Perry Matthew

 Perry, Matthew

19 Aug 1969 GREG    CAL
tuesday GREG
 | lat 42° 42' 0" | N 73°7' W
0
---------------------------------
natal (bt) 4 h 47 min
raas-rams :23h 56' 21"
reckoned bt Lat --> lmt 4 h 47 min
tu 8h 47' 0"
tsn 1h 44' 38"
---------------------------------
timezone  : 5 (+W)
DST : 1 (-)
Equation of time -0h 3' 38"
ΔT 0h 0' 49"
---------------------------------
Matthew Langford Perry (August 19, 1969 – October 28, 2023) was an American and Canadian actor. he did work with extreme hangovers and was sometimes sweating and shaking.
Perry became addicted to Vicodin after a jet-ski accident in 1997, and completed a 28-day rehab program at the Hazelden Betty Ford Foundation that year. His weight dropped as low as 128 pounds (58 kg) and he took as many as 55 Vicodin (paracetamol + hydrocodone) pills per day. At age 30, he suffered from alcohol-induced pancreatitis ; in May 2000, he was admitted to Cedars-Sinai Medical Center. In 2018, Perry spent five months in a hospital for a gastrointestinal perforation. During the hospital stay, Perry nearly died after his colon burst from opioid abuse. He spent two weeks in a coma and used a colostomy bag for nine months. Upon being admitted to the hospital, doctors told his family that Perry had a 2% chance of survival. On October 28, 2023, Perry was found unresponsive in his hot tub by his assistant at his home in Pacific Palisades, Los Angeles, and later pronounced dead by officers from the Los Angeles Police Department. [https://en.wikipedia.org/wiki/Matthew_Perry]

 THEME

We observe that one aspect has the force of law on this theme: SA opp MO (astrodynes H/D -20.58). It is coupled to two squares: ASC squ SA and ASC squ MO (-15.39 and -8.98 H/D). We also note a // MA VE (-2.75 H/D).

the SU is located in the last degrees of LEO and cannot be the hyleg.

 The dominant planet is MA (score 7, >5).

Hyleg is ASC and alchocoden MA.

 I preferred to opt for the classic method and not (here) that of Montulmo: in fact Montulmo only gives the MIDDLE years for house IV (i.e. for MA 40 years). Instead of the traditional method giving the GREATER years (65 years). I have already had the opportunity to start testing this method which is elegant but I see no reason - apart from a compromised domification - not to opt for the GREATER years (with a possible penalty of 0.8 or 0.9).

As you can see from the mundane chart, Algol (b Persei) is conjunct SA (domitude regio : 281.35). On the zodiacal chart, Algol is at 55.74° and SA at 38.56°.
 

PRIMARY DIRECTIONS

A - In 2018, the primary directions show a parallel // (m) between MO and MA.

And we still find another parallel // between MA and MO the same year; This is a configuration that we know well: an echo direction.

This type of direction should be closely examined, especially as - and this is the case here - it is accompanied by a radix aspect such as MO opp SA.

B - In 2023, the primary directions show the same first parallel // (m) between MO and MA.

This time, the orb is 1.88.

PROGRESSED (secondary progressions)

The progressed horoscope for the 7/8/2018 (underwent surgery in a Los Angeles hospital to repair a gastrointestinal perforation) :

is calculated for age = 48.967 Y and leads to 4h 2 min local hour, the 7 October 1969. The zodiacal theme shows an OPP MO-R - SA-Pr. (R= radix ; Pr = progressed). Let's not forget that natal MO is F and we have a natal MO-SA OPP.
In addition, we see that SA becomes retrograde from 8/20/69 until the end of the progression period (10/7/69).

SOLI-LUNAR PHASE

This is a method that we find outlined in Vettius Valens [book VI 9] as indicated by Anthony Louis in his blog :

'Vettius Valens had a different notion of annual returns. He felt that the return of the Sun each year was insufficient for forecasting for the year ahead because it omitted the influence of the the Sun’s partner, the Moon. As a result, Valens used a hybrid chart for the annual return which consisted of the positions of the planets when the Sun returned to its natal position each year but these positions were placed in a chart whose Ascendant and houses were determined by the moment the Moon returned to its natal degree during the zodiacal month when the Sun was in its birth sign.' [The Tithi Pravesh and its Monthly and Daily Iterations, November 5, 2022]

Placidus uses it in his Primum mobile (Tabulae primi mobilis cum thesibus et canonibus 1657) and gives the procedure to follow in the XL canon (De Progressionibus, p. 53). A complete example appears in the analysis of the theme of Charles V (Exemplum Primum Caroli V. Austriaci Imperatoris, pp. 59-62).

