The Aspects in Classical and Traditional Astrology

By “classical astrology”, I mean the astrology taught in pre-Islamic antiquity by authors like Ptolemy, Manilius, Firmicus Maternus or Vettius Valen. “Traditional astrology” denotes the monotheistic Arabic astrology as it was ultimately bequeathed to the late Renaissance/early modern period and summarized for us most notably by William Lilly (mid-17th century). The distinction is important, as we shall discover. But it would be wrong to approach them as two different astrologies. There are indeed sizable differences in emphasis, as well as refinements and, perhaps, some losses through time. Nevertheless, a full acquaintance with both classical astrology and traditional astrology proves that they are but two currents in one great stream. This is certainly true in their understanding of the aspects. This is the topic of this essay.

The social conception of the aspects

The word “aspect” comes from the Latin aspicio, “to look upon, behold”. First appearing as a technical term in the Middle Ages, it would eventually supplant a richer, more varied lexicon that conveyed an awareness of agency: “beholding”, “viewing”, “regarding”, “seeing”. We encounter it early on in the classical astrologer Marcus Manilius (1st cent. CE): “The Ram beholds (conspicit) at equal distance the two signs of the Lion and the Archer.”[1] This vocabulary would live on in the traditional astrology of the 17th century. William Lilly, for instance, speaks naturally of both signs and planets as “beholding” through aspect or ray.[2]

Even these optical metaphors fall a bit short of the more interpersonal language in use among the classical astrologers. One of Ptolemy’s (2nd cent. CE) favored expressions is syschêmatizoménôn – “cooperations” or “alliances”. This echoes Manilius, who speaks of aspects as “agreements” (consensus), “associations” (socias), “exchanges” (commercia) and “alliances”, (foedera).[3] It makes sense that they would think this way. In the ancient world, the planets were gods. As intrinsically lawful beings, their actions could of course be described mathematically, but they were no less personal and relational for that. Indeed, the planets’ mathematical lawfulness meant that their future actions – position and aspect – could be calculated beforehand, making it also possible to predict human affairs. Thus, for Manilius, the human “bonds of friendship” (amicos)[4] are forged or broken in concert with the socias of the planets, that is, the aspects.

It is therefore no coincidence that the classical sense that aspects are planetary deeds involving reason and will would begin to fade in Western astrology with the rise of the monotheistic faiths. More and more, the aspects would be conceived in theory as subtle, quasi-physical phenomena, as in Al-Kindi’s On the Stellar Rays (ca. 850 CE). This is not to say that the old sensibility disappeared. It still thoroughly permeated the traditional astrology of Lilly, as we see for example in what he says about collection of light:

“Matters are also brought to perfection, when as the two principall Significators doe not behold another, but both cast their severall Aspects to a more weighty Planet than themselves, and they both receive him in some of their essential dignities… which signifies no more in Art than this, that a Person somewhat interested in both parties and described and signified by that Planet, shall perform, effect and conclude the thing which otherwise could not be perfected.”[5]

Judgement depends upon the astrologer being able to discern a perfect correspondence between human interactions and the aspects of the planets; and the quality of the aspects are altered by the deeply social consideration of reception.

At the same time, Lilly’s worldview is obviously more in line with the Medieval/Hermetic doctrine of signs[6] than the ancient astro-theology of Manilius, Ptolemy or Firmicus Maternus. For Lilly, the aspects are not the deeds of gods, as in classical astrology. Instead, they are the dynamic elements of the articulate speech of the angels, who in turn give voice God’s decrees: “thou talkest with Angels, yea with God himself.”[7]

Dilemmas relating to the aspects

This is a profound view and one that I personally find agreeable. But it does involve a certain (perhaps necessary) desacralizing of planetary dynamics. And this would soon pave the way for those who wanted to assimilate aspect theory, along with the whole of astrology, to the quantitative mindset of the scientific revolution. This process had already begun with the Protestant mathematical genius Johannes Kepler, for whom the aspects, being the properly mathematical element of astrology, would become the whole of astrology:

I am informed that misfortune came to you from astrology. I ask you if you believe that it could be powerful enough to have such power. Ten years ago, I rejected the division into 12 equal signs, the Houses, dominations (i.e. rulerships), triplicities etc. and I am retaining only the aspects (angles) and am transferring astrology to the science of harmonics.[8]

Kepler is speaking as a reformer who wants to return astrology to its Pythagorean/Hermetic roots, via the harmonic science of aspects. But, ironically, in order to make aspects out to be everything, Kepler must uproot them from the whole, from the unitive cosmic vision of the great tradition. This will have two unfortunate consequences for modern astrology.

