers to the philosopher’s stone. Where does one go from here?
We have a few suggestions. We doubt one will be very successful in understanding what follows if one cannot geometrically visualize what has come before. If one can’t, it should be a clue to cycle back through the earlier theorems and slow down. Meditate upon them one by one.
Remember that geometry, music, art, architecture, and mysticism were not separate to the ancient Greeks, and Dee has absorbed their “monadic” view into his magic and alchemy. Apollonius of Perga wrote that, usefulness aside, the knowledge (gnosis) of different geometric propositions “are worthy of acceptance for the demonstrations themselves: indeed we accept many things in mathematics for this and no other reason.” He and other Greek geometers worked out basic “scientific” and “mathematic” principles, but they never believed they were dealing with materiality only. They believed the world was formed by spiritual principles and the world of matter ultimately reflects something higher, intimately tied to gnosis and consciousness.
From this perspective, when you start explaining the origin of geometric shapes and forms, such as progressing from point to line to square to cube, you are both describing mystical principles of formation that exist in higher realms, but also, by describing them in a certain way, you are evoking those powers or principles in your own consciousness. The odd (to us) grammar used by Greek geometers makes this even clearer: propositions are introduced in a form called the perfect imperative passive, so instead of a sentence like “draw a line from the vertex at a right angle to the plane,” a literal translation would likely be, “let a line have been drawn from the vertex having a right angle where it has intersected the plane.” The effect of this type of writing is the implicit presence of what some translators have called “The Helping Hand, the well-known factotum in Greek geometry, who sees that lines be drawn, points be taken, perpendiculars dropped. No one who has read Euclid’s Elements in Greek will have missed it. . . The Helping Hand is always there to see that these things were done.”
The form already exists, and by drawing it you are evoking it from within your own consciousness with the aid of this nameless “Helping Hand.” That’s why such mathematical principles often appear in the same context as the Hermetic maxim “as above, so below, as within, so without.”
We stress this because, if one wants to really understand the Hieroglyphic Monad, one must draw and meditate upon these images to evoke them in your own consciousness. Start with a point, a spark of light having location but no size. It does not exist in the world in its pure form, but it is part of everything that is form. The point is the basic building block of consciousness even though in and of itself it has no dimension. So to seek a true point, you must go into the realm of thought. As you contemplate this, what seems very simple becomes very profound. What things are dependent upon the formation of a point? This point is Dee’s Monad just as in another sense the Monad, or unit, is the entirety of the Great Tree. The Monad represents that ideal principle which cannot exist in its ideal form in matter, yet all of matter is dependent upon it.
From a point, move on to a line. From a line, move on to a circle. With these building blocks, move to three dimensions. Dee will introduce subjects to contemplate in every Theorem: by the time we start to meditate upon three dimensions, for instance, he’ll have referred us to the Tetractys; by Theorem V, the Pentagram as created by LVX; by VI, the Hexagram and Tiphareth, from which we can imagine a simple version of the Great Tree.
If we try to re-visualize this with the principles we ended Theorem XVII with, what would we have so far? We ideate a very far away “point,” the fiat lux of Genesis or the Limitless Light of cabbalists or the center of the galaxy to astronomers, as a vertex from which the light of all creation is emitted. Draw a line from that point to Earth; let the circumference of Earth define the circumference of our end of the cone.
Soon, on that same axis, the Middle Pillar, we will have two Spheres, the “Sun” and the “Moon,” and at the base of the cone, Malkuth, we have the “cross” from which we determine direction, which itself forms another sphere. We have a hexagram attributed to the “Sun,” which sometimes equates to Mercury/Hermes. We have a pentagram created by displacing the central point in the Cross of the Elements/Four Directions. For most of us, the Hexagram, the macrocosm, is easier to visualize in three dimensions (as two interpenetrating tetrahedra) than the microcosm. Can you see what a three-dimensional pentagram will look like?
With these ideas in mind, the student may want to cycle back through the entire first fifteen theorems and try to imagine, then draw, a 2-D representation of this three-dimensional tree. Dee has given you all of the proportions and magnitudes you need to do so. The point of discovery, where one has enough information to begin the architecture, is right at the end of this Theorem.
