Research Studies: Tropical vs. Sidereal & Related

[Dimityr Kojuharov]

The main problem in the study of ancient charts(for nativities and events) is incorrect methodology which was used from the previous scholars.
Most of ancient charts give only the longitudes of planets.Data for the month and the year of the chart most often are missing.First O.Neugebauer and later D.Pingree and others used incorrect methodology for recomputation of the charts:
1.They used MODERN, not ANCIENT astronomical tables for these calculations - what is a wrong approach.
2.They used Tuckerman's tables[1962 and 1964] which have systematical errors-the error is in all longitudes of Mars.These errors in Mars are avoided in corrected tables of Houlden and Stevenson[1986]
3.They don’t test in which zodiac are the Greek horoscopes after Ptolemy-in the tropical or in the sidereal one.Neugebauer just assumed that after Ptolemy and Theon Alexandrinus all Greek horoscopes are calculated in the tropical zodiac which is a wrong thesis.

Only in the researches of one modern scholar, Alexander Jones, we can see a right approch:
-first he gives the longitudes from the original text
-then he used Handy tables from Theon's book for recalculations of the charts together with Theon's instructions from his Small Commentaries to Handy tables
-finally he gives modern computations for these charts

This is the correct way to reconstruct the ancient astrological charts.

[Dimityr Kojuharov]

What we can see as a result for the nativities and events charts (not for solar return charts)?
Below are the results of my preliminary study of the scientific papers which deal with old nativities and events charts.This problem-with which zodiac are worked the ancient astrologers –needs new comprehensive and serious study involving recalculation of all survived charts with the methodolody described above.Errors or erroneous conclusions are possible and are not excluded in this my survey.

1.Hellenistic period
-all charts from Hellenistic period are calculated in the sidereal zodiac, including charts from the late Antiquity or many centuries after Ptolemy
-only occasionally in the late Antiquity we can see charts calculated in the tropical zodiac-chart of Proclus(for 412 A.D.) and a anonymous chart from Oxyrhynchus(for 508 A.D.)

2.Sassanian(Persian) period
-all Sassanian astrologers used sidereal zodiac and give the longitudes in this zodiac

3.Arabic period
-first generation of astrologers, which are in most cases Persians, calculated charts in sidereal zodiac.These calculations are based on Shah's zij from Sassanian period and other zijes from Indian origin which contain sidereal parameters
-later generations of Arabic astrologers after the translation of Ptolemy's Almagest, Theon’s Handy tables and Tetrabiblos too, started to calculate the charts in the tropical zodiac
-only in Maghreb and al-Andalus regions to the middle of XIV Century we can see continuation of this tradition-calculation of longitudes in sidereal zodiac

3.European period
-in which zodiac are calculated charts in the first centuries after the entry of astrology in Europe is difficult to say at the moment, but the first European tables-Toledan tables(1080) and Alphonsine tables(1240) are sidereal .After Prutenic tables(1551) and Rudolphine tables(1627) we can say with certainty that astrologers calculated charts with tropical longitudes.

[Therese_Hamilton]

Dear Mr. Kojuharov,

Thank you for your continued work and research in this area. For several years I have wondered when the transition from sidereal to tropical calculation occurred. I very much appreciate your efforts in tracking down the tables and calculation of charts. Strangely enough, in Benjamin Dyke's Persian Nativities series (three books), I have found only one tiny footnote stating that the Zij tables were sidereal. (Volume 1, p. 16) No one seems willing to explore the zodiac issue in Hellenistic or later astrology. Everyone seems to assume that the early techniques were used in the tropical zodiac.

Can you give an internet reference for Alexander Jones?

Thank you,
Therese Hamilton

[Dimityr Kojuharov]

Can you give an internet reference for Alexander Jones

Alexander Jones, Astronomical papyri from Oxyrchynchus, volumes 1 and 2, Philadelphia, 1999

The most impressive statement of A. Jones is on the p.49 of his book, where he says that the Greek astrologers(after Ptolemy) used Ptolemy's tropical longitudes from Handy tables and then they used a special formula(Theon's rule) to convert these tropical longitudes into the sidereal .So the final result is a horoscope in a sidereal zodiac.

