Traditional astrology chart - Online calculator

Senecar

Well-known member
I refer you to the following comments posted earlier on this thread :smile:


There are so many ayanamsa :smile:
Raman ayanamsa gets good results according to reports on other traditional threads

http://www.astrologyweekly.com/forum/showpost.php?p=828371&postcount=63
so if I may
I would request Raman ayanamsa



kaktuzz you're a star, Siriusly multiple thanks :smile:

Fagan-Bradley at 200CE 24° 44' 12"
at 1950 CE 24° 02' 28"
DELTA -00° 15' 48"
SPICA VIRGO 29° 06' 05"
ALDEBARAN TAURUS 15° 03'
GEN Sagittarius 05° 15' 48"
GC Sagittarius 02° 04'
table of the more common ayanamsas
scroll down at
http://www.lunarplanner.com/siderealastrology.html

So, Valens and earlier Hellenistic Astrologers are likely to have had used Sideral zodiac for their charts then :)
 

petosiris

Banned
Hi petosiris,
sorry for late answer.

I added Aldebaran 15 and now I'm trying to add rising times ... but I actually don't know much about rising times :innocent:

I found this page:
http://cura.free.fr/quinq/01hand.html
with a "tutorial" how to calculate rising times using R.A. (right ascension), Declination, A.D. (ascensional difference) and O.A. (oblique ascension)

Is "R.T." column what you want? Or do you need rising times in another format/another system?
There are several other systems on that cura.free.fr website and I'm not sure which one to choose.
(if "R.T." column is what you want, I could try to convert it into sidereal)

===
Coordinate Table for the Beginnings of the Tropical Signs for 40 Degrees North Latitude

270°-60° Tropical Longitude

Long. 270 | 300 | 330 | 0 | 30 | 60
R.A. 270 | 302.18 | 332.09 | 0 | 27.91 | 57.82
Decl. -23.45 | -20.16 | -11.48 | 0 | 11.48 | 20.16
A.D. -21.34 | -17.94 | -9.81 | 0 | 9.81 | 17.94
O.A. 291.35 | 320.13 | 341.9 | 0 | 18.1 | 39.88
R.T. 28.78 | 21.77 | 18.1 | 18.1 | 21.77 | 28.78


90°-240° Tropical Longitude

Long. 90 | 120 | 150 | 180 | 210 | 240
R.A. 90 | 122.18 | 152.09 | 180 | 207.91 | 237.82
Decl. 23.45 | 20.16 | 11.48 | 0 | -11.48 | -20.16
A.D. 21.34 | 17.94 | 9.81 | 0 | -9.81 | -17.94
O.A. 68.66 | 104.24 | 142.28 | 180 | 217.72 | 255.76
R.T. 35.59 | 38.04 | 37.72 | 37.72 | 38.04 | 35.59

In the table given above we have the following: The first row marked "Long." contains the tropical longitudes of the beginning of each sign. The second row marked "R.A." contains the right ascension of the beginning of each sign. The row marked "Decl." is declination of the ecliptic degree at the beginning of each sign. The row marked "A.D." contains the ascensional difference of the beginning of each sign. This will be explained shortly. The row marked "O.A." contains the oblique ascension of the beginning of each sign. This will also be explained shortly. And last the row marked "R.T." contains the rising times of the signs which begin at the designated longitude.
===

Hi, thank you for adding Aldebaran 15, I noticed you did a few days ago (while using the database), but I did not have time to write a proper thanks.

Btw, that paper is quite painful to read. If they said that the vernal equinox occurs at 8 or 10 or any other value than 1 Aries, they were for all intent and purpose - conscious sidereal astrologers. Are Ptolemy and Hephaistio unconscious tropicalists because they considered the constellations to have an effect on the sign? I do not think so, so let's be honest with each other. That article is from 1999 I believe, today there are modern scholarship statements that prove conscious siderealism which makes the statement ''An appeal to history will not work'' incorrect. The statement by Neugebauer that the tropical zodiac was not existant in Babylonia, and that Valens used that one is confirmed with more and more evidence.

It's important to note that the ancient values are primitive, inaccurate and just an estimation of the rising times. There is a difference of a few minutes to a couple degrees between the rising times of the sidereal and ''tropical'' at the time which is negligible for the errors made for every klimata at the time. The rising times were divided in a few geographic klima, which are not at all accurate for every latitude. Anyways, they were primarily used in the length of life technique where a difference of 3-5 years are not as important compared to finer and more easily calculated divisions of times.

