ATTERSALL James

ATTERSALL James

01 Oct 1817 GREG    CAL
wednesday GREG
 | lat 53° 15' 0" | N 0°33' W
LONDON
---------------------------------
natal (bt) 19 h 45 min
raas-rams :0h 10' 18"
reckoned bt Lat --> lmt 16 h 34 min
tu 16h 36' 11"
tsn 17h 14' 11"
---------------------------------
timezone  : 0
DST : 0 (-)
Equation of time 0h 10' 18"
ΔT 0h 0' 14"
---------------------------------

 This topic was discussed in the forum

https://skyscript.co.uk/forums/viewtopic.php?p=125144#p125144

and it comes from a collection of 30 themes by John Worsdale, contained in the 'Celestial Philosophy' (Longman, 1828), with a large discussion [pp 35-37], the square theme appearing on p. 19.

 

Born October 1st, 1817, 4:45 P.M. in London.

In the forum cited above, we can read:

'On the day of Death, the Child went into the Street unobserved by any one, and immediately accompanied several other Children who were playing very near a Horse that was feeding a short distance from the Door, near the side of the River. The Horse was always considered to be a very quiet Animal, but in the fatal Hour, he kicked at the Children, yet none were injured, except the unfortunate Child, who received the stroke in its forehead, which proved instantly mortal; his Death happened on the 22nd of September, 1819, near three o’clock in the Afternoon, Age one Year, eleven Months, and twenty days.' [...] 

 and i add this extract from Worsdale :

'The Astral causes that produced the sudden and violent Death of this Child, are plainly visible; the Ascendant is afflicted by the body of Saturn, and Square of the Moon, and Mars in Mundo; the Moon is conjoined with Mars among evil Stars in the Northern Angle, approaching the Terms of Saturn, without any relief, and that Luminary is applying- to the Mundane Square of Saturn, by direct motion. The Part of Fortune is afflicted by the opposition of the Moon and Mars; but I judged the work of Mortality to arise chiefly from the uninterrupted communication of those violent rays of Mars and the Moon from the Imum Celi, to the Sun, who is the true Apheta, or giver of Life, particularly because the Hyleg is near the Body of Mercury, and Rapt Parallel of Saturn ; and I shall here observe that Mercury is of the nature of the enemies in the Celestial constitution.'

Celestial philosophy, p. 36-37

 Now, I give the theme in a more modern form: 

 
Aspects are computed from the mundane version of the theme; the blue triangle is the mark of the hyleg (SU) and the red triangle, that of the alchocoden (ME).
If we look at the possibilities for the hyleg, we find SU (which has an aspect with ME) and ME has a TERM-like dignity; moreover the theme is diurnal. MO does not have a Ptolemaic type aspect. ASC is the 2nd candidate to be the hyleg with an aspect of VE (and two dignities, TERM and EXN, I pass on FAC which is only mentioned for the record). However, ASC cannot be retained in principle because the moon is preventional (WANING type).
The fourth point to examine is POF since the theme is conjunctional. But there is no dignity.
The last point is the dominant of the theme: VE. VE is in opposition to ASC and SA. It is in dignity of TERM with SA.
If we want to make a synthesis, it is essential to respect the order of succession of the different possibilities offered: here there is no need to hesitate. The hyleg is SU and the alchocoden can only be ME, even if ME appears, as Worsdale clearly saw it as problematic.

ME is retrograde, peregrine and also occidental. SU is in fall [LIB].

The dominance table :

We see that VE and SA (score >= 5) are 'effective'.