There is only one site on the internet that does this calculation:

https://horoscopes.astro-seek.com/calculate-planet-revolutions-returns/

but it only gives the soli-lunar return at D0; Placidus continues the progression until maturity. For example in the case of Matthew Perry, if we take the date of August 7, 2018 (serious life-threatening surgery), we must first translate this date into 'life-year equivalent': we find :

48,967    48      Y
11,615      11      M (1)
18,467     18      D
11,213    11      H
                12,79 M

The method of “embolismic lunations” as a predictive technique :

'An embolismic lunation, correctly termed an embolismic month, is an intercalary month, inserted in some calendars, such as the Jewish, when the 11-days' annual excess over twelve lunar months adds up to 30. An arbitrary application of this was used by Placidus, who applied the term Embolismic Lunation, to a Figure cast for the moment of the Moon's return to the same relation to the Sun that it occupied at birth. It was made the basis for judgment concerning the affairs and conditions of the ensuing year of life.' [https://astrologysoftware.com/community/learn/dictionary/lunation.html]

 The solar year does not have a whole number of lunar months (it is about 365/29.5 = 12.37 lunations), so a lunisolar calendar must have a variable number of months in a year. Regular years have 12 months, but embolismic years insert a 13th "intercalary" or "leap" month or "embolismic" month every second or third year [...]. Whether to insert an intercalary month in a given year may be determined using regular cycles such as the 19-year Metonic cycle [...] or using calculations of lunar phases [...]. [wikipedia]

 The whole difficulty therefore comes from the fact that there is no overlap between the solar month (30 D) and the lunar month (synodic month 29.53), consequently between the solar year (365.242) and the lunar year (354.367).

'In Vedic timekeeping, a tithi is a "duration of two faces of moon that is observed from earth", known as milа̄lyа̄ [...] in Nepal Bhasa, or the time it takes for the longitudinal angle between the Moon and the Sun to increase by 12°. In other words, a tithi is a time duration between the consecutive epochs that correspond to when the longitudinal angle between the Sun and the Moon is an integer multiple of 12°. Tithis begin at varying times of day and vary in duration approximately from 19 to 26 hours. Every day of a lunar month is called tithi.' [wikipedia]

We see that the interest of Placidus' method (outlined by Vettius Valens) comes from the fact that the individualisation structure of the progression system is no longer represented by a single point (solar return or lunar return) but by a distance ( in this case the distance between SU radix and MO radix).

In the case of Matthew Perry, we observe:

SU radix = 146°11' (146.19) ♌
MO radix = 217° 39' (217.66) ♏ 

∆ = 71°28' (6 tithi = ROUNDUP(∆/12))

Here is now the way in which Placidus would have proceeded: for 48 full years, 48 embolismic lunations are accomplished in three years after birth but with 33 days less, that is to say 11*3 since the moon covers 12 lunations in 11 days less than a whole year, as indicated in canon XL

'... if you wish to have a ready calculation of the progressions for several years, note that the moon does not complete twelve lunations in one whole year -i.e. a solar year - but in eleven days less. Having therefore the distance from the moon to the sun in the sky of birth, search for this eleventh day before the end of the first year of life and having found it, then know that the progression of twelve years of life is completed. Likewise 22 days before the end of the second year after birth gives the progressions accomplished for 24 years and so on' [De Progressionibus, op. cit., p. 54]

Therefore on August 19, 1972, by removing 33 days, we arrive at July 16 when the moon is at 185,66° from the SCO is at the same distance from the sun as that of the nativity, namely 71.47° and then, the process is thus completed for 36 full years. Then, for the twelve other years elapsed during the twelve embolistic lunations, I arrive at July 16 of this year 1972, MO is then at 182.04 LIB and SO at 113.9 CAN, in order to respect their gap at birth, the one in relation to the other, for the remaining 11 months and 18 days, on the day of the event. I add to this place of MO 28.17 D corresponding to 11.61(1) M:

JD Pr Emb = 11.61 x 30 / (365.24 /29.53) = 28.17 D

where 365.24 is the number of tropical days in a year and 29.53 is the average period for the synodic month of MO.