Yes, I need the R.T. Converting tropical rising time values will not work. The rising times equal the number of right ascension degrees that pass over the horizon during the rising of every sign. I personally do not think the Babylonians used trigonometry to find out each one, they likely observed and noted the time it took for each, giving 4 minutes for every degree. So if a sign rises in 120 minutes, its rising time is 30. If it rises in 80, its rising time is 20, if in 60 - 15, if in 100 - 25, if in 103 - 25.75.

I think it will take you a lot of time and you probably have better things to do. Very few people use rising times.
 
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Purple9

Well-known member
Hi. Just found this. Love the effort!
I tried recreating my natal using the online tool here but noticed there appears to be either something wrong with my reference table of essential dignities (Ptolemy) or the tool. I did not go through all obviously :) , but my Sun at 23 deg 22 Gemini is on Saturn term according to the table. However in the chart I did there it is on Mars term. The other placement terms correspond to the reference table. Any thoughts? Thanks
 

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petosiris

Banned
Hi. Just found this. Love the effort!
I tried recreating my natal using the online tool here but noticed there appears to be either something wrong with my reference table of essential dignities (Ptolemy) or the tool. I did not go through all obviously :) , but my Sun at 23 deg 22 Gemini is on Saturn term according to the table. However in the chart I did there it is on Mars term. The other placement terms correspond to the reference table. Any thoughts? Thanks

One table uses ordinal numbers. So Jupiter having 6 degrees means that 0 - 5 59' is the bound of Jupiter in Aries.
 

Purple9

Well-known member
One table uses ordinal numbers. So Jupiter having 6 degrees means that 0 - 5 59' is the bound of Jupiter in Aries.

I think that does not explain the case. Gemini at 23 deg 22 is not bordering the edge of a bound. According to the table attached, Saturn holds up to 25th degree, which would then be 24'59", right?

Or did I misunderstand what you meant?
 

petosiris

Banned
I think that does not explain the case. Gemini at 23 deg 22 is not bordering the edge of a bound. According to the table attached, Saturn holds up to 25th degree, which would then be 24'59", right?

Or did I misunderstand what you meant?

Ah, yes, sorry. Did not see you used Ptolemy's terms. You are correct, there is an error in one of the two. Still, I would seriously reconsider your choice, as of the dozens of unearthed Hellenistic charts in Oxyrhynchus and literary horoscopes reported by Neugebauer, all use the Egyptian bounds, but at the end of the day, it is your choice.

Edit: I checked Valens software and the Tetrabiblos, and I think kaktuzz has got them right and the table you send is wrong according to the values given by Ptolemy in the ''ancient manuscript he found''.

See - http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Ptolemy/Tetrabiblos/1B*.html#20
 
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Purple9

Well-known member
Ah, yes, sorry. Did not see you used Ptolemy's terms. You are correct, there is an error in one of the two. Still, I would seriously reconsider your choice, as of the dozens of unearthed Hellenistic charts in Oxyrhynchus and literary horoscopes reported by Neugebauer, all use the Egyptian bounds, but at the end of the day, it is your choice.

Edit: I checked Valens software and the Tetrabiblos, and I think kaktuzz has got them right and the table you send is wrong according to the values given by Ptolemy in the ''ancient manuscript he found''.

Thank you so much for taking the trouble to check. And for the advice. I did not actually settle on any at this time. I was 'using' Ptolemy's for ease as I had neater notes :) just for practicing the techniques. Interestingly, the table I use is one that I kept coming across everywhere so it is quite widespread. Which is in itself annoying if indeed it is inaccurate. Ugh. Thanks again!
 

kaktuzz

Well-known member
Hi. Just found this. Love the effort!
I tried recreating my natal using the online tool here but noticed there appears to be either something wrong with my reference table of essential dignities (Ptolemy) or the tool. I did not go through all obviously :) , but my Sun at 23 deg 22 Gemini is on Saturn term according to the table. However in the chart I did there it is on Mars term. The other placement terms correspond to the reference table. Any thoughts? Thanks

