In the Primary directions thread, Deb kindly brought to my attention a passage from Antiochus of Athens's Thesaurus, in which he discusses different kinds of configurations (aspects), including the 'temporal' variety. In a footnote to the translation, Robert Hand states that:

This section actually describes in mundo aspects of exactly the kind that Placidus made so much use of in his primary directions. The math is different but the end result is nearly the same.

As far as I can see, this is not correct. Antiochus's method is based on the rising times of the zodiacal signs (i.e., on their oblique ascensions), whereas the method of Placidus is based on proportional semi-arcs. Here is an example:

In a chart cast for my location (Lund, Sweden, 55N42, 13E11) today (1 Sep, 2008) at 00:00 CEDT, 2Cn46 rises while 1Aq56 is on the 9th Placidus cusp (using tropical positions). In the Placidean system, these two points form a mundane trine.

In Antiochus's system, two points form a temporal trine if the rising times of the intervening signs (including fractions of signs) amount to 120, or one third of the time required for the entire zodiac to rise. In the chart under consideration, the relevant rising times at the given latitude are as follows:

Aquarius 0:54:46 (fraction)
Pisces 0:42:18
Aries 0:42:18
Taurus 0:58:33
Gemini 1:40:46
Cancer 0:14:23 (fraction)

Total 5:13:04

This amounts to some 78.5 'times', not anywhere near 120.

The Antiochus text itself is not entirely clear, as in one place it seems to distinguish between 'temporal' and 'ascensional' configurations. Hand does not know what is intended (nor do I, for certain).

Any thoughts on this would be appreciated.

The maths involved make this beyond me, and I know that the translated text is not the clearest chunk of text ever written. I was wondering if your analysis suggests a similarity of philosophy that could give different results depending upon technical alternatives.

Actually, I'm not sure my question even makes sense to me ! Let me put that another way - what we seem to have evidence of, is an alternative aspect system that is in addition to zodiacal measurement. What else, other than mundane aspects, could possibly make sense of that?

One suggestion might be for you to contact Rob Hand and ask for his updated opinion on this passage. Something like 15 years has passed since this was originally published, so he may well have come across other references that place the passage in a better context now. At the end of the day I can't see how we can iron out confusions as to what the text specifically means unless we are able to cross reference it with similar references in other ancient texts.

Good luck!

Hi Deb,

Actually, I'm not sure my question even makes sense to me ! Let me put that another way - what we seem to have evidence of, is an alternative aspect system that is in addition to zodiacal measurement. What else, other than mundane aspects, could possibly make sense of that?

The key, I think, is the word 'temporal'. If we divide a sidereal day into 3, 4 or 6 parts, we get certain chunks of time (roughly, 8, 6 and 4 hours, respectively, each hour corresponding to 15 'hourly times' -- i.e., degrees of right ascension crossing the meridian). Thus, if point A rises over the horizon 8 hours (120 'times') after point B, the two are said to form a temporal trine.

This emphasis on rising alone (not culmination, setting, and anti-culmination) also marks the directional systems of several Hellenistic authors. It is criticized by Ptolemy in Tetrabiblos III.10 (using the numbering of the Robbins edition), but survived well into the Middle Ages -- Bonatti makes a feeble attempt to reconcile the two methods. Mathematically, rising times are much simpler to use than Ptolemy's proportional semi-arcs; but their usage is difficult to justify astronomically except when actually directing points to the Asc.

One suggestion might be for you to contact Rob Hand and ask for his updated opinion on this passage.

I might do that. I have searched for the Greek text as well, but it is not in any library to which I have immediate access.

Deb wrote:One suggestion might be for you to contact Rob Hand and ask for his updated opinion on this passage.

I did just that, and today received this brief response:

I am sure that there are differences in detail, perhaps even considerable ones, between Placidus and Antiochus. It is just that these are the earliest mention that I have seen of aspects in anything other than the zodiac except possible for co-ascensions and descensions.

So apparently Rob is no longer certain that these are 'in mundo aspects of exactly the kind that Placidus made so much use of in his primary directions'.

Hello Martin,

Even if that is correct surely it doesn't change the fact that Antiochus of Athens preceded Placidus in using a system of non-zodiacal aspects? Even if the maths and approach involved is fundamentally different between the ascensional rising of signs and semi-arcs?

You seem to be insisting on a definition of 'in mundo' that only complies with the approach adopted by Placidus.

Hello Mark,

Even if that is correct surely the basic point still stands that Antiochus preceded Placidus in using a system of non-zodiacal aspects? Even if the maths and approach involved is fundamentally different between the ascensional rising of signs and the semi-arcs?

Yes -- although I can't vouch for the technical term(s) used by Antiochus actually being the ones usually translated as 'aspect', as I haven't seen the Greek text. But some sort of non-zodiac-based relationship, certainly.

My main interest in the question was from the point of view of the history of primary directions, and to the best of my current knowledge, Placidus was the one who introduced mundane aspectual directions. (He writes that Maginus had proposed aspects in right ascension, but whether or not for use in directions, I can't say.)