Many fundamental techniques and methods of the true, ancient astrology are generally unknown to the modern astrologers. These methods and techniques were lost as a result of scientific revolution of 17^{th} century, the followed assertion that astrology is a pseudo-science and numerous unsuccessful attempts to squeeze an astrology into the new scientific paradigm.

One of such fundamental basis of an astrology is the system of terms--the division of an ecliptic onto 60 unequal sectors by 5 sectors per each sign of the zodiac--and the major Egyptian years directly following from terms, as it was supposed till now. The major years of the planets are: 57 years for Saturn, 66 years for Mars, 76 years for Mercury, 79 years for Jupiter and 82 years for Venus. These numbers (expressed in years) are the sums of the lengths of all terms (expressed in degrees of ecliptic) assigned to the corresponding planet. In the total these numbers give 360, as it should be.

The lord of the terms, the planet or sensitive point falls into, is considered as the limiting factor of manifestation of this planet or sensitive point. In this way, if the planet is in its own terms, it's like a man among his relatives--on the one hand he is surrounded by his people, but on the other hand certain restrictions and obligations are applied to him. Obviously, the position of the planet in the terms of another planet is like a man in someone else's family, that he is something obliged to.

The system of terms, in particular, was used by ancient Egyptian astrologers for determination of lifetime, and it was considered, that without knowing the exact lifetime, it is impossible to make any precise predictions.

The table of the Egyptian terms is given below.

6

6

8

5

5

8

6

8

5

3

6

6

5

7

6

7

6

6

7

4

6

5

7

6

6

7

10

4

7

2

6

8

7

7

2

7

4

8

5

6

12

5

4

5

4

7

7

8

4

4

7

6

7

5

5

12

4

3

9

2

Let's explain this table: the first 6 degrees of Aries belong to Jupiter, following 6--from 7^{th} till 12^{th}-- to Venus and so on.

The rule of allocation of terms in signs of the zodiac, i.e. the rules of determination of their order and length in each sign, was lost a long time ago and is worth a special consideration. In this work we will concentrate on the first indispensable step to comprehension of the principle of the construction of the system of terms, namely on the definition of the major years for each of the five planets, or in other words on the calculation of total number of degrees, those should be assigned to each planet in its rulership.

The luminaries--Sun and Moon--were never participated in the rulership of terms and, following this logic, they have to had no major years as well. However, it appears, that, possibly, the later tradition has assigned the major years of 120 and 108 to them accordingly. These years were obtained by multiplication of fardars of the Sun and Moon (the origin of fardars is even more obscure, than the origin of terms)--10 and 9 years--on 12, i.e. on number of signs of the zodiac. That is an eclectic solution and, as we'll see later, has nothing to do with the principle of calculation of the major years of the planets.

Prejudice Of Ptolemy

Today it's already became well-known, that Greek scientist Claudius Ptolemy was not a representative of a traditional Greek astrological school and, most likely, he was never the practicing astrologer at all. His work Tetrabiblos reflects his personal and sometimes disputable opinions on many questions.

The question of terms and the major Egyptian years is not the exclusion. Nevertheless, we should be very grateful to Ptolemy, that he as a true scientist, even when rejecting some views and theories, took an opportunity to briefly explain their basic ideas.

We read in the book I, chapter 20, "On terms": "Regarding some believable and rather smart statements about terms, those someone tries to state, namely the statement that years assigned to each planet by the tables of ascensions in all geographical zones in the total gives that number <of major years>, then it is false" (translation of the author). Here the tongue of Ptolemy is hazy, and his thoughts are not very clear. But the only rational interpretation of these words is that one needs to sum the times of rising of the signs ruled by one planet (expressed in degrees of right ascension), and the obtained total is the major years of a planet or a total length all of its terms.

It's absolutely obvious, what the total time of rising of 10 signs (from 12) belonging to 5 planets cannot be 360°. In order to satisfy this condition, it's necessary either to give the rulership over the signs of the Sun and Moon--Leo and Cancer--to one or two of the five planets, or to use not the 12 signs division of the zodiac, but 10 sectors division.

Also we must keep in mind that Greeks as the Egyptians and Babylonians have used the star, sidereal zodiac, unlike Ptolemy, who, according to the available sources, was the first Greek astrologer who used the tropical zodiac, and this confirms the reformative direction of his Tetrabiblos once more. In a classical Greek astrology of 1^{st}-2^{nd} century AD it was considered, that the point of a vernal equinox is in the 8° of Aries. Regarding the coordinate of an equinox point in the earlier traditions, such as Egyptian and Babylonian, we may guess only and don't know anything for certain. However, without any doubt, the beginning of the zodiac to the first centuries AD inclusively was never identified with a point of a vernal equinox.

Problem Formulation And Its Solution

Input Data:

five sums of rising times of the zodiac sectors assigned to each of the five planets

the division of the zodiac onto 12 or 10 sectors; the correspondence of planets and sectors for duodecimal division is known, and the correspondence for the 10 sectors division is not known.

It is required to find optimal:

latitude of a place for calculation of rising time of the signs

distance between the beginning of the zodiac and the vernal equinox point

for 10-sectors division: a relationship between sectors and planets

The solution was carried out by a method of exhaustive search for latitudes in a range from 0° to 60° and for distance of a vernal equinox point from the beginnings of the zodiac in a range from -90° to +90° with step 1° for an approximate solution and 1' for the precise solution within the determined optimal interval.

Result of the solution:

For 12 sectors the acceptable solution does not exist.

