Journal of the Western Mystery Tradition
No. 13, Vol. 2. Vernal Equinox 2007
Appendix - A comparison of the three shortest Theorems I-III

A Translation of Theorems 1-17 of John Dee’s Monas Hieroglyphica

by Nancy Turner and Teresa Burnes

Translators’ Notes
Since the writers of the accompanying article[1] 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.[2]

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.[3] 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.[4] 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.[5]

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.

Teresa Burns
August, 2007

The Hieroglyphic Monad
Of John Dee, London

Mathematically, Magically, Cabalistically, and Anagogically Explained
to the most wise Maximilian, King of the Romans, of Bohemia, and of Hungary.

One who does not understand should be silent or learn.

[Words on the scroll around the monad, with other markings[6]:]
Mercury becomes parent and the king of all planets when perfected by stable, pointed Stilbon[7], [8]

May God give thee of the dew of heaven, and of the fat places of the earth, Gen. 27[9]

Printed by Willem Silvius, Royal Typographer, Antwerp, 1564.

Theorem I
By means of the straight line and the circle,[10] the first and simplest production and representation of things was made in the light,[11] as were non-existent things and those that are hidden behind the veil of Nature.

Theorem II
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.[12] 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.[13], [14]

Theorem III
Therefore the middle point, which we see in the center of the HIEROGLYPHIC MONAD,[15] represents the EARTH, around which the SUN, the MOON and the other Planets complete their paths.[16] And in this movement, since the SUN assumes the supreme dignity,[17] we depict it (because of its excellence) by means of a complete circle with a visible center.


Theorem IIII
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.

Theorem V
And most definitely by bringing the lunar semi-circle to the solar completion, one day is made out of morning and evening.[18] Thus this would be the first day on which the LIGHT[19] of the Philosophers was made.

Theorem VI
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[20] 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,[21] ever observed, and which you[22] 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.


Theorem VII
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[23] 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.[24]

Theorem VIII
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[25]), 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.

Theorem IX
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[26] of our MONAD.

Theorem X
The sign of the zodiacal[27] Aries, which is very well known to everyone, has, according to the custom of astronomers, this (rather sharp-edged and pointed) form:[28] [29]. 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[30] hieroglyphic construction as follows:


Theorem XI
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.[31] The time of twenty-four hours, in the mode of the equinox,[32] denotes our most secret Proportions.[33] I say “our” with reference to the Earth.[34]

Theorem XII
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.[35] And from the same occasion it also received the name JUPITER[36] 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.[37] In this way, the purest magical spirit[38] will carry out the work of the whitening[39] 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[40] figures, or in their place, that other figure.[41]

Theorem XIII
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)?[42] 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[43] 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.[44] Indeed, some very clever people used to put the SUN itself in his place and rank.[45] This we cannot achieve in our present age, unless we put in charge of this work made of coral-gold[46] a certain SOUL[47] who has been separated from his BODY by means of the Pyrognomic[48] Art.


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[50] and even the FIRE BEING[51] to the disc of the MOON[52]—or at least of MERCURY[53]—and in the third place (as they want it)—(in order to complete our SEPTERNARY[54] 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[55] signified in both of these theorems [12 and 13].

Theorem XIIII
It has already been clearly confirmed that this whole Master Work depends upon the SUN and MOON, which is something the thrice-great HERMES[56] once taught us when he asserted that the SUN is its father and the MOON its mother.[57] We know with no doubt that it is nourished in the LEMNIAN EARTH[58] by LUNAR and SOLAR rays which exert a singular influence around it.

Theorem XV
Consequently, we suggest to philosophers that they examine the labors[59] of the SUN and the MOON around the earth; for instance, in what way the moon, while the SOLAR radiance is focused upon Aries,[60] receives a new dignity of light in the nearest sign (namely Taurus[61]) and is EXALTED above its innate powers.[62] The old ones explained this proximity of the LUMINARIES[63] (the most notable of all) by creating a certain mystical character with the distinguished name of TAURUS.[64] 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[65] of VENUS:[66] indeed the house of pure[67] and fertile conjugal love, since “Nature rejoices in Nature,”[68] as the great Ostanes[69] concealed in his most secret mysteries.



[We suggest to philosophers that they examine[70]] 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.[71] 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 [72] of the Greeks, which is always the genitive[73] singular ending of the first declension.[74] 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.[75]

Theorem XVI
At this point in the discussion of our proposition[76] we must philosophize a little concerning the CROSS.[77] 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.[78] But in the mystical arrangement of our cross we wanted to have both equal and unequal parts,[79] 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.[80] For, a certain JUSTICE of NATURE[81] 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.[82] 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.[83] 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).[84] From this it definitely is not irrational[85] 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.[86]

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?[87] And even the name of that letter, EL,[88] 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.[89] 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.[90] 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,[91] so it also represents unity.[92] 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.

Theorem XVII
As is evident from the sixth theorem, FOUR right angles can be considered to be in our CROSS,[93] and the preceding theorem teaches that the sign[94] of the QUINARY[95] 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.[96] Thus, it is very clear that the CROSS generally denotes the DENARY;[97] 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[98] signified the number twenty-one with the same letter[99]); 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.[100] 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].[101] Thus we recommend to cabalistic Tyrians[102] 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.[103] 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),[104] 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).