Hi Purple9, I also found that table of Ptolemy terms (you posted) and was confused about that :eek:
But, finally, I rather set the terms according to Morinus software and the table I found at http://www.medievalastrologyguide.com/dignities.html
 

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kaktuzz

Well-known member
Hello,

I adeed some new features in traditional astrology calculator :)

1) Secondary house system
Chart can be displayed in two different house systems simultaneously

2) Custom Ayanamsa

  • A) Ayanamsa of your own choice
  • - this option overrides other settings and set this Ayanamsa manually (independently on the date of birth)

  • B) +-Offset from another Ayanamsa
  • - this option can be used to set slightly offset from another chosen listed Ayanamsa (Lahiri, Raman, KP, Fagan-Bradley etc...)
 

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petosiris

Banned
Hello,

I adeed some new features in traditional astrology calculator :)

1) Secondary house system
Chart can be displayed in two different house systems simultaneously

2) Custom Ayanamsa

  • A) Ayanamsa of your own choice
  • - this option overrides other settings and set this Ayanamsa manually (independently on the date of birth)

  • B) +-Offset from another Ayanamsa
  • - this option can be used to set slightly offset from another chosen listed Ayanamsa (Lahiri, Raman, KP, Fagan-Bradley etc...)

They are like Arabic Parts at the time of Al-Biruni now. They multiply daily.

Wanted to say to keep up the good work.

Are you interested in adding cookbook delineations at some point?
 
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kaktuzz

Well-known member
Are you interested in adding cookbook delineations at some point?

Hello petosiris,
I would like to add some cookbook delineations, but I'm not able to write it on my own. I'm always struggling with every sentence I have to write (+English is not my native language) = it's quite impossible task for me :alien: ...

... however if there is any chance (?)to use any delineations written by somebody else(?) (open licensed, /or with author's agreement), I would be happy to add it :)
 

JUPITERASC

Well-known member
Hello petosiris,
I would like to add some cookbook delineations, but I'm not able to write it on my own. I'm always struggling with every sentence I have to write (+English is not my native language) = it's quite impossible task for me :alien: ...

... however if there is any chance (?)to use any delineations written by somebody else(?) (open licensed, /or with author's agreement), I would be happy to add it
:)
petosiris is likely to have had some cookbook delineations in mind
meanwhile I recommend Vettius Valens THE ANTHOLOGY
free online in pdf form
translated from the original Ancient Greek by Professor Mark T Riley CSU

http://www.csus.edu/indiv/r/rileymt/vettius%20valens%20entire.pdf

Professor Riley has said he offers it free to copy and circulate
as long as he is acknowledged as the source of the translation
other than that THE ANTHOLOGY itself is out of copyright
having been written almost two thousand years ago

If you scroll down the free pdf I have linked to until you get to page seventeen
you shall view multiple examples - these are just a few:

21K;19P. THE COMBINATIONS OF THE STARS
Let us append the associations and combinations of each star.
When Saturn and Jupiter are together, they are in agreement with each other
and they
bring about benefits from legacies and adoptions
and they cause men to be masters of property consisting of land
to be guardians, managers of others’ property
stewards, and tax gatherers.


Saturn and Mars are hostile, productive of reversals and ruin.
They bring family quarrels, disharmony, and hatred
along with treachery, plots , malevolence, and trials .
However, if these stars are not in their own or in operative signs
and if they have benefics in aspect, they produce distinguished
and noble nativities, although unsteady in their happiness
and prone to unexpected dangers and treachery.

/37P/
Saturn and Mercury are allies
and productive of activities/employment.
They do, however,
bring slanders about religion, lawsuits
and debts, as well as disturbances about written matters and

money.
On the other hand, these stars make men who are not without resources
and not unintelligent, with much experience and awareness
and who are curious, far-seeing scholars, seekers after mystic lore
revering the gods, but with much on their consciences.
 

petosiris

Banned
Hello petosiris,
I would like to add some cookbook delineations, but I'm not able to write it on my own. I'm always struggling with every sentence I have to write (+English is not my native language) = it's quite impossible task for me :alien: ...

... however if there is any chance (?)to use any delineations written by somebody else(?) (open licensed, /or with author's agreement), I would be happy to add it :)

Where and how do you intend to put the delineations? Do you want a small text or an elaborate description?

