Affichage des articles dont le libellé est complex disease. Afficher tous les articles
Affichage des articles dont le libellé est complex disease. Afficher tous les articles

dimanche 25 août 2024

Alan LEO

 LEO Alan [William Frederick Allan]


British astrologer, businessman and author, a Theosophist who is considered the father of modern astrology. Leo wrote a series of astrological text-books, founded a successful astrology magazine, and established an organisation that remains vibrant some 90 years later. He shifted the focus of astrological work from prediction to personal analysis and is responsible for articulating the popular astrological precept that “character is destiny”.
[https://www.astro.com/astro-databank/Leo,_Alan]
Alan Leo, born William Frederick Allan, (7 August 1860 – 30 August 1917) was an English astrologer, author, publisher, astrological data collector and theosophist. He is often referred to as "the father of modern astrology"
[https://en.wikipedia.org/wiki/Alan_Leo]

source : "The Life and Work of Alan Leo" by his widow Bessie Leo (London: Modern Astrology, 1919), p. 177: "Alan Leo was born at Westminster on August 7, 1860, and Mr Lacey has mentioned that the time originally given was 6 a.m."
This hour was rectified by Alan Leo at 5:49 am. We will use the un-rectified time. Note also that it seems unlikely that the LMT was already used at the time (it was used officially from 1880 in the United Kingdom and for the very first time the Greenwich Time on January 29, 1948, cf. Leo Alan, 'Casting the Horoscope', note 1, p. 43, 1933).
Mr Leo's wife wrote his biography until his last moments. It is not easy to know what has died her husband: it is quite possible that he presented a septicaemia, perhaps in relation to an inflammation of the bile ducts, accompanied by convulsive phenomena in relation to the fever. At that time, angiocholitis or cholecystitis was practically equivalent to a death stop in the absence of antibiotics ...

THEME  (rectified by Alan LEO at 5.49 a.m., originally 6 a.m.)

The horoscope of Alan LEO, 'The Life and Work of Alan Leo, p. 175, Bessie LEO, London : "Modern Astrology" Office, 1919


THEMA at original hour transformed from LAT to LMC (6.05 a.m.)



--------------------------------------------------

HYLEG – ALCHOCODEN – domification ,

We will first look for the somatic factors of the theme: hyleg and alchocoden. We see that MO is in X, well positioned in TAU (Exaltation) in a tropical zodiac. In the sidereal zodiac, it is in ARI (Peregrine). In global position, SA is in TRI aspect with MO and in dignity of TERM. In this occurrence, MO is HYLEG and SA is ALCHOCODEN. In zodiac position, JU is in TRI aspect with MO but has no dignity. The scope of this information depends on whether or not MO is hyleg and alchocoden at the same time because MO is in TAU. According to tradition, when the hyleg is SU or MO and does not have an aspect with another planet, this is the case. So it seems that here MO cannot be considered both hyleg and alchocoden.
In the upper chart we see that the nativity is diurnal (or nocturnal) and the moon is waxing (waning). This immediately makes it possible to orient the search for the hyleg towards SU or MO. We then seek the point which is both in Ptolemaic aspect and in dignity with the hyleg. This is the alchocoden. In the lower table, information is given on the alchocoden point (including dignity, power, retrograde, the house situation and especially the important fact of knowing if the alchocoden point is within 5° of the next cusp, in which case it must be removed (or added if he is retrograde) a certain number of degrees (life points).Finally, it may be necessary to add points depending on the place of JU and VE in relation to the upper meridian or the rising.

ZODIACAL – MUNDANE

In our research, we hypothesised that the mundane chart alone should be considered; also we must base on the aspects taken in the semiarcs the research of the degrees likely to be considered in the duration of the life.
In the case of LEO Alan we have the table above which allows us to estimate the breakdown of aspects between the different planets and the alchocoden.
When considering a theme, the first thing is to observe whether it is diurnal or nocturnal. In the case of LEO Alan, it is DIURNAL.
In this case, the first point to check is SU. If  SU is well disposed, it can claim 1st stage to be HYLEG.

SU is Ru and therefore seems strong, with a dignity score of [4],
Moreover, when we look for the dignities that appear in the zodiacal inscription of SU, we find at least one
we find at least one aspect to match with the dignities
We'll see later what we get when we search for mundane dignities.
So : the hyleg is SU as dignity is Ru and aspect is conjunction

Now we must look for the alchocoden: it is the planet which has the maximum dignity with regard to the hyleg and which exchanges a Ptolemaic aspect with the hyleg.
if we consider the MUNDANE system, we observe a conjunction aspect of SU.
At the same time, it appears that SU has  dignity of RUL over POF.
So we have two possibilities with our hypothesis : first choose SU for hyleg ; second choose the MUNDANE system and try to find another couple of hyleg/alchocoden,
If we choose now SU we must know that no trad authority agree with this choice
In case of SU is the Hyleg, there is then one candidate to be the alchocoden: SU
First, we have to see which candidate has the most dignity: here, SU has candidate alcho dignities referring to SU : [RUL]
First, SU is linked with SU by a [conjunction] aspect and a [RUL] dignity,
However, SU is [Ru] and has a power of [4], and so SU has a good Kadkhudah score of [1]
SU is located at 134,89° at more than 5° from [Δ degrees cups sup [XII] : 9,83° (330)] and has a domitude Regio of : [339,83] for a latitude of [0°]
Now, we have to take account of the radix zodiacal aspects.

We have a stellium in XII (♌in tropical)
------------------------------------------------------
STELLIUM
SU/ ME   JU SA
------------------------------------------------------

rank Trad power dignity rank Lilly power dignity








1 SU 4,00 Ru 3 SA 14 D
2 MA 2,00 E 2 MA 4 E
3 SA -6,00 D 1 SU 1 Ru
4 MO -7,00 P 4 MO -6 P
5 JU -11,00 P cb 5 JU -11 P cb
6 VE -13,00 P 6 VE -13 P
7 ME -17,00 te cb 7 ME -21 te cb


We see that in 'Trad' mod, SU has a power of 4 and that with 'Lilly' mod, power is only 1, in contradiction with its ruler dignity.
Almuten Lilly is SA and we have 3 planets retrograde : MA, VE and ME.

SU is Ru with a [7] score - house rgo 12
MO is P with a [-9] score - house rgo 9
ME is te cb with a [-11] score - house rgo 12
VE is P and retrograde with a [-20] score - house rgo 11
JU is P cb with a [-16] score - house rgo 5
MA is E with a [3] score - house rgo 12
SA is D with a [-16] score - house rgo 12

points to specially watch for the duration of life: 0 in house VI ; SU ME in house XII
no point
we see below the list of  aspects :
---------------------------------------
                  MO[0 Or 90]JU    
Algol (𝛃 Persei) domitude regio 268.8 ☌ MC                   
---------------------------------------