As you cycle through yet again, you may notice that all of the narrative allusions in the first ten Theorems are to creation stories; after Theorem II, the allusions and wordplay grow much more complex and seem to need a historical stream to fix them to. Why the allusions to the ancient city of Tyre, or the writings of Democritus, or indirectly, a Hebraicized fragment of an Isean story? Why mix all of the contexts?
Dee, we are certain, is drawing on the remnants he found in the Renaissance of a Theban magickal tradition from the third or fourth century A.D., and synthesizing it into his other ideas. While the manuscripts he had access to may not have dated before the tenth century, they draw on an older tradition, one we now have much more of a record of since the discovery and publication of Greek Magical papyri in different translations.
One may want to look at later alchemical works like the Turba Philosophorum, but keep in mind that these writings, filtered as they are through at least two additional languages and cultures, may be less helpful in terms of what they say than in terms of what they point back to.
Finally, we would like to share with you the “Helping Hand” offered us by good friends with whom we have spent some time discussing the Hieroglyphic Monad:
Squaring the Circle in the Creation of Sacred Space
This was how Bridges explained the geometries of the Great Tree to interested students back in 1991. As far as we know, he did not intend it as an explanation of the Hieroglyphic Monad. But if one visualizes this drawing of the Tree in three dimensions, one should see two spheres sharing the same axis, that axis ending at the center of a third sphere, at the center of a cross of four directions. One should see at least two cones.
If one locates where different Sephiroth are located and at the intersection of which curved or planar geometric boundaries, or puzzles over the “location” of different planets, you will indeed have a “Helping Hand” to go back through the geometries of the Hieroglyphic Monad, and proceed on the Theorem XVIII.
One Last Challenge
As the student, having mastered the material of the “Outer Mysteries,” moves past the analysis of the keyword to Theorem XVIII, he will encounter these illustrations:
The spiral, with Saturn (Lead) in the center and the Sun (Gold) on the periphery visually directs us to the alchemists Great Work of turning lead into gold, and indeed, as one studies this Theorem, one runs into some of the most common motifs of physical alchemy. But trying to derive a laboratory process from this Theorem will take one nowhere.
Neither will trying to explain the astronomy by only considering objects within our own solar system. Dee’s language near the end of this section—Helicis Revolutionibus—could easily be translated as heliacal revolutions, or revolutions around the sun, and so by the same logic some have used to suggest Theorem III shows a geocentric universe, one might say this Theorem shows a heliocentric, Copernican one.  We invite the reader to find a third alternative related to precessional astronomy and sacred geometry.
The INRI/LVX transformation should give us one clue to start: if the Outer mysteries of the Hieroglyphic Monad are encoded into this one transformation, at least part of the Inner Mysteries concern the projection of seven onto six: how to “map” the seven metals and planets of the alchemist onto a cube, thus moving our conceptualization into higher dimensional geometry.
But the easiest way to start into this Theorem is to look through the Corpus Hermeticum and Greek magical papyri for stories where similar images occur.
For instance, the first part of the Theorem, in its discussion of Ovi Metamorphosis (the metamorphosis or transformation of the egg), might direct us back to stories of Orpheus, whose musical magic, soul-travel, and journey through the underworld return us yet again to the ecstatic mystery cults of the ancient world. These stories present an entire narrative of cosmogenesis which includes the notion of time as the god that begat the world, and the universe itself as a cosmic egg. Yet the stories, to modern readers, seem to have as much to do with individual destiny as cosmological origins. We might also consider that the human aura has been seen for thousands of years as an egg-shaped energy field around the body.
Thus we start to see the outlines of the three-fold alchemical transformation of Hermes as the subject of the Inner Mystery: a cosmological unfolding of time and space, individual transformation and gnosis, and the ability, through the realization of the first and experience of the second, to aid in the perfecting of the consciousness of humanity.
 Josten 1964, pp. 84-111.
 Josten 1964, pp. 88-90.
 Yates 1972, pp. 54-55.
 McLean 1984, p. 1. McLeans’s structural analysis of the Chymical Wedding is by far the best available, and to us invites further comparison between that work and the Hieroglyphic Monad.
 French 1972, pp. 76-80.
 Ibid p. 80.
 We do not mean to imply that this entire teaching was part of the gloss Dee seems to have provided to Maximillian and Elizabeth. Given the apocalyptic concerns of heads of state at that time, and the interest of many of them in prophecy, one might suspect his teaching to both concerned precessional astronomy and what it may have predicted for their respective reigns.