The Sun - Light, Beauty, Mind, Might, Reputation, Success, Action, Fire, Authority, Judgement, Motion, Friendship, Father, Public Matters, Rank, Intelligence, Honors, Bright, Manly Eyes, Fine Figure, Youthful, Walking, Insightful, Truthful, Leading, Inventive, Secure, Kingship, High Priesthood, Leadership, Notable Figures, Harvest, Circulatory System, Nervous System, Right Eye, Gold, Yellow Colour, Bitter Taste, Anahata, Tiphareth.

Leo - Masculine, Royal, Solid, Distinguished, Independent, Reliable, Just, Despising Flattery, Haughty, Irascible, Terrestrial, Daring, Fine Face, Smooth, Small Ears, Higher Upper Part, ThinSet Teeth, Rugged, Flushy, Bright.
Leo - Action, Reputation, Superiors, Harsh Matters, Quarrels

In text:

The Sun is the light and fire of the universe, beauty, mind (and nous), might, reputation, success and action. It signifies authority, judgement, motion, friendship, the father, public matters, rank, intelligence and honor. Men born under the influence of the Sun are bright, with a fine figure and manly eyes, youthful, given to walking, insightful and given to premonitions, truthful, inventive (in the big five sense - open to experience) and secure (in the big five sense - not neurotic). It also signifies the King, the High Priesthood, leadership, notable figures and harvest. In iatromathematics, it signifies the circulatory system, the nervous system and the eyesight (the right eye in particular). It signifies gold, yellow colour, bitter taste, the Chakra Anahata and the Sephiroth Tiphareth.

The Lion is a masculine image, royal (I do not use triplicities, but you can add fiery) and solid (fixed). Depending on the placement of the ruler, men born under the influence of Leo are distinguished, independent, reliable, just, despising flattery, haughty, irascible. They are with fine face, smooth, with small ears because they rarely listen to others, the upper part of the body is higher than the lower, their teeth are thin-set, they are bright, flushy and rugged in manner. The image is terrestrial, quadrupedal, vocal and semi-infertile. It signifies wild beasts. It is of the north wind, its number is 30 and letter is ל.
In initiations (questions and elections), when rising or culminating, it signifies action (occupation), reputation, superiors, harsh matters and quarrels (I think I used the Yavanajataka and Zoroaster for this is used not as interpretative principle, but as a thought reading one).

Do you like those? Would you prefer:
Leo - masculine gender, fiery and north triplicity, fixed quadruplicity, royal, terrestrial, quadrupedal, vocal, semi-infertile
Physical Appearance - fine face, smooth, small ears (because they rarely listen to others), the upper part of the body is higher than the lower, thin-set teeth.
Mental Appearance - distinguished, independent, reliable, just, despising flattery, haughty, irascible, bright, flushy and rugged in manner (according to physiognomy, physical and mental appearance are always similar).
Other Significations - action, occupation, reputation, superiors, harsh matters, quarrels and wild beasts.

For Leo, there is change between the degrees. I have keywords for the bounds, where I have highly modified Valens and Critodemus:
The first 6° belong to Jupiter - Elevated, Good, Active - Heart
The next 5° belong to Venus - Advancing, Wealthy, Active - Mane
The next 7° belong to Saturn - Accused, Wandering, Burdened - Belly
The next 6° belong to Mercury - Intelligent, Playful, Popular - Back
The final 6° belong to Mars - Injured, Burdened, Passionate - Tail

The Sun is also heating and slightly drying (according to Ptolemy and I agree). It rules day.
 
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kaktuzz

Well-known member
Where and how do you intend to put the delineations? Do you want a small text or an elaborate description?

Hello petosiris,
thanks for reply.

Please check this "modern astrology" natal chart at astro-seek:
https://horoscopes.astro-seek.com/birth-chart-horoscope-online

I made this cookbook template for each planet:

1) main keywords about that planet
2) short description about that planet
3) short desription of planet in sign
4) short desription of planet in the house
5) aspects to other planets
...
6) short desriptions of aspects


I think that descriptions (you sent) would fit it in this template quite well ... and I can modify this template to fit traditional astrology better:
- put away what shouldn't be there;
- add new things which could/should be there;

So I would also appreciate any ideas/suggestions about "how this TA cookbook template could look like" ... and I will gladly try to modify it (if it will be technically possible :)).
 