First, having discarded so many of the basic building blocks of the old astrology (e.g., essential dignities; receptions; accurate house meanings; rich, real-world sign symbolism, etc.), modern astrology will be forced to overload “aspect theory” with too many roles in the system. Thus, with one hand, modern astrology gives us the gradeschooler’s “12 Letter Alphabet”. With the other it lays on us the heavy yoke of Kepler’s three minor aspects,[9] the aspects of the Hamburg school,[10] other minor aspects,[11] midpoints, aspects to midpoints, dials, and virtually endless harmonic iterations of the figure. And they say traditional astrology is too complicated!

Second, with their rational basis in the traditional scheme lost, the aspects will now be vulnerable to the Cartesian reduction, wherein every axiom of a science must be represented as a “clear and distinct idea”, entirely separable and independent of all other axioms. For Descartes, this led to the absurdity that, since the circle and the radius are two different clear and distinct ideas, God has the power to create a circle with different radii.[12] In modern astrology, it divorces aspects from the commerce and agency of the planets and turns them into free-standing, irreducible chart components. Thus we end up with illogical concepts like “aspectual orbs” and the instrumental notion that the aspects are basically imbedded “chart circuitry” that is merely “activated” by the transits of the planets.

Supernal origin of the aspects

For classical astrology, the aspects are certainly not irreducible chart elements. They are not even reducible to the interactions of the planets. They originate in the zodiac itself. This concept is rooted in the Platonic distinction between the “universal eternal”, or the primum mobile, and its inferior copy, the planetary spheres. This copy, Plato says, is the “moving image of eternity”, or time as measured preeminently by the planets “moving according to number”.[13] Accordingly, classical astrologers reasoned that the ultimate basis for the aspects is to be found not in the realm of “the moving image of eternity” – the realm of the planetoi, the gods who wander – but rather in the unchanging structure of the zodiac where the high gods “rest in unity”.

We see this reasoning, for example, in Ptolemy. In Tetrabiblos I.13, he explains that the particular nature of each aspect is ordained not first of all by the planets but rather by the superior relationships between signs of the zodiac (oikeioûtai de allêlois, “familiarity with one another”). The twelve signs can be divided into aliquot parts in just a few ways: by six, four, three and two. These generate four sets of equilateral shapes – six pairs of semicircles, four triangles, three squares and two hexagons.[14] It turn, these shapes comprise intervals (i.e., whole sign aspects) whose natures are determined by the relative tension or ease between the signs that make them up.

Because the planets are both physically and metaphysically subordinate to the signs, it is the aforementioned intervals alone that determine which of the many possible angular relationships between the planets are actually effective. Consequently, the Archetype admits only four planetary aspects – opposition (180°), trine (120°), square (90°) and sextile (60°). To these we must add the conjunction, even though many classical texts tell us that it is not an aspect per se, since conjoining planets do not cooperate through their rays but rather by meeting physically.[15] In practice, though, the conjunction is treated as an aspect. Still, it is useful to keep the distinction in mind, for conjunctions do operate with far greater force than aspects proper. These five together, then, make up what are commonly called the Ptolemaic aspects.

