Skyscript Astrology Forum

one other point worth considering for the glossary entry.

There is a relationship between the system of 12th parts and the decan system based on triplicity rulership used in Hindu astrology.

In A Rectification Manual, p. 6, Table 2, I show the relationship between the 12th parts and the decans based on triplicity.

Using Aries an example, the decan system divides Aries into
Decan 1: Aries (0deg 0min to 9deg 59min)
Decan 2: Leo (10deg 0min to 19deg 59min)
Decan 3: Sagittarius (20deg 0min to 29deg 0min)

The point is the dwads of Aries overlap the decans of Aries for the first 2 1/2 degrees of each decan:
Dwad 1: Aries (0deg 0min to 2deg 29min)
Dwad 5: Leo (10deg 0min to 12deg 29min)
Dwad 9: Sagittarius (20deg 0min to 22deg 29min)

Both decan and dwad systems can be considered fractals of an individual sign, with the decan system defining the fractal based purely on triplicity and the dwad system based on all 12 signs.

I have no information on whether the two systems are viewed philosophically in the Hindu system as I have described just now. But from a purely practical perspective, one has to ask for planets/points in these overlapping regions which is the predominate effect: decan or dwad? It's an open question in my book.

That is interesting. Rochberg also mentions (p.160) decans after the discussion of dodekatemoria, as being a "further development in Hellenistic astrology" but I couldn't see how the decans were so directly related to the "twelve parts". Your explanation ties the two together much more effectively.

I don't want to do any more edits on the page right now - I'll leave a little time to see if any more suggestions come in first, and then have one last amendment (maybe next week) where I'll try to incorporate your point through some kind of quote of what you have posted here. This glossary item seems to want to grow and grow! (My next mental project is to understand more about how and why the dodekatemoria were used along with rising times to establish the degree of the ascendant).

Deb wrote:Martin, as far as Babylonian sources are concerned, I am only aware of the multiplication method explained by Rochberg which shows agreement with the approach taken by Paulus Alexandrinus. If you come across reference to the other approach in Babylonian sources let me know and I?ll add it in.

It's really annoying that I didn't make a more careful note when I did read that. All I have at present is a brief comment of my own, four years old and made in passing in a different context, stating without references that both methods go back to Babylonian times and are found in both Greek and Indian sources. I suppose I trusted too much to my powers of memory to bother with sources.

I'm rushed off my feet right now marking papers, etc, so I haven't the time to hunt this down. I did look briefly at an old paper of Rochberg's ('Elements of the Babylonian Contribution to Hellenistic Astrology', 1988), thinking it might be in there, but it wasn't -- just the same apparent contradiction where she correlates twelve divisions of 2? degrees with multiplication by 12+1. (By contrast, Greek Horoscopes on p. 6 has a table that correctly shows how that method leads to each sign containing two divisions -- first and last -- corresponding to itself, thus totalling 13 divisions to a sign.)

Later addendum: not an original source, but see Holden's rich footnotes on pp. 38-39 in his translation of Paul of Alexandria, as well as pp. 17-18 in his translation of Rhetorius. In the latter he cites, specifically on the topic we're discussing, Mesopotamian Astrology by Ulla Koch-Westenholz, pp. 168-169 (which I haven't got). In the former he states, among other things:

Paul's method measures the product from the point itself, which is not consistent with the original method of subdividing a sign into twelfths. The original method is followed by Dorotheus, Ptolemy, Antiochus (probably), Porphyry, Firmicus, Hephaestio, and Rhetorius.

If this is correct (I haven't checked), Firmicus was obviously in good company, irrespective of which method is the most 'original'.

Just caught this as I am about to close my computer down. I have Koch-Westenholz's book somewhere so will dig it out and report back tomorrow. As a result of the forum feedback I have gone 360?, from initially thinking Firmicus was clearly wrong, to realising that his approach is well supported and has a strong rationale behind it, being the technique that ties the results of division and multiplication together.

The problem with Holden's footnote is that it makes assumptions - Rhetorius, for example, doesn't tell us anything about the calculation, it only explains the interpretation (the interpretation of which calculation?). Porphyry explains a method of calculation but doesn't tell us what the division by 2?? is expected to mean in interpretation - though by generating the same result as Firmicus who does talk about the effect these points have on other planets there is indirect evidence that they were used to generate associated points in the actual zodiac. What we have lacked so far is evidence that the Babylonians did it as Firmicus did, so hopefully I'll find something interesting in Koch-Westenholz's book.

More later

Deb wrote:The problem with Holden's footnote is that it makes assumptions - Rhetorius, for example, doesn't tell us anything about the calculation, it only explains the interpretation (the interpretation of which calculation?).

Actually, Rhetorius does go into the calculation in some detail (pp. 17-18 in Holden's translation), explicitly criticizing Paul. I just checked.

Here the text in Koch-Westenholz's book.

http://www.screencast.com/t/DQNV4Js4iKz

Wolfgang

Checked Koch-Westenholz's book last night (now see it's in the thread) - thanks Wolfgang! To briefly summarise, it confirms the existence of the micro-zodiac technique, and Koch-Westenholz speculates that "Since division by 2?? is cumbersome" (why?) the Babylonians would have devised an easier method, "perhaps the precursor of the method used in Hellenistic astrology". But he admits there is no evidence of this. He then details the other method, which is attested in two magico-astrological texts.

Martin wrote:Actually, Rhetorius does go into the calculation in some detail (pp. 17-18 in Holden's translation), explicitly criticizing Paul. I just checked.