The traditional almuten (Omar, Ibn Ezra) is SU
we see below the list of dignities for SU :
---------------------------------------
[ term 0 tri 4 rul 3 exn 1 fac 0 ]
[ su 2 mo 2 asc 2 syg 0 pof 0 ]
---------------------------------------
Note 1 : the ‘almuten figuris’ is the lord of the chart, but its determination obeys somewhat different rules according to the schools. The tradition is based above all on the zodiacal dignities. (see p,e,  Alcabitius, Introduction, 59-61, 117 and Avenezra, Nativites, 101) – almuten = al-mu’tazz (arabic term)
[7] As for the governor which is the <planet> predominating (al-mubtazz) over the birth from which one indicates the conditions of the native after the haylāğ and the kadhudāh,n it is the planet having the most leadership in the ascendant, the position<s> of the two luminaries, the position of the Lot of Fortune and the position of the degree of the conjunction or opposition which precedes the birth. When a planet has mastery over two, three or four positions by the abundance of its shares in them, it is the governor and the predominant <planet> (al-mubtazz) and the indicator after the haylāğ and the kadhudāh. From it one indicates the conditions of the native. Some people use it instead of the kadhudāh in giving life.  [Al-Qabisi , Charles Burnett, Keji Yamamoto, Michio Yano, The Introduction to Astrology, IV, 7, p, 117, Warburg, 2004]
Note 2 : There are at least 4 systems for determining the almuten depending on whether the combinations of triplicities and terms are used: the Ptolemaic almuten (followed by Lilly) with Ptolemaic terms ; the same with Egyptian terms; the almuten of Dorotheus with Ptolemaic terms ; the same with Egyptian terms, knowing that one can embellish the whole thing with different weighting system (like Lilly or not using weights like Montanus) [cf. Temperament: Astrology's Forgotten Key, p. 79, Dorian Gieseler Greenbaum 2005]

The Lilly (Ptolemaïc) almuten is SA

In our experience, it seems that Ptolemy's almuten allows one to first appreciate the static side of the natal chart and that the Lilly-type elaboration allows one to deepen the more ‘temporary’ or ‘dynamic ‘ relationships (cf, Shlomo Sela, Ibn Ezra, on Nativities and Continuous Horoscopy, appendix 6, quot 2  ; Horary astrology p, 458, Brill, 2014)
---------------------------------------
Ω  12,94 /
---------------------------------------
the lot of Fortune has been computed according to Placidus's revised method (see 'Primary directions', A primer of calculation by Bob Makransky, 1988, cap X: the Arabian parts, pp. 98-103; see also Mario Fumagalli,  'Il calcolo delle sorti secondo Placido', Linguaggio Astrale 103, June 1996 and 'La sorte oraria, il vero oroscopo lunare.' (Phôs 2, giugno 2001) and Placidus, Coelestis philosophiae, 1675, Brunacci and Onorati ; see finally the english traduction of Placidus, Primum mobile, John Cooper, 1814, Canon of the Part of Fortune, pp, 308-318) ; help will be found also from: : Sepharial, directional astrology, cap XII, the part of fortune, pp, 81-85, 1921 and Oxley Thomas, The Gem of Astral Sciences, cap VII, of the part of fortune or lunar horoscope, pp,45 - 48, 1848) [Placidus : 40,53° ♉]

PRIMARY DIRECTIONS

1)- at death 30 AUGUST 1917


a)- directio conversa in mundo [C] ☌☉ ◻♂



speculum Lat Dec AR MD SA HA
SU - 16,38 N 137,36 89,87 N 68,31 N -21,56 W
□MA 1,4 N 1,07 N 177,53 49,71 N 88,65 N 38,94 W

 MD = meridian distance (from MC if SA f [SU]  is diurnal or IC if Sa f  is nocturnal)
– SA = semi-arc (if f is diurnal, SA f [SU] is D and all MD’s and SA’s are D, otherwise N
– HA = horizontal distance (from the nearest horizon W or E for f [SU] and m □MA)
under bracket [] the fixed point, (here SU)
- Lat □MA 1,4 N and lat MA : -6° 13' 30"

DP REGIOMONTANUS (5)

DP REGIO-CAMPA D
DP REGIO-CAMPA C
DIRECTIO CONVERSA A2 □MA A1 SU A1 SU A2 □MA A2 □MA A1 SU
Tan A tan dec/cos dm
90,43
1,65
B (1) +LG-A or -LG+A
38,93
53,15
Tan C cot DM.cos B/cos A
-167,00
26,96
Sin pole (2) Cos C.sin LG
-49,69
44,23
Sin DA (3) Tan pole A1.Tan Dec A2
Tan pole A2. Tan Dec A1
DAP (6) -20,27 -1,26 1,04 16,63
AO (4) AR ± DA
117,09 176,27 176,49 120,73
arc AO1 – AO2

-59,18
55,75




DIRECT
CONVERS

(1) B must be treated as positive number
(2) sign of pole has the same sens of LG for DA Here, DA = DA/pole A
(3) sign [-] if pole and Dec have the opposite sign – sign [+] if planet located in western half, sign [-] if planet located in eastern half ; Signs [+] and [-] must be reversed for births in the southern hemisphere
(4) to find AO of a star A2 under the pole of A1, we calculate the  DA of A2 under the pole A1 ex: tan pôleA1.tan DecA2=sin DA A2/poleA1
(5) algorithm from : a)- Gouchon (‘Dictionnaire astrologique’, Dervy, 1946, 1975, p, 276, attributed to H. Selva) ; b)- Martin Gansten (‘Primary directions’, pp, 155-157, 2009, Wessex Astrologer) - instructions for use only appear in Gansten – c)- Astrologia gallica, Morin de Villefranche, trad Holden (appendix 5, pp, 151-153)  
(6) ascensional difference under own pole

ARC CONVERS ARC DIRECT
Y 55,75 Δ = 3,74 Y 59,2 Δ = -0,3
BRAHE : 0° 57' 32" BRAHE : 0° 57' 32"
key convert 1,043 key convert 1,043

DP PLACIDUS Plac direct Plac conv
sa1/dm1 1,78 1,24
sa2 68,31 91,35
x 38,30 73,72
dm² 89,87 130,29
sign -1 -1



arc 51,57 56,57

 FOMALHAUT-CHOISNARD
X = sa2.dm1/sa1 = and the angle x = SAm x DM f/SA f, so : SA m [68,31°] x DM f [49,71°]/SA f [ 88,65°]
sign : if the two points are on either side of the meridian, take +1 ; otherwise -1
Arc = dm2 ± sign.x We find the direction by DMm - x, so : DM m [49,71°] ± x [38,3]

precision direct convers
REGIO -3,74 -0,32
PLAC -7,92 -2,92

b)- directio directa : ◻♂ ☌⊕ (POF)

We have noted above how weak the SU radix was in XII. However, its position in tropical LEO (traditional even if it is appropriate to imagine its real place in VIR) imposes it in RULER and as such gives it the dignity of HYLEG. However, it appears that the POF can also play the role of HYLEG in this theme (the alchocoden then being ME, in XII under the dignity of TERM).
Let us first return to the determination of the POF. The traditional calculation (i.e. since Ptolemy) had been imposed until Placidus by:

"The part of fortune must be calculated, both day and night, by counting the number of degrees separating the Sun from the Moon, and by reporting this same distance from the horoscope in the direction of the signs, in such a way that the ratio and configuration of the Sun with respect to the horoscope are also those of the Moon with respect to the part of fortune, the latter appearing as a lunar horoscope" (Tetr. III, 11)

'The formula for composing a lot, which is usually expressed algebraically in modern times,
starts with the longitude of the ascendant (A) which is then added to the longitude of a planet (B), and
then the longitude of a second planet (C) is subtracted from that number in order to determine the
specific position of the lot in the chart. Thus the general algebraic formula looks like this:
Lot = A + B – C
While this is the most precise method for calculating the lots, it is not necessarily the most conceptually
satisfying, nor is it the way in which the lot calculations were actually presented in the texts of the
Hellenistic and Medieval astrologers themselves.'
[cf. Chris Brennan, The Theoretical Rationale Underlying the Seven Hermetic Lots, Tradition journal, issue 2, spring 2009, available online at http://thetraditionjournal.com.]