The Ptolemaic aspects

The specific properties of the Ptolemaic aspects are well-established and remain consistent from the classical period through the tradition as recapitulated by William Lilly.[16] We need only summarize them. The opposition is uniformly bad, and indisputably much more harmful than the square – a fact somehow lost on modern astrology. The trine is the aspect most favorable to the perfection of any matter, because ease and balance are inherent in its shape. It offers a “more forcible… argument of Love”[17] tempering the malefics and enhancing the benefics.[18] The square is powerful but of indeterminate quality – Lilly calls it the aspect of “imperfect hatred”, but Dorotheus “a medium amount of love” – its effects depending on the nature and receptions of the planets. The power of the sextile was underestimated by some classical authors because it is an obtuse angle.[19] Yet, Dorotheus and Lilly are in agreement that it is like a less robust trine, but effective to conclude matters peaceably none the less.[20] Finally, the bodily conjunction produces the most definite effects. Yet, as Lilly says, they “are good or bad, as the Planets in conjunction are friends or enemies to one another.” The variable quality of the conjunction is plainly evident, for example, in Firmicus Maternus’ delineations.[21]

For the whole tradition, only the five Ptolemaic aspects are effective (i.e., able to affect reality for good or ill), for they alone subsist in the archetypal creativity of the zodiac. Through them alone are the planets able to behold one one another, whether with friendship or enmity.[22] This holds further implications for the traditional doctrine of aspects, relating to (a) planetary “application” and orbs, and (b) the question of so-called “minor aspects”.

Planetary application & orbs

As we have seen, classical astrology emphasized the signs as being the archetypal basis of the aspects. Because of this, prevalent technique allowed that where two signs are in aspect, any planets within those signs will be in aspect as well, irrespective of their degrees. For example, it seems that Vettius Valens preferred to calculate aspect by sign, for he only rarely gives planetary positions by degree in the roughly 130 charts of his that have come down to us.[23]

Still, degree to degree aspects were recognized. This was mainly to establish whether an aspect was applying (synapheiôn) or separating (aporroiôn) and so, in a general way, whether its influence would be stronger or weaker.[24] Perfection of aspect, so important for traditional horary, is not an overriding concern. Manilius also reminds us that when reckoning an aspect by sign alone subverts the philosophy of the shapes, we ought to consider the actual degrees.[25] In classical astrology, this is what was known as a partile aspect, since it was measured by the pars – “parts” or degrees – instead of the signs. An aspect judged in the prevailing manner was platick (vulgar Latin plattus = flat, broad) since it was measured broadly by sign relationships.

Yet, even in these cases, it was understood that aspects ended at the sign boundaries. This old point of view was reported – but not adopted! – by the 12th-century astrology Ibn Ezra: “If the two planets are [found] in two separate signs, yet each one is within the influence of the other, they are not said to be joined because they are in different signs, and that is the opinion of the ancients. But I, Abraham, the scribe of this book, differ with them, as I shall explain in the Book of Nativities.”[26]

Ibn Ezra’s readiness to approve of out-of-sign aspects points to an important development in the doctrine of aspects: the calculating of planetary aspects independently of the signs. With the evolution of horary among the Arabic astrologers and into the European Middle Ages, we see the growing importance of the timing of events as astrologers leaned more and more on interrogations in their routine practice. Primary directions, based on aspects formed via the rapt motion, were perhaps felt to be too exalted for transient matters. And, of course, the calculations were much too cumbersome for quotidian use.

Given this practical demand, astrologers would quickly learn to wrestle exact prediction from the secondary motion of the planets. But this required them to sharpen what had hitherto been a too-blunt tool, namely, planetary dynamics. Since events were known to be caused by exact aspectual relations of the planets, commonly known as “perfection”, traditional astrologers came more and more to shift emphasis away from sign boundaries to the actual limits the planets’ own spheres of influence, or orbs.

The Latin orbis literally means a “sphere” and came to denote a radiant field saturated with the nature of the planet whose body occupies the center. The planets apply to and separate from aspect through the orbs, with “perfection” now  the moment when the planetary bodies actually meet either corporeally or through their rays. The meanings of partile and platick change along with this evolution of the aspect doctrine in traditional astrology. Lilly explains:

“There is also a Partile or Platic aspect: Partile aspect is when two Planets are exactly so many degrees from each other as make a perfect aspect… and this is a strong sign or argument for performance of anything or that the matter is near hand concluded when the aspect is so partile, and signifies good; and it’s as much a sign of present evil when mischief is threatened. A Platic Aspect is that which admits of the Orbs or Rays of two Planets that signify any matter…”[27]

Instead of signifying broadly waxing and waning influence, as was generally the case in antiquity, application would now more clearly describe an impending event, separation a past one. Perfection of aspect, given the cooperation of other factors, precipitates the event itself. And, as any horary astrologer well knows, the number of degrees wanting until perfection gives the measure of time.