The disposition of the stars (I am only talking about the group of Behenian stars here) shows:
- conjunction cusp of XII and Algol (β Per) in Regio domitude at 331.36
- conjunction of ASC and Deneb algedi (δ Cap) at 359.76 (Regio domitude)

The primary directions  :

1)- DIRECTION : □MA conj ASC
---------------------------------
For a direction between ASC and any planet or aspect (zodiacal or mundane),  we must compute ASC OA and m OA (here □MA) ; the inner circle contains the AR (right ascension) values of ASC and MA or SA.  The outer circle contains the values of the same elements in OA (oblique ascent). Natal ASC is always indicated with a round symbol (o) and the natal significator (MA or SA) with a cross (x). The direction is simulated  by a segment of a circle that ends counter-clockwise at the value in OA. A symbol reflects either a conjunction aspect or a quadrature aspect.

OA ASC = 348,55°
OA □ MA progr = 353,59

 D= 1,01°

1)- DIRECTION : CSA conj ASC
---------------------------------
For a direction between ASC and any planet or aspect (zodiacal or mundane),  we must compute ASC OA and m OA (here CSA) ; the inner circle contains the AR (right ascension) values of ASC and MA or SA.  The outer circle contains the values of the same elements in OA (oblique ascent). Natal ASC is always indicated with a round symbol (o) and the natal significator (MA or SA) with a cross (x). The direction is simulated  by a segment of a circle that ends counter-clockwise at the value in OA. A symbol reflects either a conjunction aspect or a quadrature aspect.

OA ASC = 348,55°
OA C SA progr = 355,41

 D= 0,52°

It is notable that at birth we have respectively :

- for MA D = 2.55° and for SA D = 3.04°

2)- DIRECTION : □ VE conj MA

Problem XVI gives the means of finding if a star is in the same circle of position, with a planet or any significator. Find the arc position ET [3.21], which assumes the hour angle of the star and its semidiurnal arc. With ET and H [H' 4.29] you will have the angle O [5.36] of the position circle with the meridian; you will compare this circle to that of the signifier and you will see if it differs [adapted from Delambre, Histoire de l'Astronomie du Moyen Âge, p. 489, 1819]

2.1 MAGINI – REGIOMONTANUS   
---------------------------------
converse   
---------------------------------
If dir is converse,  change in [P] dec and h of [□ VE] for [C MA]  and in [ET], change DA of [□ VE] for [C MA]   
    
modified from [ Delambre, Hist Astron Moyen Âge, Magini, pp, 486-491 Paris 1819]   
    
    Eq for Fig 129 (pl 12)  see fig for location and explanation of spherical triangles
    
    h (altitude  of the promissor) - H (latitude of the observer) - D (declination of the promissor) –
    D' (declination of incident horizon = position circle of promissor) - PH=H -
---------------------------------   
P (horary angle, from midnight)    0
-178,58    ||  cosP = (sinh-sin Hsin D)/(cosHcosD)
    
PHA (HAO angle)   
5,36    ||  TanPHA = sinP/((sinD+cosP)cosH)
    
PR (pole HAO)   
4,289    ||  sinPR=sinPHsinPHA
    
ET (arc meridian/HAO)   
3,21    ||  tanET=cosHtanPHA
    
H'    ||  H' (incident horizon = B50
4,29    ||  tanH'=sinETtanH
    
PAR (position angle)   
4,67    ||  sinPAR=sinH'/cosD
    
QS, HPR (Az PR)   
86,79    ||  cosQS=sinET
    3,2104838638743
ΔAR' (DA/HAO)   
1,79    ||  sinΔAR'=tanDtangH'
    
OTE, HTQ, ETH (equat/HAO angle)   
85,71    ||  tanOTE=cotH/sinET
    
KO (≠AR □ VE C MA)    Eq for Fig 130 (pl 12) see fig for location and  Explanation of spherical triangles
0,45    ||  KO=AR□ VE - ARC MA
    
A (AET angle)    ||  EA = 90-H
5,36    ||  sinA=sinETsinOTE/sinEA
    
T (angle horizon/OTH)    ||  pole of PRS (=90-H')
85,71    ||  cosT=sinAETsinH
    
[+] TO ΔAR' □ VE    ||  D boreal --> sign [+] = switch for [-]
1,84    ||  sinTO=tanDcotT
-1   
[-] TV ΔAR' C MA    ||  D' boreal-> sign [-] = switch for [-]
1,79    ||  sinTV=tanVZcotT
1   
tasyir    ||  If OS (D) [+], TO ~ sign,  If RK (D') [-], TV ~ sign
0,41    ||  KV=KO – OT – TV
    