We find : date forJD 28.17D = 13 august 1972 at 0h 11 (4h 11 TU).

 

 The orb is ± 2°. We find : #(Z) SA-SU, #(Z) MO-SU, square MO-VE and square JU-VE.

Solar return

Do not forget that the solar return is calculated in relation to the location where the subject is located in the year of the solar revolution. The time is determined in TU. In the case of Perry Matthew, we have :

date even : 7 august 2018
birth data : 19 august 1969
so the date of solar return to compute must be : 19 august 2017 because we have a delta of -12 days between 7 august (bd) and date (19 august).

We find that the SU longitude is 146.19° the  18 august 2017 for 16h21 TU.

We find : MA # MO (orb ≤ 2°).

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)

Adolf, Duke of Holstein-Gottorp

25 Jan 1526 JUL    CAL
thursday JUL
 | lat 54° 46' 59" | N 9°26' E
Flensburg, Germany
---------------------------------
natal 23h 30' 0"
lmt 22h 52' 16"
tu 22h 52' 16"
tsn 8h 26' 54"
---------------------------------
timezone
Equation of time 0h 14' 54"
ΔT 0h 3' 3"
---------------------------------

source : Garcaeus, p. 16, Astrologiae Methodus (Bale, 1576)

https://www.astro.com/astro-databank/Adolf,_Duke_of_Holstein-Gottorp
cf. Astrodient : Adolf, b. 25 Jan. 1526 in Flensburg ... born at 11:30 o'clock in the evening.

We note 1 hour difference between Garcaeus and Johannes Peter Frederik Kønigsfeldt ["Genealogisk-historiske tabeller over de nordiske rigers kongeslægter" by Johannes Peter Frederik Kønigsfeldt, Danske historiske forening, Copenhagen (B. Lunos bogtrykkeri, 1856), p. 51, quoted by Sy Scholfield]

 

HOROSCOPE

Adolf of Denmark or Adolf of Holstein-Gottorp (25 January 1526 –1 October 1586) was the first Duke of Holstein-Gottorp from the line of Holstein-Gottorp of the House of Oldenburg.

 

dominance

almuten

dignities

hyleg - alchocoden

alchocoden diagram

primary directions

zodiacal

 

mundane

 

An example of a quasi-integral graphic presentation. Attention is drawn to the alchocoden diagram after Montulmo, which was edited by Robert Hand around 1992 (Coreldraw 4.0)... Here Libreoffice Calc is used (7.4.7.2).

ARTHUR Chester

 ARTHUR Chester A.

05 Oct 1829 GREG    CAL
monday GREG
 | lat 44° 47' 59" | N 72°57' W
Fairfield (Vermont)
---------------------------------
natal 6h 8' 0"
lmt 1h 16' 12"
tu 10h 59' 47"
tsn 7h 3' 24"
---------------------------------
timezone
Equation of time -0h 11' 30"
ΔT 0h 0' 14"
---------------------------------
source : https://www.astro.com/astro-databank/Arthur,_Chester_A.
Rodden Rating A
---------------------------------

THEME

SU is F with a [-10] score
MO is D with a [-12] score
VE is Fa  with a [1] score
JU is Ru with a [1] score

MA is 0 with a [-3] score

SA is D with a [-6] score

American President of the US. 1881-85 after the death of James A. Garfield. Honest, efficient, dignified and elegant, Arthur was called "The Gentleman Boss." He formerly taught school a few years before becoming a lawyer in 1853. Arthur was a Republican delegate in 1860; State Officer; Custom House Collector; and Vice President.

Arthur left office in 1885 and returned to his New York City home. Two months before the end of his term, several New York Stalwarts approached him to request that he run for United States Senate, but he declined, preferring to return to his old law practice at Arthur, Knevals & Ransom. His health limited his activity with the firm, and Arthur served only of counsel. He took on few assignments with the firm and was often too ill to leave his house. He managed a few public appearances until the end of 1885.
After spending the summer of 1886 in New London, Connecticut, he returned home where he became seriously ill, and on November 16, ordered nearly all of his papers, both personal and official, burned.[214][q] The next morning, Arthur suffered a cerebral haemorrhage and never regained consciousness. He died the following day, on November 18, at the age of 57.
---------------------------------------
we see below the list of ZODIACAL aspects :
---------------------------------------
           Or  JU 60 SU Oc  SA 60 SU   ME 60 MO Oc                                            SA 90 VE Oc          SA 120 JU Oc
---------------------------------------
The best aspect is  [best :mo 60° (0,6) me]  and the worst aspect is  [worst :ve 90° (-1,27) sa]


