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°

---------------------------------
arc D Regio = -53,07°
---------------------------------
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°

---------------------------------
arc C Regio = -45,54°
---------------------------------
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°]
---------------------------------
So, pole MO regio = 44,02°
---------------------------------
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°]
---------------------------------
So, pole □MA regio = 20,99°
---------------------------------
Now go back to (1)

Exemple of armillary spherae

 

ARMILLARY SPHERAE

This armillary sphere presents us with a true stereographic projection of the
---------------------------------
DIRECTION : ꝏSA conj VE
---------------------------------
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])
---------------------------------
so DA f VE = 2,17°
---------------------------------
Ascensional difference (DA) for m ꝏSA is = sin DA = -tan(lat [48,83]) x tan(dec f [22,67])
---------------------------------
so DA m ꝏSA = 28,54°
---------------------------------
- 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]