Lacking this more sophisticated understanding of orb and planetary dynamics, classical astrology naturally tended to overstress the fixed sign relationships of the Archetype. It was as if the planets were thought merely to pass through the sign aspects without every enjoying a dynamism fully their own. We might say that the “universal eternal” – the primum mobile – overshadowed the “moving image of eternity” – the planetary spheres – to such a degree that the planets were deprived of vital powers proper to their domain. As a result, Deborah Houlding concludes, “we presently have no clear and unambiguous examples of the use of orbs in classical astrology”,[28] notwithstanding a tantalizing handful texts anticipating the later doctrine.

This is one area where “traditional astrology” clearly improves upon the received “opinion of the ancients”. This is because it follows from a more careful deduction from first principles. By allowing orbs rather than sign boundaries to limit the aspects of the planets, the later “traditional astrology” would much more effectively apply the fundamental insight that planetary spheres bear the richest likeness of the great zodiacal circle, reproducing the structure of the Archetype at their own, admittedly lesser, register.

Thus, for example, a planet or luminary – even the Moon! – can indeed apply to aspect across a sign boundary.[29] For planetary dynamics abide by a set of laws that imitate but are not identical those belonging to the zodiac. Clearly conceptualizing these two symbolic registers – Sky and Planets – greatly enriches the symbolic language of the art. Sign cusps no long need necessarily be treated as barriers. They become symbolic in themselves, representing dramatic changes of state or circumstance.

“Minor aspects”

For the tradition, all planetary angles apart from the five Ptolemaic aspects, are indifferent, indicating, says Dorotheus, “estrangement from the other”. They simply cannot to be counted as aspects (i.e., modes of beholding). It should come as no surprise, then, that today’s innumerable “minor aspects” simply did not exist for classical astrologers. They were too rigorous to entertain them, and their success in prediction proves that they did not need them. In fact, only two of the minor aspects – the inconjunct and the semi-sextile – have a background in antiquity.

The inconjunct (asyndeton, literally “disconnected”) of 150° or five full signs fails the test of philosophical geometry because it “divides the whole circle into unequal parts”[30] and “exhausts the circle.”[31]  It denoted a kind of “blind spot” (ableptum)[32] – the opposite of an aspectum. Here the planets are mutually estranged (apêllotriôména)[33] and unable to engage with one another.[34]

As for the 30° semi-sextile, it is possible for this angle to inscribe a single dodecagon into the zodiac. Nonetheless, classical astrologers generally dismissed this division as being both trivial and weak. It was thought trivial because it merely reproduces the unity of the circle;[35] weak, because the angle between adjacent signs is too obtuse to create a line of sight: “sympathy between them is blunted because the sight of each other is denied them.”[36]

Yet, weakness is not nullity. And it must be conceded that the semi-sextile does meet the geometrical standard and might therefore have its uses. William Lilly evidently thought its sparing use was justified. He employs it in the question “If she should marry the man desired?”: “… yet were both Significators in a Semisextile, and in good houses, from which I gathered hopes, that there were some sparks of love between them.”[37] It does not give us enough to hang a judgement on, but it does show inclination and opportunity. As a minor testimony, that can certainly lend support.

What are we to make of Kepler’s contribution, that is, his three “new aspects”? In spite of his luminous intellect, it is difficult to see how we can reconcile them with the veto pronounced by the classical system. That is not to say that his use of harmonic theory is not elegant and, in a certain respect, continuous with the tradition. Ptolemy, after all, sought to establish the correspondence between the aspects and the musical scale, and Kepler’s new aspects artfully extend this analogy.[38] Even so, the musical argument is tentative in Ptolemy, while the origin of the Ptolemaic aspects in sacred geometry is a primary intuition of the early expounders of the tradition.[39] Kepler’s aspects make hash of that.