The arc is determined from the sect luminary – the Sun by day and the Moon by night.

POF  = Asc + Moon – Sun (D) or Asc + Sun – Moon (N)

and these arcs are taken in longitude. Let us now read Placidus in Primum Mobile :

'This man [Negusantius] subscribes to the truth of every thing I lately mentioned in my Celestial Philosophy, wherein I said, that the moves upon the orbit or way of the's latitude, and, therefore, not in the ecliptic. But as I have shown that the distances and rays to the angles are, by no means, made in the zodiac, but upon the parallel of every star, he argues, and, indeed, very ingeniously, that the , in like manner, is elongated from the East, viz. upon his parallel; and, also, the , who has not by any other method nor way different than when the  is in the horizon, by her real presence, posited the place of   ; for no other fundamental principle is seen to constitute this part in nature, unless by such an assignation and impression of virtue, exhibited by the , at  rise. When this learned man adds, “ For when the  comes to the Cardinal Sign of the East, then it is necessary the  be found in its horizon ; afterwards, in an equal space of time, the  digressing, he is removed from it according to his ascension ;" wherefore, if we study the matter with accuracy, we shall find that, entirely in the same manner as the  departs from the East, the  is likewise separated from the  that is, both upon their parallels, so that as many degrees as the , in his parallel circle, is elongated from the East, so many is the  in her parallel, distant from the  : whence it follows, that the true place of  does not always remain in the zodiac, but always under the ’s parallel circle, that is, with the  ’s declination. the same both in number and name, and, therefore, the  does not receive any aspects from the stars in the zodiac, but only in mundo. We may make a calculation of the  several ways, but it will be shorter, as well as easier, if, in the diurnal geniture, the ’s true distance from the East is added: to the ’s right ascension, and, in the nocturnal, subtracted, for the number thence arising will be the place and right ascension of  : and it always has the same declination with the , both in number and name, wherever it is found. Again, let the ’s oblique ascension, taken in the ascendant, be subtracted always from the oblique ascension of the ascendant, as well in the day as in the night, and the remaining difference be added to the ☽'s right ascension, the sum will be the right ascension of  , which will have the ☽'s declination." [Canon de Parte Fortunae, pp. 409-413, Tabulae Primi mobilis..., Placido de Titis, Patavii, MDCLVII ; Primum mobile, trad John Cooper, pp. 308-316, London, 1814]

Add to this that the cannot be directed in converse movement in the world because it does not participate in the universal movement of the Primum Mobile, nor in the aspects of the zodiac in direct or converse direction.

To calculate according to Placidus (corrected by Negusantius and Fumagalli), we must first determine the horary distance of : to do this, we must first know in which quadrant the is located: we will have its position in quadrant by calculating the difference between its oblique ascension (ao) and its right ascension (ar):

ao = ao asc (137.23) + oa MO (-0.75) - oa SU (115.67) = 20.8
and ar = oa asc (137.23) + ra MO (14.06) - ra SU (137.36) =  35.62
and hd  = oa ASC (137.23) - oa (20.8) = -116.43

which gives
upper md = ra MC - ra = 11.62.

So we know that the is in IX (according to Gansten, see Primary directions, calculating the Placidean part of fortune, pp. 158-160, the Wessex astrologer, 2009). But we have another simpler method to determine that is in quadrant 2 : it is to compute with the traditional method and we find =  32.26° ♉ (even though we now know that this purely ecliptic value is wrong.)

Let us now calculate th(temporary hour) in order to determine the horary distance (hd) of :
th = th MO = 17.47
Now, the hd = upper md/TH = 0.665

We have now to compute the pole of POF (recall : in the Placidean method, we use the MO da and the MO dec) :

tan pole = sin(1/6*HD pof*DA MO)*cot(DEC MO)
pole =  8.02 

Now we compute the oblique descension under the own pole of (the DOCH of italian astrologers, see Fumagalli and Il Calcolo delle coordinate dei Cardini e degli astri di nascita, introduzione alle Tavola del Primo Mobile.pdf) :

doch (pof) = ra mc - 15 x dh = 47.23 - 15*0.665 = 37.25

tang (𝛝) = sin(doch)/(cos(doch)*cos(𝛜) ± sin(𝛜)*tan(pole)
         𝛝   = 40.31 ° ♉

speculum Lat Dec AR MD SA HA
MO 5,05 N 10,74 N 12,25 34,99 D 103,8 D 68,81 W
□MA 1,4 N -1,07 S 357,53 49,71 D 88,65 D 38,94 W


– MD = meridian distance (from MC if SA f [MO]  is diurnal or IC if Sa f  is nocturnal)
– SA = semi-arc (if f is diurnal, SA f [MO] is D and all MD’s and SA’s are D, otherwise N
– HA = horizontal distance (from the nearest horizon W or E for f [MO] and m □MA)
under bracket [] the fixed point, (here MO)
- Lat □MA 1,4 N and lat MA : -6° 13' 30"

recall : hd, dec and da of <=> these of ☽.

At the age of 57 (exactly, 57.06 in 1917.66) the Primum Mobile has runed through 3h 56 which gives 1.94 of motu proprio for MO. Added to the lunar parameters, we obtain: = 40°37'♉
At this time, we see a conjunction with the ◻♂ which then reaches: 42°12' ♉

At the time of Alan Leo's death, we therefore observe two directions to take into account and involving the hyleg.

additional bibliography
- Auguste Bouché-Leclercq, l'Astrologie Grecque, cap IX, $ II le sytème des sorts, pp.288-310 , Leroux, 1899
- Mark Riley, a survey of Vettius Valens, book II, the lot of fortune




mercredi 22 mars 2023

OURSEL Luc

 OURSEL Luc

07 Sep 1959 GREG    CAL
monday GREG
 | lat 48° 50' 0" | N 2°14' E
Boulogne-Billancourt
---------------------------------
natal 9h 10'
lmt 22h 1' 4"
tu 8h 10' 0"
tsn 7h 21' 34"
---------------------------------
timezone
Equation of time -0h 1' 43"
ΔT 0h 0' 38"
---------------------------------

source : https://www.astrotheme.fr/astrologie/Luc_Oursel / - Didier Geslain

Luc Marie Bernard Oursel, (7 September 1959 – 3 December 2014),was the former chairman of the board of the nuclear company Areva and member of its executive committee. He resigned on 20 October 2014 for health reasons six weeks before his death, which occurs on December 3 from pancreatic cancer.