[Dimityr Kojuharov]

In the root of the whole discussion is one mess that start from Otto Neugebaeur and continues in David Pingree and all other later authors writing on this topic.I will give a quote from Rupert Gleadow's book "The Origin of the Zodiac".When he comment the horoscope of Emperor Augustus on p.64 of his book he says:

The question is which of five possible zodiacs did Theogenes us? Eudoxus has put the equinox in 15°Aries, Cleostratos of Tenedos in 15°, Naburiannu in 10°, Kidinnu in 8°and Hipparchus in 0°!And all these systems were still current.

The truth is that there are NO FIVE different zodiacs!There is ONLY ONE zodiac and this zodiac was in use by all ancient astrologers-Babylonian, Greek, Persian and Indian.This zodiac is FIXED and only the equinox point is MOVING through the zodiac in the same way as the clock-face is fixed and the hour-hand is moving. The features and characteristics of this zodiac every one can see in the Liber Hermetis translated by R.Zoller.This zodiac is fixed to the stars and every fixed star has a determined place-for example Aldebaran (α Tauri) in this zodiac is on 15˚ Taurus.This zodiac is of Babylonian origin and very good article on the thema is : P.Huber, Ueber den Nullpunkt der babylonischen Ekliptik, Centaurus 1958, vol.5, No.3-4, pp.192-208.


The confusion come from this small but very important trick which initially is very difficult to understand.

[Therese_Hamilton]

Dear Mr. Kojuharov,

I would like to respond to your post in which you stated that "There is ONLY ONE zodiac and this zodiac was in use by all ancient astrologers--Babylonian, Greek, Persian and Indian."

Perhaps I misunderstand you, but you seem to suggest that the stars in the zodiac were in exactly the same position in these different cultures, and you refer to Liber Hermetis. Although these cultures all used a sidereal zodiac, the zero Aries point was in different locations in relation to the stars. First, let's take Mesopotamian zodiac measurements: http://www.snowcrest.net/sunrise/AMesoStars.htm

We can see from the references in this article that the measurement of the zodiac in Mesopotamia was imprecise, though close to today's Fagan and Lahiri values.

We can see here that longitudes from Babylonian texts don't agree precisely with the Fagan-Bradley zodiac: http://www.snowcrest.net/sunrise/arochberg.htm In general, they are closer to the Krishnamurti/Lahiri values.

The consideration of 22 ancient Greek and 5 Babylonian birth charts fits better with Spica at zero Libra than with Aldebaran at 15 Taurus and Spica at 29 Virgo (Fagan/Bradley) The reference here is Nick Kollerstrom in Culture and Cosmos in 1997 (Vol.1, #2).

Rayomond Mercier has shown that all the ancient Greek and the medieval Arabic astronomical works located the zero point of the ecliptic somewhere between 10 and 22 arc minutes east of the star Zeta Piscium.

The Persian and Indian zero ayanamsa date is the product of a Sassanian (Persian) reform of astronomical tables in the year 556. The resultant zero date was calculated using the cycle of Jupiter, which we know today is not the way to compute precession. However this ayanamsa and zero date became the value of the Greek-Arabic-Hindu zodiacs at the time, and later appeared in the Surya Siddhanta. The first degree of Aries was aligned with Reveti (zeta Piscium). This star is approximately 25 degrees of Pisces in the Fagan-Bradley zodiac. (The ayanamsa question is discussed in detail on the Swiss Ephemeris site.)

I have made a careful study of the star positions in Robert Zoller's translation of Liber Hermetis as well as Anonymous of 379. I'll discuss these positions in my next post.

Therese Hamilton

[Therese_Hamilton]

STAR POSITIONS IN LIBER HERMETIS AND THE TREATISE ON THE BRIGHT FIXED STARS (Anonymous of 379)

The star positions in Liber Hermetis, Chapter 3 are correct in Tropical longitudes for approximately 128 B.C.