William Lilly has been derided for being an early adopter of Kepler’s aspects.[40] He introduces them early in Christian Astrology and includes not only Kepler’s quintile, biquintile and sesquiquadrate but also, against Kepler’s design, even the semisextile, semiquintile, semisquare and sesquiquintile.[41] Later, in the section on “Effects of Directions”, Lilly gives further guidelines for finding and interpreting these aspects and then puts them to practical use in his lengthy delineation of the chart of “an English merchant”.[42] David Plant remarks that Lilly’s delineations would emerge as “the standard textbook interpretation of the ‘minor aspects’” through the present day. He too is disappointed in Lilly.

Has Lilly’s incorporation of this new material really led him outside the tradition? A careful review of the facts leads me to think not. Context is important. When we first meet the minor aspects in Christian Astrology, it is in the section dealing with how to read the annually published ephemerides in his popular almanac Merlini Anglici:

“…we seldom use more aspects than the conjunction, sextile, square, trine, opposition: to these of late one Kepler, a learned man, has added some new ones… I only acquaint you with these, that finding them any where you may apprehend their meaning.”[43]

Lilly is telling the truth here. We have already seen that in the entire horary portion of Christian Astrology he factors in only one minor aspect, the semisextile. None of the “new ones” put in an appearance. That counts as seldom use in my book. For that reason, I do not think that there any reason to doubt him when he goes on to say that he has included a list of Kepler’s aspects for the sake of completeness. Lilly was after all in the almanac business and would probably have felt some pressure to remain au courant so as not to limit his customer base. Evidently nobody else much cared for them, either. By 1651 Lilly had dropped the minor aspects from Merlini Anglici and never revived them.[44]

As for their rather prominent place in the natal portion of Christian Astrology, it may be significant that he involves them only in the delineation of primary directions. Never does he consider them in connection with the geniture, revolutions or profections. What is going on here, I believe, is that Lilly perfectly understands the link between the zodiacal signs and the Ptolemaic aspects. However, primary directions are formed not through the secondary motion of the ecliptic but rather through the primary motion of the equatorial, measured in right ascension. Perhaps, then, Lilly permitted these minor aspects in relation to primary directions because, in this context, they simply do not refer to the twelve-fold zodiac. They are appropriate on their level, given that the rapt motion of the sky supersedes the secondary motion of the planets. This would also help explain why Lilly quickly dropped the minor aspects from his almanac. Why waste the time on the tedious calculations if they cannot be used?


We have seen that aspect doctrine remains consistent in its main features from antiquity through the 17th century. They hold many features in common: the ideal basis of the aspects in the sign relationships, the social character of the aspects, the Ptolemaic aspects (and absurdity of “minor” ones) and the distinct effects of applying and separating aspects. Where there are differences, they arise over time with the growth of horary, wherein the emphasis on the secondary motion will lead to an immense clarification of the roled played by planetary dynamics in foretelling the future. Thus, in “traditional astrology”, the orbs of the planets, their application and separation, and the perfection of their aspects become well-honed tools for prediction.

There were undoubtedly some losses. Horary’s huge success in getting exact prediction from the secondary motion of the planets almost certainly contributed to the virtual abandonment of primary directions for secondary progressions. We would do well to reclaim primaries, not to mention the math. I wonder, too, if the stress laid by traditional astrology on exactitude has not led us in the contemporary revival to exaggerate the orbs while understating the power of “beholding” and whole sign aspects. It seems to me that John Frawley goes too far in tossing them out completely.[45] Yet even William Lilly does not fixate on having them be razor-sharp.[46]Maybe we would do well to relearn some of lateral thinking style – the fuzzy logic – that was a stronger feature of the ancient astrology. Intuition, after all, begins as a kind of peripheral vision. And what is that if not a whole sign aspect of the inner eye?

[1] Astronomica 2.278-279.

[2] CA 26, 109, 126, 159, 165, 171, et passim frequenter.