You are right - I hadn't seen that section, only the later one in ch 6. Now I see the footnote you referred to by Holden (p.18 ), where he uses Koch-Westenholz's book pp.168-169 to state that the Babylonians had two calculation methods "These amount to multiplying the degree of the planet by either 12 or 13 ..." But I don't see how he can conclude that from what Koh-Wstenholtz has written here: one method is attested; the other is not (so far).

Going back to Rhetorius, I 'll check those references he gives and post the results here - then if anyone knows of anything else, they can add to it. What is especially interesting in that passage is that Rhetorius says that he found by trial that the results of multiplying by 12 generated the same result a dividing the signs by 2??, so this appears to have been something he (thought he) discovered personally. Whether others realised this or not before him, it couldn't have been explicitly stated in any of the sources he had access to.

Dorotheus:

Rhetorius says (p.17) "Dorotheus says in the 11th book to multiply the degrees by 12".
Reference to 'the 11th book' introduces a bit of a mystery, since we only have five, though Arabic sources report there were more. All we have from the Pentateuch (that I can find) are:

[I.8] A chapter. Knowledge of the masculine and feminine "hours" of the nativity.
Know the masculine and feminine "hours" as, if the Moon is in a masculine dodecatemorion, he [the native] is masculine. If the Sun and the ascendent and the Moon are in masculine signs, then, even if the "hour" of the nativity is double [i.e., even], males are born in it. If the Sun is in the ascendent in a masculine sign and the "hour" is double, males are born in it. If the ascendent is a two-bodied sign and is masculine and a masculine planet is in it, then, even if the "hour" of the nativity is double, males are born in it. If you find a masculine planet in the ascendent and another masculine [planet] in the seventh sign and the "hour" is double, males are born in it. If the Moon is in a masculine sign and the Sun also is in a masculine sign and the ascendent is what it is and the lord of the ascendent is Jupiter, similarly males are born. Count the dodecatemoria according to this manner: in a masculine sign two and a half "days" [i.e., degrees] masculine and two and a half "days" feminine, and in a feminine sign: two and a half "days" feminine and two and a half "days" masculine.

V 5 The corruption of the Moon.
...
4 If it is an action which its master wishes to keep secret, commence it when the Moon is immersed under the Sun?s rays as there is good for him, and it will be more concealed if he commences it at the with? drawal of the Moon from the Sun and [its] appearance from under the Sun's rays. If the Moon is in the dodecatemoria of Mars or Saturn and if the Moon is in the middle of the equator descending towards the South and if the Moon is in opposition to the Sun, then it is bad and it indicates the accession of quarrels and that the younger of the two will be the winning antagonist.

If we had text telling us to multiply by 12, the matter would be settled, but whilst we have evidence that the Babylonians recognised the micro-zodiac divisions of 2??, yet still multiplied by 13 for other techniques, we can't conclude from this that Dorotheus did any different (though Rhetorius' belief that he did might count for something).

Ptolemy makes only brief reference to the micro-zodiac of the dodekatemoria, where he discusses these and the monomoria at I.22 "Of Places and Degrees", and then dismisses them for having no natural (astronomical) basis:

Some have made even finer divisions of rulership than these [terms], using the terms "places" and "degrees". Defining "place" as the twelfth part of a sign, or 2??, they assign dominion over them to the signs in order. Others follow other illogical orders, and again they assign each "degree" from the beginning to each of the planets of each sign in accordance with the Chaldean order of the terms. These matters, as they have only plausible and not natural, but rather, unfounded, arguments in their favour, we shall omit.

Rhetorius seems unaware of the work of Firmicus, which (if I have this right) is the only other Greek source we have that specifically mentions the technique of multiplying by 12 as he does, though perhaps it was also mentioned in a now lost work by Dorotheus as Rhetorius reports it was.

Deb wrote:Checked Koch-Westenholz's book last night (now see it's in the thread) - thanks Wolfgang! To briefly summarise, it confirms the existence of the micro-zodiac technique, and Koch-Westenholz speculates that "Since division by 2?? is cumbersome" (why?) the Babylonians would have devised an easier method, "perhaps the precursor of the method used in Hellenistic astrology". But he admits there is no evidence of this. He then details the other method, which is attested in two magico-astrological texts.

I don't read Ulla Koch-Westenholz (who incidentally is a she ? Ulla is a Scandinavian women?s name ? and apparently now just Koch) the way you do, Deb. She does say that the method of dividing by 2? is attested in Babylonian sources; the only speculation she offers is that this method was probably developed into a method of multiplying by 12 (and then dividing by 30). It doesn't matter much whether it was or not, as both methods would give the same result: as Koch-Westenholz points out, n/2.5 = n?12/30. (I personally agree with her that division by fractions is cumbersome, but I suppose that's subjective.) She also remarks in footnote 4 that Rochberg-Halton (now just Rochberg) 'discusses only the second procedure', that is, the multiplication by 13.

Deb wrote:Rhetorius seems unaware of the work of Firmicus, which (if I have this right) is the only other Greek source we have that specifically mentions the technique of multiplying by 12 as he does, though perhaps it was also mentioned in a now lost work by Dorotheus as Rhetorius reports it was.

Firmicus wrote in Latin rather than Greek, which probably accounts for Rhetorius not being familiar with his work. But clearly Rhetorius thought (as Holden did, and Koch-Westenholz, and my humble self) that it doesn't matter whether you divide by 2? or multiply by 12, as you get the same result either way -- just like multiplying either by 13 or by 12+1 will give you a Pauline dodecatemorion.

I will try my philosophical obfuscation skills:


12 and Thirteen

While 12 is the representative of micro cosmos etc, thirteen is the number or regeneration ,change.Thirteen is appropriate as it includes itself- a regeneration of cyclical change that includes endings(12+1)

I see no conflict with basic concept, it is just stating it in another way.

PD