VZ    ||  D' (declin of C MA)
22,65   
    
OS    ||  D (declin of □ VE)
23,17   
    
ST    distance ST
23,24    ||  sinST=sinD/sinT
    
TZ    distance TZ
22,72    ||  sinTZ=sinD'/sinT
    
ZS    ≠dist
0,52    ||  If D/D'<0 [-]
    
EPA (EPV, EV) ± ΔAR'    horary angle of □ VE
5,00    ||  if d is [-] ~ ΔAR'
    
IOANNIS ANTONII MAGINI  PRIMI MOBILIS LIBER NONUS QUI AGIT DE DIRECTIONIBUS pp, 214-232 PROBLEMA XVIII p, 230   
    
KV = KO [+] TO [-] TV   
0,41    ||  KV = KO [+] TO ΔAR' □ VE [-] TV ΔAR' C MA
-0,05    ≠AR'
---------------------------------
DIRECTION = TASYIR = 0.41
---------------------------------

2.2 PLACIDUS - AL BIRUNI - AL BATTANI

PLACIDUS        □VE C MA
choose if  sign alt □ VE = sign alt C MA       
Actually, -13,58 / -14,09       
-------------------------------------------       
semiarc    □ VE    55,04
dm            □ VE    0,96
semiarc    C MA    56,03
second. Dist.    C MA    0,98
              
dist from MC or IC    C MA    1,42
 -------------------------------------------       
arc of dir    DIRECTIO DIRECTA    0,44
-------------------------------------------                
semiarc     C MA    56,03
dm            C MA    1,42
semiarc    □ VE    55,04
second. Dist.    □ VE    1,39
       
dist from MC or IC    □ VE    0,96
-------------------------------------------         
arc of dir    DIRECTIO CONVERSA    0,43
------------------------------------------- 

 
DP PLACIDUS        METHOD FOMALHAUD-CHOISNARD       

This is the method which appears in the work of Paul Choisnard "Langage Astral" (Editions Traditionnelles, reed 1963), pp. 149-173. Choisnard bases himself on Ptolemy's process (Tetrabiblos, III, 10 and IV, 11) which Neugebauer analyzes in his "History of Ancient Mathematical Astronomy", pp. 898-899 (see also : Neugebauer - Van Hoesen "Greek Horoscopes", p. 12 in the 'Starter' article where he gives a basic bibliography).

    Plac     direct    Plac conv
-------------------------------------------
sa1/dm1    57,33        39,46
sa2            56,03        55,04
x                0,98        1,39            (x = sa2.dm1 / sa1)
dm²            1,42        0,96
sign            -1        -1                   if the two points are on either side of the meridian, take + ; otherwise -
-------------------------------------------
arc            0,44        -0,43            arc = dm2 ± x
-------------------------------------------    

William Cavendish 1s Earl of Devonshire

 William Cavendish, 1st Earl of Devonshire

27 Dec 1551 JUL    CAL
sunday JUL
 | lat 50° 15' 0" | N 1°25' W
0
---------------------------------
natal (bt) 2 h 30 min
reckoned bt Lat --> lmt 2 h 23 min
tu 2h 32' 51"
tsn 9h 21' 3"
----------------------------------
timezone
Equation of time -0h 6' 24"
ΔT 0h 2' 30"
---------------------------------

THEME

SU is P with a [-6] score
MO is cb with a [-1] score
VE is P and retrograde with a [-21] score
JU is E with a [-8] score