THEME


SU is P with a -7 score
MO is F with a 0 score
VE is F and retrograde with a -11 score
JU is P with a -12 score

MA is R/Ex D with a -14 score
we see that moreover, MA is in mutual reception by exaltation with SA which is in this case an unfortunate circumstance (cf, Abumashar, The Great Introduction to Astrology, Burnett Charles, Yamamoto Keiji, vol I, part VII, 785, 2019, Brill
SA is in his nocturnal domicile (CAP) so we don't count it as ruler sign with a 2 score
Moreover, SA is in mutual reception by exaltation with MA which is an unfortunate circumstance (cf, Morin de Villefranche, Astrologia gallica, book XVII, cap VII, 39-51, La Haye, 1636)

we see below the list of aspects :
---------------------------------------
MO 60 SU Or        VE 0 ME Or          SA 120 ME Or          SA 120 VE Or      SA 90 MA Or    
---------------------------------------
The best aspect is  [best :me 0° (4) ve]  and the worst aspect is  [worst :ma 90° (-1,91) sa]
We find that not only MA  and SA are in mutual reception but moreover they exchange an aspect : 90° ; it is a square by mutual exaltation and this 'double' aspect may be aggressive

The traditional almuten (Omar, Ibn Ezra) is VE
we see below the list of dignities for VE :
---------------------------------------
[ term 3 tri 3 rul 1 exn 0 fac 3 ]
[ su 3 mo 3 asc 1 syg 3 pof 0 ]
---------------------------------------
Note 1 : the ‘almuten figuris’ is the lord of the chart, but its determination obeys somewhat different rules according to the schools. The tradition is based above all on the zodiacal dignities. (see p,e,  Alcabitius, Introduction, 59-61, 117 and Avenezra, Nativites, 101) – almuten = al-mu’tazz (arabic term)
[7] As for the governor which is the <planet> predominating (al-mubtazz) over the birth from which one indicates the conditions of the native after the haylāğ and the kadhudāh,n it is the planet having the most leadership in the ascendant, the position<s> of the two luminaries, the position of the Lot of Fortune and the position of the degree of the conjunction or opposition which precedes the birth. When a planet has mastery over two, three or four positions by the abundance of its shares in them, it is the governor and the predominant <planet> (al-mubtazz) and the indicator after the haylāğ and the kadhudāh. From it one indicates the conditions of the native. Some people use it instead of the kadhudāh in giving life.  [Al-Qabisi , Charles Burnett, Keji Yamamoto, Michio Yano, The Introduction to Astrology, IV, 7, p, 117, Warburg, 2004]
Note 2 : There are at least 4 systems for determining the almuten depending on whether the combinations of triplicities and terms are used: the Ptolemaic almuten (followed by Lilly) with Ptolemaic terms ; the same with Egyptian terms; the almuten of Dorotheus with Ptolemaic terms ; the same with Egyptian terms, knowing that one can embellish the whole thing with different weighting system (like Lilly or not using weights like Montanus) [cf. Temperament: Astrology's Forgotten Key, p. 79, Dorian Gieseler Greenbaum 2005]

The Lilly (Ptolemaïc) almuten is MO

In our experience, it seems that Ptolemy's almuten allows one to first appreciate the static side of the natal chart and that the Lilly-type elaboration allows one to deepen the more ‘temporary’ or ‘dynamic ‘ relationships (cf, Shlomo Sela, Ibn Ezra, on Nativities and Continuous Horoscopy, appendix 6, quot 2  ; Horary astrology p, 458, Brill, 2014)

Hyleg – alchocoden – domification REGIOMONTANUS,


In the upper chart we see that the nativity is diurnal (or nocturnal) and the moon is waxing (waning). This immediately makes it possible to orient the search for the hyleg towards SU or MO. We then seek the point which is both in Ptolemaic aspect and in dignity with the hyleg. This is the alchocoden. In the lower table, information is given on the alchocoden point (including dignity, power, retrograde, the house situation and especially the important fact of knowing if the alchocoden point is within 5° of the next cusp, in which case it must be removed (or added if he is retrograde) a certain number of degrees (life points). Finally, it may be necessary to add points depending on the place of JU and VE in relation to the upper meridian or the rising.


ZODIACAL – MUNDANE


In our research, we hypothesized that the mundane chart alone should be considered; also we must base on the aspects taken in the semiarcs the research of the degrees likely to be considered in the duration of the life.
In the case of OURSEL Luc we have the table above which allows us to estimate the breakdown of aspects between the different planets and the alchocoden.
When considering a theme, the first thing is to observe whether it is diurnal or nocturnal. In the case of OURSEL Luc, it is DIURNAL.
In this case, the first point to check is SU. If  SU is well disposed, it can claim 1st stage to be HYLEG.

SU is P and therefore seems weak, with a dignity score of -1,
Moreover, when we look for the dignities that appear in the zodiacal inscription of MO, we find none.
We'll see later what we get when we search for mundane dignities.
Now that we doubt to take SU as hyleg, we are left with the choice of ASC and that of POF. It is the way in which is laid out MO which will indicate the choice to us. If MO is waxing, we take ASC for hyleg ; if MO is waning, we take POF for hyleg,

It turns out that MO is waxing; so we will take ASC,
Now we must look for the alchocoden: it is the planet which has the maximum dignity with regard to the hyleg and which exchanges a Ptolemaic aspect with the hyleg.
If we see the ZODIACAL system, it turns out that we find none aspect to ASC. if we consider the ZODIACAL system, we observe a square aspect of SU.
At the same time, it appears that SU has  dignity of TRI over ASC.
So we have two possibilities with our hypothesis : first choose POF for hyleg ; second choose the MUNDANE system and try to find another couple of hyleg/alchocoden,
 If we choose now POF we must know that Dorotheus and Al Qabisi, but no Ptolemy, agree with this choice, in the absence of the possibility of taking the ASC into account.)
In case of POF is the Hyleg, there is then one candidate to be the alchocoden:SU
First, SU is linked with POF by an square aspect and a TRI dignity,
However, SU is P and has a power of -7, SU has a Kadkhudah score of 2
SU is located at 150 at more than 5°  (16,04°) from the next (cad) cusp
Now, we have to take account of the radix zodiacal aspects,
------------------------------------
 MO 60 SU: 1,25    
------------------------------------
Without any change, we find with SU as Kadhkhudah : Y = 69 as a result of SU SUCCEDENT years
But as SU is P, following William Lilly in Christian astrology, p, 115 (London, 1647) on his table of Fortitudes and debilities, we remove 1/5 of his value, ie -13,8
------------------------------------
So, zodiacal Y =56,45
------------------------------------

 MUNDANE DIRECTIONS


Below, you’ll see the ‘true’ converse ‘modern’ directions (see Leo, the progressed horoscope 1923 ; Pearce, the text-book of astrology 1911) - A true converse direction means a point that is directed towards an aspect (ie when an aspect is directed to the conjunction of a planet by the  primum mobile) – cf, Placidus, thesis 33, 59, (ex tertio Libro Physiomathematica sive Coelesti Philosophia, Mediolani 1647, 1650) in Tabulae Primi Mobilis... Patavii, 1657 - according to the ancient terminology, when the planets are "moving forward" (in the direction of the diurnal movement, "in the direction of the leading signs," or east to west) they are "retreating" with respect to their (west to east) motion in their own orbits; cf. Bouché-Leclercq, p 429, 1 [in Tetrabiblos published in the Loeb Classical Library, 1940]
------------------------------------------------------
CMEMA orb 271,52 asp □ - CSAMO orb -0,52 asp C -  □MAME orb 181 asp □
------------------------------------------------------
Here appear the converse directions (in the ‘modern’ sense of the term) for the event corresponding to the year .1991,  i.e. for planets or aspects 'moving'  i.e. flowing from the West to the East, which we do not retain. Moreover, the question is not resolved (is it anyway?). We can consult Bouché-Leclercq on this ('L’Astrologie Grecque', p. chap XII, p. 418 n. 2, 1899, Leroux), : 'The apheta once found, following laborious comparisons, it is necessary to determine the direction in which it launches life, to from its aphetic place; straight direction, i.e. conforming to the proper motion of the planets, when it follows the series of signs, retrograde when it follows the diurnal motion".
We find in this last sentence what is perhaps the key to the question: indeed, when we say 'when the planets follow the order of the signs' it is a direct reference to the ecliptic which precisely has nothing to do with diurnal motion. Now, it is precisely the examination of the diurnal movement which is at the base of the system of the primary directions. The 'retrograde direction' for its part refers expressly to the diurnal movement and is in conformity with the doctrine. We can therefore see that there was progressively, and particularly from the 18th century onwards, a nonsense which was introduced by considering the converse direction as an antenatal, whereas the retrograde direction is that of the primum mobile.