Actually, it's absolutely clear even without any complex calculations. If we assume, that two of five planets obtain their years by the way of addition of rising times of not two, but three signs, it can be Venus and Jupiter only, because they have maximal values of major Egyptian years. In the standard rulerships Jupiter is placed between Saturn and Mars, therefore its major years obtained by addition of rising time of the signs of its rulership will be approximately equal to a half-sum of Saturn and Mars major years, that is 61.5. For Venus the similar half-sum of years of Mars and Mercury is 71. In this case the missing years for Jupiter are 79 - 61.5 = 17.5, and for Venus the missing years are 82 - 71 = 11. The obtained values--17.5 and 11--cannot be equal to rising time of Leo and Cancer at latitudes of Egypt and Mesopotamia in any way. Thus it's absolutely clear, that the major Egyptian years cannot be obtained by combination of rising times of the 12 signs.

For 10 sectorsthere is an optimal solution:

25°10' of northern latitude

distance of vernal equinox point from the beginning of the sidereal zodiac -- 29°02'

rulership:

Saturn rules 1^{st} and 10^{th} sectors and obtains 57.51 years

Mars--2^{nd} and 9^{th}--65.62 years

Mercury--3^{rd} and 8^{th}--75.04 years

Jupiter--4^{th} and 7^{th}--80.48 years

Venus--5^{th} and 6^{th}--81.35 years

mean square deviation of the retrieved solution from the major Egyptian years = 1.98 years.

The Analysis Of Results

The mean square deviation of the calculated years from the settled by the ancient Egyptian astronomers is found within the tolerance of the error of the ancient methods of determination of rising time of the sectors on ecliptic.

It's easy to see, that the latitude retrieved from our solution differs from latitude of Thebes 25N40--an ancient capital of Egypt--by half-degree only.

If we take, that in 1^{st} century BC -- 1^{st} century AD the vernal equinox point was in 8° Aries, than the retrieved coordinate of the vernal equinox corresponds to approximately 17^{th}-15^{th} centuries BC.

Thus, we obtain the dating and precise geographical place of fixation of the Egyptian system of terms, passed to us through the Greeks: Thebes, Egypt,17^{th}-15^{th} centuries BC.

It's known from historically reliable sources, that in middle of the 2^{nd} millennium BC the system of decanes (36 stars, later simplified to 36 equal sectors of ecliptic 10° each) was already developed in Egypt, and in Mesopotamia the collecting of a major series of omens Enuma Anu Enlil has already began.

Certainly, the dating the system of major Egyptian years by middle of the 2^{nd} millennium BC arouses some doubts, because the known historical information tells us, that the astrology as system of knowledge was developed only in middle of the 1^{st} millennium BC. However, we should not reject with a rush a possibility of existence of much more ancient astrological tradition, than it is known to us nowadays in conformity with archaeological discoveries.

Besides it is possible, that the Egyptians and Greeks used different points of the beginning of the sidereal zodiac. Then our dating can differ from the real time of fixation of the major years by a few centuries at least.

As for the 10-sectors division, it's known, that in ancient times there were no constellations of Aries and Libra: Libra was called Claws of Scorpio and was considered as part of a constellation of Scorpio, and Aries was not recognized as constellation too and was a part of constellations of Taurus and Pisces.

Thus, logical assumption in the beginning of this article about 10-sectors division of the zodiac, has found a strict mathematical confirmation in the solution of the formulated problem, and a historical confirmation in the most ancient division of a zodiac belt onto 10 constellations.

The Egyptian system of decanes is another surprising confirmation of our correctness, compare:

10 signs of 36 degrees

36 decanes of 10 degrees

Apparently, these two divisions were the fundamental basis of an ancient Egyptian astrology. We succeeded in reconstruction of the first division on the basis of system of major Egyptian years and the Egyptian terms, carefully preserved by the Greeks, and the second division has the direct historical confirmations.

Regarding the order of planets in the rulership of 10 signs of the ancient Egyptian zodiac, retrieved by the solution of the formulated problem, it strictly corresponds to the order, defined by the rays of a five-pointed star, where planets are placed in order of their cycles, and the counting starts from Saturn--the slowest planet--in the direction of lessening of cycles (see diagram).

So, the received solution is in complete accordance with the basic astrological principles, rose to us from Egypt, and is harmonically blended with the facts on ancient Egyptian astrology already known to us.

Thus, it's possible to consider the reconstruction of a calculation principle of the major Egyptian years completed.

Conclusions

Main conclusion that follows from the received reconstruction is the necessity of complete recalculation of system of major years and system of terms individually for each latitude, as the primary system was constructed for Thebes and is applicable with relatively small errors (less than 2 years) in a very narrow range of latitudes--approximately from 22° to 29° of northern latitude only.

This fact completely explains why the Egyptian system of lifetime determination doesn't work at all in the latitudes outside the mentioned interval, including Alexandria--the center of the Greek astrological school.

Other important conclusion is that the ancient Egyptian astrologers used 10 signs zodiac closely connected with system of decanes.

The third important conclusion is that the rulers of the signs of the zodiac were only the planets--wandering stars. The luminaries--Sun and Moon--apparently, took the special place in the Egyptian astrology. Probably, the stars and only the stars (wandering and fixed) were considered in charge of the destiny of the men. And Sun and Moon, most likely, were considered as setting the rhythm, measuring the time when things determined by the decree of the stars should happen.

In closing it would be useful to note, that we have found the solution for the first stage of the construction of the system of terms and we have approached to reconstruction of an ancient astrological system only by a half-step. In the further we have to do a great job on the reconstruction of the rules of determination of the order and length of terms of the planets, and also on the reconstruction of the system of decanes.