MA is P cb with a [-12] score

SA is Ru with a [1] score


we see below the list of planetary MUNDANE aspects :
---------------------------------------
MO 0 SU Oc        MA 0 SU Oc                 MA 0 MO Or                                                  
---------------------------------------
The best aspect is  [best :su 0° (-0,35) ma]  and the worst aspect is  [worst :mo 0° (-1,74) ma]


The traditionnal almuten (Omar, Ibn Ezra) is JU
we see below the list of dignities for JU :
---------------------------------------
[ term 2 tri 0 rul 0 exn 2 fac 2 ]
[ su 0 mo 0 asc 2 syg 1 pof 2 ]
---------------------------------------
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  171,8 / conj unfortune with caput draconis  but fortunate with cauda draconis if alchocoden is SA or MA
---------------------------------------

hyleg - alchocoden

HYLEG – ALCHOCODEN – domification ,

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 semi-arcs the research of the degrees likely to be considered in the duration of the life.
In the case of William Cavendish, 1st Earl 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 William Cavendish, 1st Earl, it is NOCTURNAL.
In this case, the first point to check is MO. If  MO is well disposed, it can claim 1st stage to be HYLEG.

MO is cb and therefore seems weak, with a dignity score of [-1],
Moreover, when we look for the dignities that appear in the zodiacal inscription of ASC, 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.

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 square aspect of SA.
At the same time, it appears that SA has  dignity of TERM over ASC.
So we have two possibilities with our hypothesis : first choose ASC for hyleg ; second choose the MUNDANE system and try to find another couple of hyleg/alchocoden,
If we choose now ASC we must know that Al Qabisi agree with this choice
In case of ASC is the Hyleg, there is then two candidates to be alchocoden: VE and SA.
First, we have to see which candidate has the most dignity: here, SA has candidate alcho dignities referring to ASC : [EXN]. VE is P and has [TRI] dignity over ASC.
First, SA is linked with ASC by a [square] aspect and a [TERM] dignity,
Moreover, SA is [Ru] and has a power of [-2], SA has a Kadkhudah score of [3]
SA is located at 302,31 °at 3,22° (°) from the precedent (ASC) cusp
------------------------------------------------------

ASC - 

For a direction between ASC and any planet or aspect (zodiacal or mundane),  we must compute ASC OA and m OA (here CSA)the inner circle contains the AR (right ascension) values of ASC and MA or SA.  The outer circle contains the values of the same elements in OA (oblique ascent). Natal ASC is always indicated with a round symbol (o) and the natal significator (MA or SA) with a cross (x). The direction is simulated  by a segment of a circle that ends counter-clockwise at the value in OA. A symbol reflects either a conjunction aspect or a quadrature aspect.

OA ASC = 205,6°
OA SA = 351,1

 orb =  -1,68°

Primary direction

square SA (m) conj VE

	Lat	Dec	AR	MD	SA	HA
VE	5,21 N	-18,12 S	277,20	43,07 N	113,17 N	70,1 E
□SA	0 S	-13,91 S	214,73	105,54 N	107,32 N	1,78 E

MD = meridian distance (from MC if SA f VE  is diurnal or IC if Sa f  is nocturnal) – SA = semi-arc (if f is diurnal, SA f VE 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 VE and m □SA)

ARMILLARY SPHERAE

This armillary sphere presents us with a true stereographic projection of the
---------------------------------
DIRECTION : □SA conj VE
---------------------------------
We see the superior meridian upper the pole 50,25° 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 39,75° and the prime vertical
 - the horizon with ecliptic inclination of 57,17° and the ecliptic pole at 32,83°
 - 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 [50,25]) x tan(dec f [-18,12])
---------------------------------
so DA f VE = 23,17°
---------------------------------
 - Ascensional difference (DA) for m □SA is = sin DA = -tan(lat [50,25]) x tan(dec f [-13,91])
---------------------------------
so DA m □SA = 17,32°
---------------------------------
 - You see  also an almucantar circle for the mundane primary directions : actually the altitude of f VE = -17,96° ; it is therefore almost equal to the altitude of the su and therefore m and f are in mundane conjunction because Δ alt <2° (1,06°), This altitude corresponds to that of point f VE (alt f = -1,06), 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 □SA 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  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 thème céleste en astrologie'. Vigot, Paris, 1917]