Anonymous of 379 states that he is adjusting his star positions from Ptolemy's positions. He uses an approximaely 3 degree adjustment. Rob Hand has noted that the positions (from all appearance purely by accident) are similar to today's Fagan/Allen zodiac. Actually only a few stars in this list match the Fagan/Allen values. These are Regulus at 5 Leo, Spica at 29 Virgo, and Antares at 15 Scorpio. The remaining stars are closer to the degrees in the Lahiri/Krishnamurti zodiacs. (53 and 59 minutes greater than the Fagan values)

Chapter 25 in Liber Hermetis (LH) is the most challenging source of ancient star locations. This chapter combines fixed star longitudes with terms (bounds) and other types of symbolism. I constructed a table of all the stars listed in the Anonymous text and compared them with the longitudes in Chapter 25 of Liber Hermetis as well as the longitudes in the Krishnamurti zodiac. (I have all my tables set up in this zodiac rather than the Lahiri zodiac. Longitudes are approximately 6 minutes greater than Lahiri.)

Out of 27 stars in LH 25, 23 longitudes were less than a degree greater than those in Anon 379. Four longitudes were less. This comparison suggests that at a slightly later date than 379, someone adjusted the longitudes to account for precession. However, these longitudes (if Tropical) are incorrect for that date.

The LH 25 longitudes are very close (often within a few minutes) to the Lahiri/Krishnamurti longitudes. A computer printout places the LH 25 longitudes at approximately 300 C.E. The zero ayanamsa date for the Krishnamurti zodiac is 291 C.E.; for Lahiri: 285 C.E. This is why there is such a close match in the longitudes of stars.

LH 25 gives the longitude of Aldebaran as 16Tau06. The Krishnamurti value is 16Tau02.
Antares isn't mentioned under Scorpio, but under Taurus is noted to be at 15 degrees, opposite Pi Orion. (Antares is not mentioned with Aldebaran.) The Krishnamurti value of Antares is 16Sco00.

LH 25 places Spica at 0Lib06. The Krishnamurti longitude is 0Lib05.

It's tempting to suggest that the zodiac used in LH 25 is an actual sidereal zodiac in use in ancient times, similar to today's Lahiri/Krishnamurti zodiacs. But it is just as probable that the similarity in degrees is strictly an accident. At any rate, the Tropical values are wrong for 379 and for a slightly later date in LH 25. I have not worked with Ptolemy's values to see how Anon of 379 might have adjusted his stellar longitudes. And we can only guess at how the LH 25 values were obtained.

Therese Hamilton

[Abd-Allah Meyers]

Good evening dear Ms. Hamilton,

Thank you for waking up this forum. Your posts concerning fixed zodiacs are both informative and useful.

One issue seldom addressed by those favouring a fixed zodiac is the varying proper motions of the fixed stars. Each of the main fiducial stars used in antiquity and often still today, Aldebaran, Regulus, Spica, Antares and Fomalhaut exhibits a different proper motion in both celestial longitute and latitude (and / or right ascension and declination). The least proper motion amongst these five is reportedly exhibited by Antares, who is also the furthest away from our solar system. This means that the positions of these and other fixed stars relative to each other are shifting gradually. The 'fixity' of the 'fixed' stars is, like nearly everything else, relative and thus an object of detachment by the sages.

A simple glance at the list of fixed zodiac precession factors included in widespread astrology computer programmes shows a few dozen such factors, often one of more for each researcher and / or for each famous astrologer. Like house systems, precession factors appear to be a gate of astrologers to immortal fame.

Turning to the two moving symbolic zodiacs, one for each hemisphere, six zoidia apart, a point often made in basic writings of 20th century astrologers e. g. Reinhold Ebertin who explicitly refers to the northern hemisphere, they have the advantage of being far less numerous than their fixed counterparts with little probability of proliferation.

One can observe attempts by current astrologers to peg the zodiac to some other object than a fixed star near the ecliptic, e. g. to the gallactic centre or to the solar apex. This will most probably result in further generation of fixed zodiacs.

May we also remind ourselves that, according to current astronomy, precession is not a constant but, at least in part, a variable? And may we ask ourselves what the existence of two kinds of zodiacs, currently in aversion to each other by zoidia, symbolises?