 


DIRECTION : ꝏSA conj VE
---------------------------------
We must take into account an important element: the ascensional difference (DA); it can be observed on the  graph in a dotted line (measured between the horizon and the axis of the pole). This is the difference between Right Ascension (AR) and Oblique Ascension (OA). This is the difference between Right Ascension (AR) and Oblique Ascension (OA). DA is always calculated in absolute value |DA| and it is added or subtracted from 90° (SA = 90° corresponds to a point on the equator cut by the horizon; depending on whether a star approaches or moves away from the line of horizon, SA is > 90° or < 90°, i,e, (+) depending on whether it is diurnal and northern ; or nocturnal and southern ; (-) depending on whether it is diurnal and southern ; or nocturnal and northern.

sin(DA) = -tan(φ)tan(δ)
φ = latitude 48,83 N
δ VE = 1,93 +
DA-VE = 2,21°
δ ꝏSA =22,67 +
DA-ꝏSA =28,54°

We will first use the Placidus system of mundane directions. The simplest system is that of Choisnard-Fomalhaut. First you need to retrieve the data from the SA (semi-arc) and the DM (meridian distance) of the diurnal point because the altitude of VE is 30,52°. important note: the SA and DM of the two points are always counted diurnal if the first point (here VE) is above the horizon even if the second is below. They are counted nightly if the first point (VE) is below the horizon regardless of the position of the second point.
For DMs, they are counted in AR from the diurnal meridian if the fixed point VE is diurnal, and from the nocturnal meridian if it is nocturnal.

diurnal meridian MC = 110,39°
AR VE = 153,22°
AR ꝏSA = 90,5°

SA D (d+) VE=92,21°
DM D  VE=42,83°

For the  significator  ꝏSA altitude (h) =59,47°. so :

SA D (δ+) ꝏSA=118,54°
DM D ꝏSA=-19,89°

Then we compute Saf/DMf (so : SA f [92,21°] / DM f [42,83°])

Sa f / DM f =2,15

and the angle x = SAm x DM f/SA f, so : SA m [118,54°] x DM f [42,83°]/SA f [92,21°]

 x = 55,05°

We find the direction by DMm - x, so : DM m [-19,89°] ± x [55,05]
We must now have regard to the double ± sign of the last expression; in the case where f (VE) and m (ꝏSA) are on either side of the meridian, the direction arc is obtained by taking the sum (instead of the difference) of the two quantities DMm and x. this is the case here so sign = (-)
the computation of the arc requires, depending on the case, a reduction of 360° (so arc modulo 360°)
---------------------------------
arc D =74,94°
---------------------------------
in the technical sense, It is a direct direction but in the astrological sense, it is a true converse direction since it is an aspect considered as a promissor which goes towards the significator. ; so the m point is an aspect (here ꝏSA) and the f point is a planet or an axis, (here VE)

We can now compute the converse direction : point f is directed towards point m, i.e. the star is directed towards the aspect. This is where the problem of the orientation of the primum mobile arises because it is not concevable to rotate the local sphere in both directions… It does not seem convenient to postulate that the arc of direction is counted in the order of the signs of the zodiac (when it is direct, i.e. when one directs a promissor towards a significator): indeed, the ecliptic has nothing to do with a direction since this one depends only on the diurnal movement ( primum mobile). It is therefore otherwise that we must pass judgment on this.

That time, we compute Sa m / DM m (so : SA m [118,54°] / DM f [-19,89°])

Sa m / DM m =-5,96

and the angle x = SA f x DM m/SA m, so : SA f [92,21°] x DM m [-19,89°] / SA m [118,54°]

x = 15,47°

We find the direction by DM f - x, so : DM f [42,83°] ± x [15,47°]
We must now have regard to the double ± sign of the last expression; in the case where m (ꝏSA) and f (VE) are on either side of the meridian, the direction arc is obtained by taking the sum (instead of the difference) of the two quantities DM f and x. this is the case here : so, signe = (+)
---------------------------------
arc C =58,3°
---------------------------------
Now we can study the same direction with the Regiomontanus system. To obtain the arc of direction between two signifying points (planets in body, aspect versus planet, planet versus axis) one must find AO (oblique ascent) of f and of m, calculated under the pole of f.
The formulas to use can be found either in the Dictionnaire astrologique of Henri Joseph Gouchon (Dervy Livres, 1937) pp. 266-267, or in his Horoscope annuel simplifié (Dervy, 1973) p.181. Other formulas can be found in Les moyens de pronostic en astrologie, Max Duval (editions traditionnelles, 1986) and Domification et transits (Editions traditionnelles, 1985). We can also cite by André Boudineau : Les bases scientifiques de l’astrologie (Chacornac, 1937) These are references in French but there are many other references in English or German of a less obvious but equally valid use.

First, compute the ascensional difference under f (VE) : cot DAP f = (cot de f x cot lat) / in DM f ± cot DM f, i,e, :  cot (DAP f) = (Cot dec f[1,93°] x Cot Lat [48,83°]) /sin DM f [42,83°] ± cot DM f  [42,83°]

DAPf = 1,46°

We find the pole of f (VE) by formula : tan(pole f) = sin (DAP f) x cot (dec f) i,e, tan(pole f) = tan f [178,54°] x cot f [1,93°]

pole VE regio  =37,14°

(1) We need now the DAP of m (ꝏSA) under the pole of f, sin (DAP m) = tan (pole f) x tan (DEC m), i,e, : (VE) : sin (DAPm/f) = tan [37,08°] x tan [22,67°]

DAP m/f = 18,4°

then we find for the points located in the eastern part of the chart : AO f = AR f± DAP f ; sign (+) if Dec f boreal or sign (–) if Dec f Austral ; so : AO f VE = 154,68° and AO m = AR m ± DAP m ; idem for sign ; so  AO mꝏSA = 108,91°

---------------------------------
arc D Regio = 79,66°
---------------------------------
We are now going to compute the converse Regiomontanus direction corresponding to the arc  f VE / p ꝏSA

First, compute the ascensional difference under m (ꝏSA) : cot DAPm = (cot dec m x cot lat)/sin DM m ± cot DM m, i,e, :  Cot(DAP m) = (Cot decm[22,67°] x Cot Lat [48,83°]) / Sin DM f [19,89°] ± Cot DM m [19,89°]

DAP m = 6,4°

We find the pole of m (ꝏSA) by formula : Tan(pole m) = Sin (DAP m) x Cot (dec m) i,e, Tan(pole m) = Sin m [173,6°] x Cot m [22,67°]

pole ꝏSA regio  =14,94°

We need now the DAP of f (VE) under the pole of m, Sin (DAP f) = Tan (pole m) x Tan (DEC f), i,e, : (ꝏSA) : Sin (DAP f/m) = Tan[14,94°] x Tan [1,93°]

DAP f/m = 0,52°

then we find for the points located in the eastern part of the chart : AO m = AR m ± DAP m ; sign (+) if Dec m boreal or sign (–) if Dec m Austral ; so : AO m ꝏSA = 97° and AO f = AR f ± DAP f ; idem for sign ; so  AO f VE = 153,74°

---------------------------------
arc C Regio = 56,84°
---------------------------------
H.J. Gouchon [l’Horoscope Annuel simplifié, Dervy, 1973, p, 181-182 and Dictionnaire astrologique, p, 277, 1937-1942, Gouchon ed., 1975, Dervy, but be careful because in DAP's equation, the double sign ± was mistakenly replaced by the sign (-) ] advises to avoid errors, to always place the star A1 (for us f, i.e. SU) in the eastern houses; in fact it is enough to change the registration number of the house based on the transformation (IV-V-VI) -> (X-XI-XII) and (VII-VIII-IX) -> (I-II-III ) to adapt the double sign ± in the calculation of DAP f or DAP m; moreover, this sign must be reversed if |DM| > 90°.