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kaktuzz

Well-known member
petosiris is likely to have had some cookbook delineations in mind
meanwhile I recommend Vettius Valens THE ANTHOLOGY
free online in pdf form
translated from the original Ancient Greek by Professor Mark T Riley CSU

http://www.csus.edu/indiv/r/rileymt/vettius%20valens%20entire.pdf

Professor Riley has said he offers it free to copy and circulate
as long as he is acknowledged as the source of the translation
other than that THE ANTHOLOGY itself is out of copyright
having been written almost two thousand years ago

If you scroll down the free pdf I have linked to until you get to page seventeen
you shall view multiple examples - these are just a few:

21K;19P. THE COMBINATIONS OF THE STARS
Let us append the associations and combinations of each star.
When Saturn and Jupiter are together, they are in agreement with each other
and they
bring about benefits from legacies and adoptions
and they cause men to be masters of property consisting of land
to be guardians, managers of others’ property
stewards, and tax gatherers.


Saturn and Mars are hostile, productive of reversals and ruin.
They bring family quarrels, disharmony, and hatred
along with treachery, plots , malevolence, and trials .
However, if these stars are not in their own or in operative signs
and if they have benefics in aspect, they produce distinguished
and noble nativities, although unsteady in their happiness
and prone to unexpected dangers and treachery.

/37P/
Saturn and Mercury are allies
and productive of activities/employment.
They do, however,
bring slanders about religion, lawsuits
and debts, as well as disturbances about written matters and

money.
On the other hand, these stars make men who are not without resources
and not unintelligent, with much experience and awareness
and who are curious, far-seeing scholars, seekers after mystic lore
revering the gods, but with much on their consciences.

Hello JUPITERASC, thanks for info.

It's great there are people like professor Riley offering his translations under these conditions.
 

JUPITERASC

Well-known member
Hello JUPITERASC, thanks for info.

It's great there are people like professor Riley
offering his translations under these conditions.
Vettius Valens THE ANTHOLOGY
free online in pdf form
translated from the original Ancient Greek by Professor Mark T Riley CSU

http://www.csus.edu/indiv/r/rileymt/...s%20entire.pdf


Classics Scholar Robert Schmidt of PROJECT HINDSIGHT
began translating THE ANTHOLOGY for his wife who has an interest in astrology
Schmidt however has written detailed footnotes to Valens :smile:
so his translations are not cheap
whereas
Professor Mark T Riley randomly translated Valens
because of his interest in the mathematical content
of THE ANTHOLOGY by Vettius Valens
Rileys translation was intended for his students at CSU
he gave it away freely then after he realised it would be helpful
for those who cannot afford PROJECT HINDSIGHT translations
which by the way are excellent also and available at
http://www.projecthindsight.com/index1.html
 

petosiris

Banned
Hello petosiris,
thanks for reply.

Please check this "modern astrology" natal chart at astro-seek:
https://horoscopes.astro-seek.com/birth-chart-horoscope-online

I made this cookbook template for each planet:

1) main keywords about that planet
2) short description about that planet
3) short desription of planet in sign
4) short desription of planet in the house
5) aspects to other planets
...
6) short desriptions of aspects


I think that descriptions (you sent) would fit it in this template quite well ... and I can modify this template to fit traditional astrology better:
- put away what shouldn't be there;
- add new things which could/should be there;

So I would also appreciate any ideas/suggestions about "how this TA cookbook template could look like" ... and I will gladly try to modify it (if it will be technically possible :)).

If you use seven planets, you need bigger orbs. I use whole sign configurations, but not every traditional astrologer does that. Also most description of planets in signs and houses are very short, for example Saturn in XI according to Abu Ali signifies ''anxiety and pain from friends, hindrance of things wished for.'' - translation from James Holden. I wonder if you are ok with a sentence for placement by sign and by house, because that is all I can offer either. So for example:

1) The Sun - Light, Reputation, Father
2) The Sun is the light and fire of the universe, beauty, mind, might, reputation, success and action. It signifies authority, judgement, motion, friendship, the father, public matters, rank, intelligence and honor. Men born under the influence of the Sun are bright, with a fine figure and manly eyes, youthful, given to walking, insightful and given to premonitions, truthful, inventive and secure. It also signifies the King, the High Priesthood, leadership, notable figures and harvest. In medical astrology, it signifies the circulatory system, the nervous system, the eyesight and the right eye in particular. It signifies gold, yellow colour, bitter taste, the Chakra Anahata and the Sephiroth Tiphareth.
3) Sun in Capricorn - bold, boastful, spendthrift, ambitious and it signifies an infirmity for the father.
4) Sun in the bound of Saturn - vicissitudes, burdened, difficult, wealth and it signifies an infirmity for the father. (it would be more correct to say if it rules the Lot of the Father or if the Lot of the Father is poorly placed, otherwise everyone born in the same month will have an injured father)
5) Sun in the 4th House - discovery of buried treasures, revelation of secret and hidden things and arts, praise, dignity.
6) Conjunction with Jupiter
7) The Sun with Jupiter in the same sign signify vigor, wealth and eminence, but also uncertainty, pretentiousness and hostility, especially if Jupiter happens to be setting under the beams.

Using this cookbook model we can't place the properties of the signs.

Edit: What about the following:
1) Description of the Planet
2) Description of the Sign (it is not very long and the user can add interpretation himself)
3) Placement by sign (and bound?)
4) Placement by house
5) Aspects by Whole Signs or using Orbs - http://www.skyscript.co.uk/gl/moiety.html, although I personally prefer aspects by signs, the approach of orbs developed in the mid-late Middle Ages. Out-of-sign aspects also begin to appear for the first time in the works of Abraham ibn Ezra, so they are ''traditional'' you can argue. I imagine you do not have whole sign aspects coded? I've seen other software do it by using a 30 degree orb while toggling of out-of-sign aspects.
...
6) Cookbook aspects.

Thus a person can synthesize 1) and 2) depending on the placement for which we can't account, while the average and estimated result will be in cookbook 3), 4), 5) and 6)
 
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petosiris

Banned
Let's give an example with the Moon at 5th degree Scorpio in the VI house.

The Moon is light, life, body, knowledge, appearance, direction, outcome (fortune/luck). It signifies water, possessions, gathering, cohabitation, the mother, the household, affluence, nourishment, conception, travel and wandering, because the Crab does not walk straight. Men born under the influence of the Moon are white (those are written with the ancient Greek in mind, some Arabic astrologers used more planets as indicating darker skins, but I think the Moon was not one of them), with beautiful eyes, with a fine figure, thick legs, wide body, rough, truthful, accepted, changeable, if poorly placed - sensitive. It also signifies the King, the High Priesthood, the city, assemblies and ships (vehicles like cars today). In medical astrology, it signifies the respiratory system, the upper gastrointestinal tract, the eyesight and the left eye in particular. It signifies silver, green colour, salty taste, the chakra Muladhara and sephiroth Yesod (you can remove the chakras, but please keep the traditional Sephirah). It is moistening and slightly heating. It also signifies affairs and messengers.

Scorpio is a feminine, prolific, solid (fixed), terrestrial, fertile, passionate and silent (mute) sign of the east wind (''watery'' triplicity). Depending on the placement of the ruler men born under this sign are tricky, turbulent, base, covetous, lying, bitter, competitive, powerful, with short head, delicate voice, round light green eyes, sharp nose, lower lip bent, coarse hair and dark skinned. It also signifies inquiries, fights, deception, lawsuits, mysticism, reptiles, expectations of something good and the anchor of the ship.

The Moon in the degrees of Mars depending on the placement of the ruler signify inquisitive, challenging and bold individuals, injury, or it signifies infirmity or weakness of the mother. The Mars bound of Scorpio signifies accusations, burden, but also benefits from travel.

The Moon in the VI house signifies an injury or weakness of the native or his mother. (according to Abu Ali - ''profit from animals'', as the VI house signifies quadrupeds and slaves according to the early astrologers, so a lot of ancient astrologers would say that the native or the mother is low-born, not sure how much the animals is applicable today for 1/12 of the population)

Moon conjunct Venus
Moon conjunct Saturn
...

Venus and the Moon are harmonious and together they signify rank and wealth, but also with unsteady friendships and affairs.
Saturn and the Moon are inharmonious and together they signify anxiety, infirmities, but also benefits from property, ships and the deceased (like inheritances).

Those do not account for the inoperative placement of the stars, so Venus and the Moon will not promise rank and wealth, nor will Saturn signify much benefit from property and inheritances. If you have an idea that will account for angularity, it will be great.
 
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