DIRECTION : □SA 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 50,25 N
δ VE = -18,12 -
DA-VE = 23,17°
δ □SA =-13,91 -
DA-□SA =17,32°

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 VE is -43,08°. 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.

nocturnal meridian MC = 320,27°
AR VE = 277,2°
AR □SA = 214,73°

 = 113,17°
DM N  VE = -43,07°

For the  significator  □SA altitude (h) =-1,06°. so :

 = 107,32°
DM N  □SA = -254,46°

Then we compute Saf/DMf (so : SA f [ 113,17°] / DM f [ -43,07°])

Sa f / DM f =2,63

and the angle x = SAm x DM f/SA f, so : SA m [ 107,32°] x DM f [ -43,07°]/SA f [ 113,17°]

 x = 40,85°

We find the direction by DMm - x, so : DM m [ -254,46°] ± x [40,85]
We must now have regard to the double ± sign of the last expression; in the case where f (VE) 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 =64,69°
---------------------------------
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 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 [ 107,32°] / DM f [ -254,46°])

Sa m / DM m =1,44

and the angle x = SA f x DM m/SA m, so : SA f [ 113,17°] x DM m [ -254,46°] / SA m [ 107,32°]

x = -78,52°

We find the direction by DM f - x, so : DM f [ -43,07°] ± x [-78,52°]
We must now have regard to the double ± sign of the last expression; in the case where m (□SA) 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 not the case here, so sign = (-)
---------------------------------
arc C =68,22°
---------------------------------
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[-18,12°] x Cot Lat [50,25°]) /sin DM f [43,07°] ± cot DM f  [43,07°]

DAPf = 159,34°

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 [11,79°] x cot f [-18,12°]

pole VE regio  =-31,97°

(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, : (VE) : sin (DAPm/f) = tan [31,98°] x tan [-13,91°]

DAP m/f = -8,9°

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 = 288,98° and AO m = AR m ± DAP m ; idem for sign ; so  AO m□SA = 223,62°

---------------------------------
arc D Regio = -65,36°
---------------------------------
We are now going to compute the converse Regiomontanus direction corresponding to the arc  f VE / 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[-13,91°] x Cot Lat [50,25°]) / Sin DM f [74,46°] ± Cot DM m [-105,54°]

DAP m = 14,88°

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 [17,32°] x Cot m [-13,91°]

pole □SA regio  =-50,24°

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, : (□SA) : Sin (DAP f/m) = Tan[50,24°] x Tan [-18,12°]

DAP f/m = -23,16°

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 = 232° and AO f = AR f ± DAP f ; idem for sign ; so  AO f VE = 300,35°

---------------------------------
arc C Regio = -68,3°
---------------------------------
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 [-18,12°] / cos DM f [-43,07°]

A = -24,13°

Then : B = Lat [50,25°] + A [24,13°]

B = 26,12°

And, Tang C = Cot DM f [-43,07°] x Cos B [26,12°] / Cos A [24,13°]

C = -46,46°

Then, we have Sin pole f = Cos C [-46,46°] x  Sin LG [50,25°]
---------------------------------
So, pole VE regio = 31,98°
---------------------------------
Now go back to (1)

For m □SA; we have : A => Tan m = tan dec m [-13,91°] / cos DM m [-105,54°]

A = -137,24°

Then : B = Lat [50,25°] + A [137,24°]

B = -86,99°

And, Tang C = Cot DM m [-254,46°] x Cos B [-86,99°] / Cos A [137,24°]

C = 178,86°

Then, we have Sin pole m = Cos C [178,86°] x  Sin LG [50,25°]
---------------------------------
So, pole □SA regio = 50,24°
---------------------------------
Now go back to (1)