[3] Astronomica 2.271; 300-301; 358.

[4] Astronomica 2.300-301.

[5] CA 126.

[6] Genesis 1.14: “And God said, Let there be lights in the firmament of the heaven to divide the day from the night; and let them be for signs, and for seasons, and for days, and years…”

[7] CA xxxi.

[8] Letter to Oxford scientist Thomas Harriot (1606). Kepler’s statement is more aspirational than real, inasmuch as he continued to practice astrology along traditional lines into the 1620s.

[9] sesquiquadrate (135°), quintile (72°), and biquintile (144°), quindecile (165°), vigintile (18°), etc.

[10] multiples of 15° (15°, 75°, 105°, & 165°) and multiples of 22.5° (22.5°, 67.5°, 112.5°, & 157.5°)

[11] e.g., quincunx (150°), semisquare (45°), semisextile (30°), etc.

[12] “You ask what necessitated God to create these truths; and I reply that he was free to make it not true that all the radii of the circle are equal — just as free as he was not to create the world. And it is certain that these truths are no more necessarily attached to his essence than are other created things.” See “To [Mersenne], 27 May 1630,” AT 1:152, CSMK 25.

[13] Timaeus, 37c-d. This is also the basis of Plato’s distinction between the motion of the Same and the motion of the Different later in Timaeus.

[14] Manilius make the geometrical basis of the aspects even more explicit (Astronomica 2.270-432). The division into semicircles has always bothered me, for semicircles are not polygons and they are not regular, except for their areas.

[15] Ptolemy asserts this distinction in his discussion of application and separation in Tetrabiblos I. 24: “Such a relation is taken to exist whether it happens by bodily conjunction or through one of the traditional aspects, except that with respect to the bodily applications and separations of the heavenly bodies it is of use also to observe their latitudes, in order that only those passages may be accepted which are found to be on the same side of the ecliptic.” Ptolemy takes the minority position that the conjunction requires physical proximity by parallel of latitude. For everyone else, to my knowledge, conjunction by celestial longitude suffices to the join the influence of the planets involved.

[16] Compare for example the social construction of the aspects in Dorotheus (ca 75 CE) and William Lilly (1647 CE), both of whom compare them to degrees of love and hate. Dorotheus, Carmen Astrologicum I.20: “If you wish to know what of love and other than that there is between him [the native] and his brothers, then look from the lord of the lot of brothers. If its lord aspects it from trine, it indicates love between them, and if it aspects from quartile, it indicates a medium amount of love. If you find it in opposition to the lot, then it is an indicator of enmity and separation. If if [the lord] does not aspect it [the lot], it indicates the estrangement of one of them from the other.” William Lilly, CA 105-106: “You must understand amongst these Aspects, the Quadrate Aspect is a sign of imperfect enmity; and that the Opposition is an aspect or argument of perfect hatred;… the Sextile and Trine aspects are arguments of Love, Unity and Friendship, but the trine is more forcible…”.

[17] William Lilly, CA 106.

[18] Firmicus Maternus, Matheseos Libri VIII, 6.3.1: “If all the planets, whether benefic or malefic, were in trine to each othe, their predictions would be improved by that location. The evil of the malefic would be lessened and the helpful benefits of the good ones would be strengthened.”

[19] Manilius, Astronomica 2.258: “Weak (debilia) is the connection between between alternate signs, nor do they maintain with unfailing constancy the federation between each other, because the line is reluctant to bend in its circuit of short chords.”

[20] Dorotheus, Carmen Astrologicum II.17; William Lilly, CA 106.

[21] Matheseos Libri VIII 6.22-28.

[22] The insistence that aspects be derived from harmonious divisions of the twelve-fold zodiac may also have arisen from two other considerations. First, it is primarily because the ecliptic is a circle of twelve living signs that it can create. And so the creative power of the planetary aspects subsists in the signs as such, not in the sheer mathematical division of the 360 degree circle. Second, the geometric shapes that give rise to the aspects are unities and to varying degrees reproduce the unity of the circle (= the zodiac) with its proper center (= the earth). Only through these shapes, therefore, can the planets truly cooperate in one activity, as their rays meet and coincide in the unity of the same point: “In the case of applications and separations by aspect… all rays always fall and similarly converge from every direction upon the same point, that is, the center of the earth.” Tetrabiblos I.24.