For the Regiomontanus directions, there is another mode of computing, mentioned by Gouchon (Dictionnaire astrologique, op. cit., p. 276) and especially Martin Gansten (Primary directions, pp. 155-157, the Wessex Astrologer, 2009)
This method consists at computing first 3 auxiliary angles before  the pole. It then joins the other method. Contrary to what Gouchon says, I find it easier than the previous one because we avoid the double sign ± in the determination of DAP f.

So, initially, we have A => Tan f = tan dec f [1,93°] / cos DM f [42,83°]

A = 2,63°

Then : B = Lat [48,83°] + A [-2,63°]

B = 46,2°

And, Tang C = Cot DM f [42,83°] x Cos B [46,2°] / Cos A [-2,63°]

C = 36,78°

Then, we have Sin pole f = Cos C [36,78°] x  Sin LG [48,83°]
---------------------------------
So, pole VE regio = 37,08°
---------------------------------
Now go back to (1)

For m ꝏSA; we have : A => Tan m = tan dec m [22,67°] / cos DM m [19,89°]

A = 23,95°

Then : B = Lat [48,83°] + A [-23,95°]

B = 24,88°

And, Tang C = Cot DM m [19,89°] x Cos B [24,88°] / Cos A [-23,95°]

C = -69,97°

Then, we have Sin pole m = Cos C [-69,97°] x  Sin LG [48,83°]
---------------------------------
So, pole ꝏSA regio = 14,94°
---------------------------------
Now go back to (1)


DIRECTION : □SA conj MO
---------------------------------
We must take into account an important element: the ascensional difference (DA); it can be observed on the  graph in a dotted line (measured between the horizon and the axis of the pole). This is the difference between Right Ascension (AR) and Oblique Ascension (OA). This is the difference between Right Ascension (AR) and Oblique Ascension (OA). DA is always calculated in absolute value |DA| and it is added or subtracted from 90° (SA = 90° corresponds to a point on the equator cut by the horizon; depending on whether a star approaches or moves away from the line of horizon, SA is > 90° or < 90°, i,e, (+) depending on whether it is diurnal and northern ; or nocturnal and southern ; (-) depending on whether it is diurnal and southern ; or nocturnal and northern.

sin(DA) = -tan(φ)tan(δ)
φ = latitude 48,83 N
δ MO = -12,49 -
DA-MO = 14,67°
δ □SA =2,21 +
DA-□SA =2,53°

We will first use the Placidus system of mundane directions. The simplest system is that of Choisnard-Fomalhaut. First you need to retrieve the data from the SA (semi-arc) and the DM (meridian distance) of the nocturnal point because the altitude of MO is -23,01°. important note: the SA and DM of the two points are always counted diurnal if the first point (here MO) is above the horizon even if the second is below. They are counted nightly if the first point (MO) is below the horizon regardless of the position of the second point.
For DMs, they are counted in AR from the diurnal meridian if the fixed point MO is diurnal, and from the nocturnal meridian if it is nocturnal.

nocturnal meridian MC = 290,39°
AR MO = 221,19°
AR □SA = 181,46°

 = 104,67°
DM N  MO = -69,21°

For the  significator  □SA altitude (h) =14,03°. so :

SA N (δ+) □SA = 87,47°
DM N  □SA = -108,93°

Then we compute Saf/DMf (so : SA f [ 104,67°] / DM f [ -69,21°])

Sa f / DM f =1,51

and the angle x = SAm x DM f/SA f, so : SA m [ 87,47°] x DM f [ -69,21°]/SA f [ 104,67°]

 x = -57,83°

We find the direction by DMm - x, so : DM m [ -108,93°] ± x [-57,83]
We must now have regard to the double ± sign of the last expression; in the case where f (MO) and m (□SA) are on either side of the meridian, the direction arc is obtained by taking the sum (instead of the difference) of the two quantities DMm and x. This is not the case here, so sign = (+)
the computation of the arc requires, depending on the case, a reduction of 360° (so arc modulo 360°)
---------------------------------
arc D =51,1°
---------------------------------
in the technical sense, It is a direct direction but in the astrological sense, it is a true converse direction since it is an aspect considered as a promissor which goes towards the significator. ; so the m point is an aspect (here □SA) and the f point is a planet or an axis, (here MO)

We can now compute the converse direction : point f is directed towards point m, i.e. the star is directed towards the aspect. This is where the problem of the orientation of the primum mobile arises because it is not concevable to rotate the local sphere in both directions… It does not seem convenient to postulate that the arc of direction is counted in the order of the signs of the zodiac (when it is direct, i.e. when one directs a promissor towards a significator): indeed, the ecliptic has nothing to do with a direction since this one depends only on the diurnal movement ( primum mobile). It is therefore otherwise that we must pass judgment on this.

That time, we compute Sa m / DM m (so : SA m [ 87,47°] / DM f [ -108,93°])

Sa m / DM m =-1,3

and the angle x = SA f x DM m/SA m, so : SA f [ 104,67°] x DM m [ -108,93°] / SA m [ 87,47°]

x = 57,86°

We find the direction by DM f - x, so : DM f [ -69,21°] ± x [57,86°]
We must now have regard to the double ± sign of the last expression; in the case where m (□SA) and f (MO) are on either side of the meridian, the direction arc is obtained by taking the sum (instead of the difference) of the two quantities DM f and x. This is not the case here, so sign = (-)
---------------------------------
arc C =52,94°
---------------------------------
Now we can study the same direction with the Regiomontanus system. To obtain the arc of direction between two signifying points (planets in body, aspect versus planet, planet versus axis) one must find AO (oblique ascent) of f and of m, calculated under the pole of f.
The formulas to use can be found either in the Dictionnaire astrologique of Henri Joseph Gouchon (Dervy Livres, 1937) pp. 266-267, or in his Horoscope annuel simplifié (Dervy, 1973) p.181. Other formulas can be found in Les moyens de pronostic en astrologie, Max Duval (editions traditionnelles, 1986) and Domification et transits (Editions traditionnelles, 1985). We can also cite by André Boudineau : Les bases scientifiques de l’astrologie (Chacornac, 1937) These are references in French but there are many other references in English or German of a less obvious but equally valid use.