Best regards,

Abd-Allah Meyers

[Rumen_Kolev]

Dear Therese and Abdullah,

Kugler in 1900 discovered the fixed Babylonian zodiac and found its exact beginning.
Huber only confirmed Kugler.
Its roots are in around 870 BC to 670 BC.
Indeed Aldebaran is in 15 Taurus in this zodiac.
There is only difference in nine arc-minutes that even does not cross the statistical significance level!
Kugler: Aldebaran in 14d 54 Tauri
Huber: Aldebaran in 15d 03 Tauri

Placidus_7_screen_Babylonian_Zodiac.gif (187.01 KiB) Viewed 1399 times

Hermes (Liber Hermetis 25): Aldebaran in 15d 00 Tauri (stella splendida Orionis, opposita stellae Antaris)

Liber Hermetis 25 has several time-levels,

the most ancient is in fact the Babylonian fixed zodiac from around 700 BC Babylon.




-------------------------Babylonian fixed zodiac--------Liber Hermetis 25
Aldebaran ------------------- 15 Tauri---------------------15 Tauri ---- Constant
(Tauri ... 15 gradus ... stella splendida Orionis, opposita stellae Antaris)

Altair-------------------------6 : 36 Tauri -------------------7 : 16 Tauri

Antares-----------15 : 03 Scorpio (in 760 BC) -----------15 Scorpio
14 : 59 Scorpio (year 2011)

Regulus------------------------- 5 : 16 Leonis ----------- 5 : 50 Leonis
Castor -------------------- 25 : 35 Geminorum -----------25 Geminorum
Zubeneschamali ----------- 24 : 40 Librae ----------- 25 : 30 Librae
(Babylonian stellar catalogue gives this star in the 25th degree)

Vega ---------------------- 20 : 21 Saggittarii------------------ 20 : 46 Sagittarii

========================================

This is the Babylonian fixed zodiac in Liber Hermetis 25.
The precision was around one degree.

Also proven by the LBAT 1499 text and its likes (in fact this texts are like modern Table of Houses. It tells you which dodekatemoroia of which sign is rising on the eastern horizon when certain stars are in culmination). This text also confirms the fixed Babylonian zodiac.

Indeed, the fixed zodiac division in 12 with the exact borders, is coming from 770 BC.
This does not say that they did not know it before.
But only that overwhelming evidence points to 770 BC Babylon as the place and time of the last restoration of the Astral Tradition.

Not that they did not know the tropical division of the year.
They knew and used this too.

The Greeks used the Babylonian fixed zodiac until end of antiquity.
The anonymous may in fact compute with addition to Ptolemy.

There is one place in Liber Hermetis 25 where is stated that
"21 gradus Cancri ... a pluribus dicitur stella Canis"

'21st degree of Cancer ... by many called the Star of the Dog', which is Sirius.
Huebner thinks that this is paranatellonta and rightly so, because Sirius projects by simple ecliptical projection in 19 : 49 Geminorum of the fixed Babylonian.
(Liber Hermetis 25 puts Sirius in 21 : 06 Geminorum)

Some data in Liber Hermetis 25 comes from paranatellonta.
If we compute when and where is Sirius in paranatellonta with the 21st degree of fixed Cancer, we will know.



Luckily, we can do this with the new versions of the program Placidus 7 (with Porphyrius Magus 2) which I am lucky to announce today.

Placidus_7_screen_Sirius_rising_paranatellonta_700_BC_Babylon.gif (216.41 KiB) Viewed 1395 times

for more info: http://www.babylonianastrology.com/inde ... &Itemid=43

[Rumen_Kolev]

Liber Hermetis chapter XXV (Gundel 1936: 54) has at 15° of Taurus
“stella splendida Orionis, opposita stellae Antaris ... facit tribunos, duces exercitus, militiae principes vel milites magnos et terribiles...”
(“a bright star in Orion, opposite Antares... makes politicians, generals leading armies, militia chiefs or warriors great and terrible...”).
This, without doubt, must be Aldebaran.
Here is also given the degree of Antares: 15 Scorpio.
If we look further in the section for Scorpio, we will see that Antares is not mentioned, but for 15 Scorpionis is given the same interpretation as for 15 Tauri.