 Its worth noting that the cipher manuscript, written in the Trithemian cipher that was in Dee’s age a state secret, invites one to study how directly many of the ideas come from Dee’s magical circle as filtered through Rosicrucianism. For instance, the different projections of the Moon, Venus, and Mercury in the knowledge lectures connects almost directly to the Monas Hieroglyphica.
 For further explication, see Turner and Burns translation in this issue, notes 93-96.
 See Turner and Burns, n. 102.
 Regardie 1989, p. 11.
 Weidner and Bridges, p. 319.
 Regardie points this out in his introduction to the second edition of The Golden Dawn, p. 13.
 See Turner and Burns, notes 99 and 100.
 Turner and Burns, n. 27.
 Josten 1984, p. 175 n. 71.
 Thank you to Vincent Bridges for pointing this out to us.
 See Roberts & Watson 1990, pp. 3-19.
 See discussion in Bridges and Burns. Certainly, he had copied parts of alchemical manuscripts in Paris and Venice, and likely works of Cabbala of which we have no record.
 Josten 1964, p. 123.
 See Turner and Burns, translation and notes 7-10.
 Some would dispute that Dee had access to Hebrew texts beyond grammars and Biblical passages, but we think the evidence suggests otherwise. Dee visited most of the libraries in Europe which had Cabbalistic texts and he could read Hebrew; its inconceivable that he would not have read and copied some of them. Certainly he had access to, read, and copied parts of all three of the oldest extant alchemical manuscripts, two of which were in Paris and one in Venice.
 For instance, the Perseus Digital library at http://www.perseus.tufts.edu/ allows browsers to word-search through their entire Latin and Greek classical library, and their Latin and Greek dictionaries will return usage information along with entries. Sometimes this isn’t useful: for instance, learning that Dee uses the word “crux” or cross often, and so does the Vulgate Bible doesn’t particularly take us anywhere. But noting that Dee is occasionally using words in contexts similar to those Vitruvius in De Architectura might suggest an entirely new line of student.
 Josten 1964, p. 123.
 Turner and Burns, note 12.
 Josten 1964, p. 113.
 See http://www.jwmt.org/v2n12/appendix2.html.
 For a succinct explanation, see Donald Tyson’s Tetractys page at http://www.donaldtyson.com/tetract.html. Tyson also looks at a tetractys of Tetragrammaton.
 See Turner and Burns, notes 28-30.
 Ibid., notes 31-34.
 Ibid., notes 35-41.
 A Latin version is available on-line at: http://www.billheidrick.com/Orpd/Dee/JDMH.pdf. Also, Ibid. notes 42-55.
 See discussion in Bridges and Burns in this issue.
 Betz 1986, pp. 338, 338.
 Regardie 1989, p. 79.
 For instance, consider this dialog in the Turba Philosophorum: “Frictes saith . . . ‘Oh how this nature changes body into spirit! Oh how admirable is Nature, how she presides over all, and overcomes all! Pythagoras saith: Name this Nature, O Frictes! And he: It is a very sharp vinegar, which makes gold into sheer spirit, without which vinegar, neither whiteness, nor blackness, nor redness, nor rust can be made” (Waite 1973, pp. 51-52).
 Turner and Burns, notes 56-58.
 Turner and Burns, notes 60-64.
 It suggests the same shape, though it is not exactly a vesica. If it were, the circumference of each circle would intersect the central point of the other.
 Taylor, in his survey of Greek alchemical texts, notes that the three earliest known manuscripts (as opposed to papyri) are Marcianus 299 in Venice (tenth or eleventh century;) Paris 2325 (thirteenth century) and Paris 2327 (fifteenth century.) Dee may have had access to all three; one wonders what papyri he, or the authors of these manuscripts, had access to. Taylor (1930, p. 113) says that the authors, as opposed to the copyists, of these alchemical texts wrote at dates no later “than the second half of the third century of the Christian era nor earlier than the first century” and include Democritus, Iamblichus, Ostanes, Cleopatra, Isis, Maria, and Hermes.” The names, obviously, are often pseudonyms.