First, compute the ascensional difference under f (MO) : cot DAP f = (cot de f x cot lat) / in DM f ± cot DM f, i,e, :  cot (DAP f) = (Cot dec f[-12,49°] x Cot Lat [48,83°]) /sin DM f [69,21°] ± cot DM f  [69,21°]

DAPf = 165,42°

We find the pole of f (MO) by formula : tan(pole f) = sin (DAP f) x cot (dec f) i,e, tan(pole f) = tan f [12,26°] x cot f [-12,49°]

pole MO regio  =-43,78°

(1) We need now the DAP of m (□SA) under the pole of f, sin (DAP m) = tan (pole f) x tan (DEC m), i,e, : (MO) : sin (DAPm/f) = tan [43,79°] x tan [2,21°]

DAP m/f = 2,12°

then we find for the points located in the eastern part of the chart : AO f = AR f± DAP f ; sign (+) if Dec f boreal or sign (–) if Dec f Austral ; so : AO f MO = 230,52° and AO m = AR m ± DAP m ; idem for sign ; so  AO m□SA = 183,59°

---------------------------------
arc D Regio = 54,1°
---------------------------------
We are now going to compute the converse Regiomontanus direction corresponding to the arc  f MO / p □SA

First, compute the ascensional difference under m (□SA) : cot DAPm = (cot dec m x cot lat)/sin DM m ± cot DM m, i,e, :  Cot(DAP m) = (Cot decm[2,21°] x Cot Lat [48,83°]) / Sin DM f [71,07°] ± Cot DM m [71,07°]

DAP m = 2,36°

We find the pole of m (□SA) by formula : Tan(pole m) = Sin (DAP m) x Cot (dec m) i,e, Tan(pole m) = Sin m [2,36°] x Cot m [2,21°]

pole □SA regio  =46,87°

We need now the DAP of f (MO) under the pole of m, Sin (DAP f) = Tan (pole m) x Tan (DEC f), i,e, : (□SA) : Sin (DAP f/m) = Tan[46,82°] x Tan [-12,49°]

DAP f/m = -13,65°

then we find for the points located in the eastern part of the chart : AO m = AR m ± DAP m ; sign (+) if Dec m boreal or sign (–) if Dec m Austral ; so : AO m □SA = 184° and AO f = AR f ± DAP f ; idem for sign ; so  AO f MO = 234,84°

---------------------------------
arc C Regio = 55,73°
---------------------------------
H.J. Gouchon [l’Horoscope Annuel simplifié, Dervy, 1973, p, 181-182 and Dictionnaire astrologique, p, 277, 1937-1942, Gouchon ed., 1975, Dervy, but be careful because in DAP's equation, the double sign ± was mistakenly replaced by the sign (-) ] advises to avoid errors, to always place the star A1 (for us f, i.e. SU) in the eastern houses; in fact it is enough to change the registration number of the house based on the transformation (IV-V-VI) -> (X-XI-XII) and (VII-VIII-IX) -> (I-II-III ) to adapt the double sign ± in the calculation of DAP f or DAP m; moreover, this sign must be reversed if |DM| > 90°.

For the Regiomontanus directions, there is another mode of computing, mentioned by Gouchon (Dictionnaire astrologique, op. cit., p. 276) and especially Martin Gansten (Primary directions, pp. 155-157, the Wessex Astrologer, 2009)
This method consists at computing first 3 auxiliary angles before  the pole. It then joins the other method. Contrary to what Gouchon says, I find it easier than the previous one because we avoid the double sign ± in the determination of DAP f.

So, initially, we have A => Tan f = tan dec f [-12,49°] / cos DM f [-69,21°]

A = -31,96°

Then : B = Lat [48,83°] + A [31,96°]

B = 16,87°

And, Tang C = Cot DM f [-69,21°] x Cos B [16,87°] / Cos A [31,96°]

C = -23,19°

Then, we have Sin pole f = Cos C [-23,19°] x  Sin LG [48,83°]
---------------------------------
So, pole MO regio = 43,78°
---------------------------------
Now go back to (1)

For m □SA; we have : A => Tan m = tan dec m [2,21°] / cos DM m [71,07°]

A = 6,78°

Then : B = Lat [48,83°] + A [-6,78°]

B = 42,05°

And, Tang C = Cot DM m [71,07°] x Cos B [42,05°] / Cos A [-6,78°]

C = -14,38°

Then, we have Sin pole m = Cos C [-14,38°] x  Sin LG [48,83°]
---------------------------------
So, pole □SA regio = 46,82°
---------------------------------
Now go back to (1)


DIRECTION : □MA conj MO
---------------------------------
We must take into account an important element: the ascensional difference (DA); it can be observed on the  graph in a dotted line (measured between the horizon and the axis of the pole). This is the difference between Right Ascension (AR) and Oblique Ascension (OA). This is the difference between Right Ascension (AR) and Oblique Ascension (OA). DA is always calculated in absolute value |DA| and it is added or subtracted from 90° (SA = 90° corresponds to a point on the equator cut by the horizon; depending on whether a star approaches or moves away from the line of horizon, SA is > 90° or < 90°, i,e, (+) depending on whether it is diurnal and northern ; or nocturnal and southern ; (-) depending on whether it is diurnal and southern ; or nocturnal and northern.

sin(DA) = -tan(φ)tan(δ)
φ = latitude 48,83 N
δ MO = -12,47 -
DA-MO = 14,65°
δ □MA =-23,2 -
DA-□MA =29,36°

We will first use the Placidus system of mundane directions. The simplest system is that of Choisnard-Fomalhaut. First you need to retrieve the data from the SA (semi-arc) and the DM (meridian distance) of the nocturnal point because the altitude of MO is -22,48°. important note: the SA and DM of the two points are always counted diurnal if the first point (here MO) is above the horizon even if the second is below. They are counted nightly if the first point (MO) is below the horizon regardless of the position of the second point.
For DMs, they are counted in AR from the diurnal meridian if the fixed point MO is diurnal, and from the nocturnal meridian if it is nocturnal.

nocturnal meridian MC = 290,39°
AR MO = 220,38°
AR □MA = 261,33°

 = 104,65°
DM N  MO = -70,01°

For the  significator  □MA altitude (h) =-55,63°. so :

 = 119,36°
DM N  □MA = -29,07°

Then we compute Saf/DMf (so : SA f [ 104,65°] / DM f [ -70,01°])

Sa f / DM f =1,49

and the angle x = SAm x DM f/SA f, so : SA m [ 119,36°] x DM f [ -70,01°]/SA f [ 104,65°]

 x = -79,85°

We find the direction by DMm - x, so : DM m [ -29,07°] ± x [-79,85]
We must now have regard to the double ± sign of the last expression; in the case where f (MO) and m (□MA) are on either side of the meridian, the direction arc is obtained by taking the sum (instead of the difference) of the two quantities DMm and x. This is not the case here, so sign = (+)
the computation of the arc requires, depending on the case, a reduction of 360° (so arc modulo 360°)
---------------------------------
arc D =-50,78°
---------------------------------
in the technical sense, It is a direct direction but in the astrological sense, it is a true converse direction since it is an aspect considered as a promissor which goes towards the significator. ; so the m point is an aspect (here □MA) and the f point is a planet or an axis, (here MO)

We can now compute the converse direction : point f is directed towards point m, i.e. the star is directed towards the aspect. This is where the problem of the orientation of the primum mobile arises because it is not concevable to rotate the local sphere in both directions… It does not seem convenient to postulate that the arc of direction is counted in the order of the signs of the zodiac (when it is direct, i.e. when one directs a promissor towards a significator): indeed, the ecliptic has nothing to do with a direction since this one depends only on the diurnal movement ( primum mobile). It is therefore otherwise that we must pass judgment on this.