Hephaestion in book II of his Apotelesmata towards the end of chapter 18 (p. 166 from the 1973 edition of Pingree), quoting Antigonus of Nicaea, says:

“He (Antigonus of Nicaea) says, that always when the Moon or any from the planets are on a corner (the Meridian and the Horizon more exactly and generally the four signs that are on the horizon and the meridian, i.e. the signs on the ascendant, the descendant and the culminating and the lower-culminating signs), moving forward (direct) in length (longitude) as well as in breadth (latitude) and (in conjunction) with some from the bright fixed stars, as for example, the so called ‘Royal one’ which is in the heart of the Lion, around the fifth degree, makes great and most famous destinies. The star in 20° of Aquarius does the same. And the Moon coming near 15° of Taurus and in breadth (in the same latitude?), makes rich people, managers (of estates) and chiefs and at 27° of Taurus, in the same way, makes distinguished magistrates, profitable in everything and righteous. (The Moon) being near the bright star in 30° of Taurus, makes commanders or distinguished sea admirals. The same is also valid for 7° of Scorpio. It makes friends of kings or savage second in command, hazardous, banished, warlike. In this way, indeed, says he (Antigonus), is to be proceeded also with other fixed stars.” (my translation from Pingree's edition)

Is there now still doubt, what zodiac was Antigonus using ? Or what was the zodiac in the basis of Liber Hermetis 25 ?
********************************
Liber Hermetis 25 is a compilation probably form late antiquity and it has data from Ptolemy and also data that seems to come from around AD 470 because there are several star positions computed by adding 3 d. 26 min. to the positions in Ptolemy. These same coordinates are also found in the untranslated treatise of Hermes 'De stellis beibeniis' (On the fixed stars)

they are: Spica: 00 : 06 Librae (LH 25)------00 : 06 Librae ('De stellis beibeniis') ---------- 26: 40 Virginis (Ptolemy) difference: 3 : 26
Aldebaran: 16: 06 Tauri (LH 25) oritur splendida stella Hyadum ------------ ---------- ---12: 40 Tauri (Ptolemy) difference: 3 : 26

These positions though are few. Huebner, the scholar expert on paranatellonta, even thinks that these are paranatellonta.

This is open for further research.
*********************************
What is clear though, is that the bulk of the data in LH 25 in fact describes the positions of the stars in the Babylonian Fixed Zodiac
(Aldebaran 15 Tauri). We can deduce that the compiler has used a source coming directly or indirectly from Babylon 700 BC.
The time and place of the last restoration of the Original Astral Revelation by the third Hermes.

***
It is beyond belief to see how heavy-weight, but ideologically very opinionated scholars like Neugebauer and Pingree, malicious critics of Astrology and spirituality, try to date Antigonus (Haefestion) and Liber Hermetis assuming that they all used the catalogue of Ptolemy and added 1 degree for one century !
What would they say about the Babylonian tablet with stellar positions of 6 stars that confirm that same zodiac given by Antigonus and LH 25??!

Neugebauer 1987: 187 arrives at year AD 400 for Hefaestion and Gundel 1936: 146 at year AD 480 for Liber Hermetis XXV.
The stellar positions, however, given by Hermes (in Liber Hermetis XXV) and Hefaestion (QUOTING ANTIGONUS), are the same as those given by a fragment of a Babylonian star catalogue (Huber 1958: 203).
In this tablet a Librae is in 20° fixed Libra and b Librae in 25° fixed Libra which translates in Aldebaran in 15° fixed Taurus.
This means only one thing: They all used one and the same ecliptic – the Babylonian fixed ecliptic.

The few paranatellonta data in LH 25 will have a decisive weight for exact dating because which degree of the fixed ecliptic rises together with a given star on the horizon, changes with geo latitude and with time. The further from the ecliptic the star, the higher the rate of change of its paranatellonting ecliptical degree with time and geo latitude.