[23] See Neugebauer & Van-Hoesen, Greek Horoscopes, p. 176 & 179.

[24] Ptolemy, Tetrabiblos I. 24.

[25] Astronomica 2.305-340: “And though a man compute a fourth sign from a fourth, the degrees in themselves will cause the wreck of a whole sign. It is therefore not enough to count trigons by signs or to expect a true square from signs at intervals of four.”

[26] (trans. M. Epstein) The Beginning of Wisdom, chapter 7, p. 117.

[27] CA 106-107.

[28] “The Classical Origin and Traditional Use of Aspects”,

[29] CA 112: “A planet is Void of Course, when he is separated from a planet, nor doth forthwith, during his being in that sign, apply to any other: This is most usually in the Moon; In judgements do you carefully observe whether she be Void of Course yea or no; you shall seldom see a business go handsomely forward when she is so.” Lilly certainly allowed the Moon to perfect in the next sign an aspect initiated in her present one. It is curious indeed that the modern definition of the void of course Moon is much more restrictive than the traditional one.

[30] Ptolemy, Tetrabiblos  I.16.

[31] Manilius, Astronomica, 2.394.

[32] Firmicus Maternus, Matheseos Libri VIII, II.XXIII.7.

[33] Ptolemy, Tetrabiblos  I.16.

[34] Dorotheus, Carmen Astrologicum I.20: “… it indicates the estrangement of one of them from the other.” Here, estrangement is more concrete than in Ptolemy. The inconjunct denotes active alienation.

[35] I think this triviality is what Ptolemy is driving at when he says, “…and although the said space between them may extend into two signs, the whole only contains an angle equal to that of one sign.” Tetrabiblos I.16. I am using the clearer Ashmand translation here instead of the Loeb edition.

[36] Manilius, Astronomica 2.386.

[37] CA 390.

[38] The major third (= quintile), the minor sixth (= sesquiquadrate) and the major sixth (= bi-quintile) See David Plant, “Kepler & the Music of the Spheres.” Kepler also rejected divisions of the circle that could not be made with pure geometry (i.e., with compass and straight edge) and in this way adhered to the theoretical integrity of the tradition.

[39] Concerning the intrinsic uniqueness of the circle’s division by twelve, see Koenraad Elst, Ph.D., “Why twelve?” at

[40] See John Frawley, “What is the Tradition in Astrology?”, September 2009 ( “Far from being the stern traditionalist of modern legend, Lilly was in fact a gung-ho modernist. The innovations that Kepler was cooking up – the self-contradictory nonsense that is minor aspects – Lilly was first in the queue. I’m quite sure that if you’d gone up to him and said, ‘Hey, Bill, have you heard about Sedna?’ he’d have bitten your hand off. ‘Wow, look – it’s right on my Chiron!’”

[41] CA 31-32.

[42] CA 785 ff.

[43] CA 32.

[44] This is based on my own examination of 25 editions Merlini Anglici between 1846 to 1881.

[45] The Horary Textbook, p. 97: “Orb is probably the most overrated concept in traditional astrology…Which is why you don’t need to bother with it.” His position is something of a corollary his inflexible rule that aspects end at the sign cusp. Because the sign cusp now takes over the role played by moiety, Frawley is free to let the influence of any planet extend throughout the whole sign. There are many reasons that this cannot be entirely right, not the least of which is that experience proves that some planets are stronger than others at the same distance. Orb is a very useful way of quantifying this difference in effectiveness.

[46] CA 107. He is not over-rigid about cusp orbs either. In one chart, the Part of Fortune is placed more than a degree from the 2nd house cusp. Lilly nevertheless deliberately gives it to the 2nd: “…and though the Part of Fortune is some minutes more than 5 degrees removed from the Cusp of the second, yet were it absurd to think it had signification in the first” (CA 180).

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