That time, we compute Sa m / DM m (so : SA m [ 119,36°] / DM f [ -29,07°])

Sa m / DM m =0,79

and the angle x = SA f x DM m/SA m, so : SA f [ 104,65°] x DM m [ -29,07°] / SA m [ 119,36°]

x = -25,49°

We find the direction by DM f - x, so : DM f [ -70,01°] ± x [-25,49°]
We must now have regard to the double ± sign of the last expression; in the case where m (□MA) and f (MO) are on either side of the meridian, the direction arc is obtained by taking the sum (instead of the difference) of the two quantities DM f and x. This is not the case here, so sign = (-)
---------------------------------
arc C =44,53°
---------------------------------
Now we can study the same direction with the Regiomontanus system. To obtain the arc of direction between two signifying points (planets in body, aspect versus planet, planet versus axis) one must find AO (oblique ascent) of f and of m, calculated under the pole of f.
The formulas to use can be found either in the Dictionnaire astrologique of Henri Joseph Gouchon (Dervy Livres, 1937) pp. 266-267, or in his Horoscope annuel simplifié (Dervy, 1973) p.181. Other formulas can be found in Les moyens de pronostic en astrologie, Max Duval (editions traditionnelles, 1986) and Domification et transits (Editions traditionnelles, 1985). We can also cite by André Boudineau : Les bases scientifiques de l’astrologie (Chacornac, 1937) These are references in French but there are many other references in English or German of a less obvious but equally valid use.

First, compute the ascensional difference under f (MO) : cot DAP f = (cot de f x cot lat) / in DM f ± cot DM f, i,e, :  cot (DAP f) = (Cot dec f[-12,47°] x Cot Lat [48,83°]) /sin DM f [70,01°] ± cot DM f  [70,01°]

DAPf = 165,42°

We find the pole of f (MO) by formula : tan(pole f) = sin (DAP f) x cot (dec f) i,e, tan(pole f) = tan f [12,34°] x cot f [-12,47°]

pole MO regio  =-44,03°

(1) We need now the DAP of m (□MA) under the pole of f, sin (DAP m) = tan (pole f) x tan (DEC m), i,e, : (MO) : sin (DAPm/f) = tan [44,02°] x tan [-23,2°]

DAP m/f = -24,47°

then we find for the points located in the eastern part of the chart : AO f = AR f± DAP f ; sign (+) if Dec f boreal or sign (–) if Dec f Austral ; so : AO f MO = 230,6° and AO m = AR m ± DAP m ; idem for sign ; so  AO m□MA = 285,8°

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arc D Regio = -53,07°
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We are now going to compute the converse Regiomontanus direction corresponding to the arc  f MO / p □MA

First, compute the ascensional difference under m (□MA) : cot DAPm = (cot dec m x cot lat)/sin DM m ± cot DM m, i,e, :  Cot(DAP m) = (Cot decm[-23,2°] x Cot Lat [48,83°]) / Sin DM f [150,93°] ± Cot DM m [-29,07°]

DAP m = 22,61°

We find the pole of m (□MA) by formula : Tan(pole m) = Sin (DAP m) x Cot (dec m) i,e, Tan(pole m) = Sin m [170,53°] x Cot m [-23,2°]

pole □MA regio  =-20,99°

We need now the DAP of f (MO) under the pole of m, Sin (DAP f) = Tan (pole m) x Tan (DEC f), i,e, : (□MA) : Sin (DAP f/m) = Tan[20,99°] x Tan [-12,47°]

DAP f/m = -4,87°

then we find for the points located in the eastern part of the chart : AO m = AR m ± DAP m ; sign (+) if Dec m boreal or sign (–) if Dec m Austral ; so : AO m □MA = 271° and AO f = AR f ± DAP f ; idem for sign ; so  AO f MO = 225,25°

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arc C Regio = -45,54°
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H.J. Gouchon [l’Horoscope Annuel simplifié, Dervy, 1973, p, 181-182 and Dictionnaire astrologique, p, 277, 1937-1942, Gouchon ed., 1975, Dervy, but be careful because in DAP's equation, the double sign ± was mistakenly replaced by the sign (-) ] advises to avoid errors, to always place the star A1 (for us f, i.e. SU) in the eastern houses; in fact it is enough to change the registration number of the house based on the transformation (IV-V-VI) -> (X-XI-XII) and (VII-VIII-IX) -> (I-II-III ) to adapt the double sign ± in the calculation of DAP f or DAP m; moreover, this sign must be reversed if |DM| > 90°.

For the Regiomontanus directions, there is another mode of computing, mentioned by Gouchon (Dictionnaire astrologique, op. cit., p. 276) and especially Martin Gansten (Primary directions, pp. 155-157, the Wessex Astrologer, 2009)
This method consists at computing first 3 auxiliary angles before  the pole. It then joins the other method. Contrary to what Gouchon says, I find it easier than the previous one because we avoid the double sign ± in the determination of DAP f.

So, initially, we have A => Tan f = tan dec f [-12,47°] / cos DM f [-70,01°]

A = -32,9°

Then : B = Lat [48,83°] + A [32,9°]

B = 15,93°

And, Tang C = Cot DM f [-70,01°] x Cos B [15,93°] / Cos A [32,9°]

C = -22,62°

Then, we have Sin pole f = Cos C [-22,62°] x  Sin LG [48,83°]
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So, pole MO regio = 44,02°
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Now go back to (1)

For m □MA; we have : A => Tan m = tan dec m [-23,2°] / cos DM m [-29,07°]

A = -26,12°

Then : B = Lat [48,83°] + A [26,12°]

B = 22,71°

And, Tang C = Cot DM m [-29,07°] x Cos B [22,71°] / Cos A [26,12°]

C = -61,59°

Then, we have Sin pole m = Cos C [-61,59°] x  Sin LG [48,83°]
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So, pole □MA regio = 20,99°
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Now go back to (1)

Exemple of armillary spherae


 

ARMILLARY SPHERAE

This armillary sphere presents us with a true stereographic projection of the
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DIRECTION : ꝏSA conj VE
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We see the superior meridian upper the pole 48,83° N LAT , the inferior meridian, and the other great circles : equator, ecliptic λ, latitude circle β, azimuth circle A and horary circle H
- the zenith with colatitude 41,17° and the prime vertical
- the horizon with ecliptic inclination of 61,39° and the ecliptic pole at 28,61°
- the line Nord-Sud, as a circle, is the equinoctial colure ; the meridian circle can be considered as the solsticial colure (i,e, the equinoctial colure is a meridian passing through the equinoctial points ; and the solsticial colure is a meridian passing through the solsticial points). The colures therefore divide the apparent annual path of the Sun into four parts which determine the seasons,
- Ascensional difference (DA) for f VE is = sin DA = -tan(lat [48,83]) x tan(dec f [1,9])
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so DA f VE = 2,17°
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Ascensional difference (DA) for m ꝏSA is = sin DA = -tan(lat [48,83]) x tan(dec f [22,67])
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so DA m ꝏSA = 28,54°
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- You see  also an almucantar circle for the mundane primary directions : actually the altitude of f VE = 30,52° ; it is therefore almost equal to the altitude of the su and therefore m and f are in mundane conjunction because Δ alt <2° (-51,11°), This altitude corresponds to that of point f VE (alt f = 30,52), assumed to have remained fixed during the displacement of the diurnal movement.
note that if the m point is a counter parallel, it is retrograde (and it is not a zodiacal aspect because one uses declination to compute mundane parallel),

We can see too two or three parallels of declination ; for point m ꝏSA with dashed line (between equator and equinoctial colure) to design the m DA (see above) ; for point f VE (idem) and for a star (Algol i,e, β Persei or another if present in the sky path of the natal chart ),
- Then we find the index for rising, transit and setting the two points f and m,
- Houses are shown in shaded lines. The grid setting is based on the REGIOMONTANUS system. The cusps are immobile since the movement is based on that of the primum mobile. [cf, John North, 'Horoscopes and history',  (London : The Warburg Institute, 1986) and Henri Selva, 'La Domification , ou construction du theme celeste en astrologie'. Vigot, Paris, 1917]