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[1] Burns and Moore, this issue.

[2] For a comparison of this frontispiece to those from two different versions of Dee’s Propaedeumata Aphoristica, Ibid.

[3] These sources are referred to throughout these notes and in the bibliography.

[4] See Appendix.

[5] 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.

[6] 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.

[7] Dee chooses to present this word in Greek letters: . Transliterated into Roman letters the word reads as Stilbon, the name of the the god of the wandering star Hermaon, or the planet Mercury, and literally means “the shining one.” (Thank you to Michael Westbrook for pointing this out to us.) Josten translates this with the adjoining Latin as “a stable pointed hook” (p. 113), and Hamilton-Jones ignores it. The word-play inherent in this choice gives us an example of Dee’s complex use of words. A “pointed” stilbon 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, and comes into English referring to an instrument with one pointed end used for incising letters on a wax tablet and a long flat side used for wiping it clean; bonum, of course, means moral or metaphysical “goods,” and also puns on French bon, “good.” Recall 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, and so further suggests the Caduceus or staff of Hermes and its myriad of alchemical associations. Finally, Latin stilus is an etymologically unrelated homophone of Greek style, or pillar. This constellation of meanings also tells us to look closely when Dee invents words, presents them in Greek letters, or uses them in an unusual way.

[8] 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).

[9] 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.

[10] 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.

[11] 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.

[12] 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.

[13] 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).

[14] 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)

[15] 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.

[16] 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.

[17] Though this could be translated simply as “highest rank,” we’ve used “supreme dignity” to keep the astrological overtone.

[18] Cf. Genesis 1:5.

[19] 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.

[20] 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.

[21] 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.

[22] Throughout, Dee’s “you” is plural.

[23] 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.

[24] 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.

[25] 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.

[26] 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.

[27] 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.

[28] 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.

[29] 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.

[30] Latin unico, often translated “unique,” also echoes Greek (monas) meaning “singularly.” In Pythagorean, then Platonic philosophy, is now often directly translated as “monad,” just as it is when it appears in many recently translated Greek magical papyri such as the “Monad” of Moses. See examples in Betz.

[31] 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.

[32] 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).

[33] 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.

[34] See note 16 above.

[35] 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).

[36] This refers to the symbol for Jupiter in the first column.

[37] 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).

[38] I.e. Hermes/Mercury.

[39] 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.

[40] 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.

[41] The fifth figure, which results from the first four.

[42] Mars in the graphic accompanying Theorem XII, which includes the cross of the elements.

[43] 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.

[44] 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.

[45] 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.

[46] 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 ( 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).

[47] 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.

[48] 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.

[49] 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.

[50] 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.

[51] 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.

[52] 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.

[53] 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.

[54] 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.”

[55] 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.

[56] Hermes Trismegistus, another reference to the Emerald Tablet.

[57] 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.

[58] 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.

[59] 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.

[60] 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.

[61] 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).

[62] 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.”

[63] 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.

[64] TAURI, here and later in the theorem, suddenly is placed in all capitals, first as a name, nomine, then as a hieroglyph, TauriHieroglyphica” (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].

[65] 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.

[66] 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.

[67] Josten and Hamilton-Jones both translate this as “chaste,” which seems rather forced in this context.

[68] 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)”.

[69] 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.

[70] The “Philosophis proponimus Considerando” of the theorem’s very first line seems echoed in this second paragraph.

[71] The sun is exalted in Aries, as the Moon is in Taurus.

[72] Usually written , pronounced like the “ou” in English “soup.” A dipthong is a glide from one vowel sound to another.

[73] Gignitiuam, another word Dee has invented.

[74] 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).

[75] 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.

[76] 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.

[77] 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.

[78] 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.

[79] See Elements Book X, especially the propositions concerning unequal straight lines. Book X depends on the discussion of ratio and proportion in Book V.

[80] Dee describes a cross as composed of right angles, likely again directing a reader to Euclid’s discussion of right angles in Elements.

[81] 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.

[82] 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.

[83] 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).

[84] 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.

[85] Possibly an allusion to Elements Book X, which depends on Book V, and in part concerns irrational lines.

[86] In Roman numerals L + L = C

[87] Dee seems to be rediscovering this great mystery as he tells his reader.

[88] 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).

[89] 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.

[90] 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.

[91] Unicus. See note 30.

[92] Unum. See note 30.

[93] Another sign for the cross is X.

[94] Josten and Hamilton-Jones both omit “sign.” The simplest “sign” for five is V.

[95] 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.

[96] In other words, L. By reprising past theorems, Dee gives the sign LVX backwards.

[97] A Reprise of his earlier reference to the DENARY as the cabalistic Tree and the Pythagorean Decad.

[98] Mecubalist comes from Hebrew Mekubalim, and is one of several terms used to refer to a learned sage of the Cabala.

[99] 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.

[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.

[101] 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.

[102] 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).

[103] 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.

[104]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.