 See Turner and Burns, n. 68. Waite gives a longer translation in his edition of the Turba Philosophorum: “When thou hast attained, my child, to the understanding of these things by way of a preliminary, consider creation and generation as a whole, and know that the man is able to bring forth man, the lion begets the lion, and the dog procreates the dog. Should it happen that a creature is produced that is contrary to nature, it is a monster which is engendered, and it hath no consistence. Nature charms nature, and nature triumphs through nature. The adepts having participated in the divine power, and having succeeded by the divine assistance, illuminated by the fruit of the prayers of Isis, made preparations with certain metallic minerals, without having recourse to other substances. Thus they succeeded by means of the substantial nature in triumphing over the matter employed in the preparations. In fact, even as I have previously said that wheat begets wheat and man sows man, so also gold serves for the increase of gold, and like things generally for the reproduction of their like. Now hath the mystery been revealed” (1973, pp. 22-23, 95.) Waite does not tell us what he is quoting from, but it appears he is paraphrasing Berthelot’s French translation of the ancient Greek given in Collection des anciens alchimistes grecs.
 Isis frequently is called the Patroness of magic, and this fragment echoes the more familiar story of her tricking Ra and learning the secrets of healing and eternal life.
 Turner and Burns, notes 65-75.
 Ibid., notes 76-92.
 Roberts & Watson note the history of the earliest version of Conica owned by Dee, now located in the Massachusetts library of Arthur Vershbow, who supplied these details: “The titlepage is inscribed ‘Joannes Deeus: Anglus: 1549’ and there are some Dee notes on the text. The front flyleaf has an extensive chronology of Greek scientists by Dee. The book also bears John Winthrop’s signature with the date 1631. Winthrop (1605-76) probably added Dee’s monad. The book belonged to other members of the Winthrop family. It is bound in calf with the small tool of the Habsburg eagle which appears on several of Dee’s Antwerp or Louvain acquisitions of this time” (1990, p. 82). We assume this is Books 1-IV in ancient Greek, as no Latin or English translations existed in Dee’s time, and Books V-VII have only been found in Arabic.
 Euclid’s actual treatise on conics has not survived, but part of the reason was that its ideas were completed and built upon by Apollonius of Perga, who is generally considered the greatest Greek thinker on the subject. For instance, Apollonius proved that all conics are sections of circular cones, and explored how to work with cones not produced by a right-angle, both of which seem key ideas in Dee’s use of conics in astronomy.
 Our term “parabola” comes from the Conica of Apollonius of Perga and was first used by Dee’s mathematical “son” Thomas Digges, with whom Dee was certainly sharing Federico Commandino’s 1566 Latin translation. Commandino may have shared an early version of his translation with Dee when the two met in Urbino the year before Dee’s publication of the Monas, and possibly Dee’s understanding of the Greek text he already had shaped Commandino’s interpretation. Dee and Commandino worked together to produce a Latin and Italian translation of the De superficierum Divisionibus of Machometus Bagdedinus (See Rose 1972), and the two men were clearly sharing manuscripts, with Dee as the teacher and Commandino as the student.
 Fried 2003, pp. 2-3.
 Taisbak, qtd by Fried in the introduction to his translation of Apollonius’s Conica Book IV, p. xxix.
 For an excellent discussion of this tradition as a Greco-Egyptian-Hebraic synthesis, see Betz 1986, pp. xlii-xlvii. Of the mix of often incomprehensible languages in some of the papyri, he says, “Many of the texts depict the magician as a wondering craftsman who "seems keen to adopt and adapt every religious tradition that appeared useful to him" (p. xlvi). "This craftsman no longer understood the ancient languages, although he used remnants of them in transcriptions. He recited and used what must have at one time been metrically composed hymns, but he no longer recognized the meter". . . "For these magicians, there was no longer any cultural difference between the Egyptian and the Greek Gods, or between them and the Jewish God and the Jewish angels." (xlvi). Dee, as a scholar and linguist, clearly was trying to understand these ancient languages and re-synthesize the synthesis by understanding its geometries.
 The more usual line of thinking has been to equate the order of planets with an order of the spheres, thus using this Theorem for further evidence that Dee had a geocentric conception of the solar system.
 The references to Anaxagorus and Oedipus point us directly back to this Theban current. Also, in the stories of Orpheus and the underworld, we find our easiest connection to the “dark goddesses” of the underworld so common in the Greek magickal papyri. See Betz 1986, p. xlvi.