The traditional almuten (Omar, Ibn Ezra) is SA
we see below the list of dignities for SA :
---------------------------------------
[ term 1 tri 3 rul 0 exn 3 fac 1 ]
[ su 2 mo 0 asc 2 syg 4 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)

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 ARTHUR Chester A. 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 ARTHUR Chester A., 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 F 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 that we doubt to take SU as hyleg, we are left with MO we find aspect to match with the 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 sextil aspect of SA.
At the same time, it appears that SA has  dignity of TRI over ASC.
First, SA is linked with ASC by an sextil aspect and a TRI dignity,
However, SA is D and has a power of [-6], SA has a Kadkhudah score of [1]
SA is located at 135,53 °at 4,96° (°) from the next (succ) cusp
Now, we have to take account of the radix zodiacal aspects,
------------------------------------------------------
SU 60 SA: 9,5   VE 90 SA: -8  JU 120 SA: 12
------------------------------------------------------
Without any change, we find with SA as Kadhkhudah : Y = 57 as a result of SA GREATER years
But as SA is TRI, 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 -11,4
------------------------------------------------------
So, zodiacal Y =59,21
however, SA is located within 5° of the point (MC). In this case, we are led to modify its value which, otherwise, would be 57 Y.

To do this, the procedure is not unequivocal but one of the most logical seems to me to be the one mentioned by Auger Ferrier in ‘Jugements astronomiques sur les nativités’, Rouen, 1583 (pp, 39-51 and notably pp, 43-48). Note that Auger Ferrier's comments appear directly related to those of Montulmo in his’ De Nativitatum liber praeclarisimus’ (Nuremberg, 1540), cap IV & VII. Book translated by Robert Hand (‘On the Judgment of Nativities’, part 1 & 2, Project Hindsight, vol X)
the years of life are identified for the [ang] and [cad] houses relative to the alchocoden.

ang = 57
succ = 43
we take the difference = 14
take the 1/5 of this difference = 2,8
then take the difference between 5 and the actual position of the point = 0,05 (4,95)
take the rule of three = 0,05
Then we add the ang Y 57 and 0,05 = 56,95
we must add [ domSA (295,05) - cusp (270) ] x [ cusp ang (57) - cusp succ 43) ]/5/5
So, we add to Y : Δ = 0,14
Now, we have to take account of the radix mundane aspects,
SU 60 SA: 9,5     JU 120 SA: 12   minus alcho dy (4,95)


SA appears to be D and his power is -6
Given that SA is D, we need to remove 1/5 from Y =67,24 so : -11,4 Y
Y=   55,84

PRIMARY DIRECTION

□MO conj SA (mundane direct)

	Lat	Dec	AR	MD	SA	HA
SA	0,73 N	16,89 N	138,23	32,38 D	107,55 D	75,17 E
□MO	0 S	-3,3 S	187,64	-81,79 D	86,72 D	168,51 E

DIRECTION : □MO conj SA

---------------------------------
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 44,8 N
δ SA = 16,89 +
DA-SA = 17,55°
δ □MO =-3,3 -
DA-□MO =3,28°

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 SA is 51,09°. important note: the SA and DM of the two points are always counted diurnal if the first point (here SA) is above the horizon even if the second is below. They are counted nightly if the first point (SA) 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 SA is diurnal, and from the nocturnal meridian if it is nocturnal.

diurnal meridian MC = 105,85°
AR SA = 138,23°
AR □MO = 187,64°

SA D (d+) SA=107,55°
DM D  SA=32,38°

For the  significator  □MO altitude (h) =3,47°. so :

=86,72°
DM D □MO=-81,79°

Then we compute Saf/DMf (so : SA f [107,55°] / DM f [32,38°])

Sa f / DM f =3,32

and the angle x = SAm x DM f/SA f, so : SA m [86,72°] x DM f [32,38°]/SA f [107,55°]

 x = 26,11°

We find the direction by DMm - x, so : DM m [-81,79°] ± x [26,11]
We must now have regard to the double ± sign of the last expression; in the case where f (SA) and m (□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 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 =55,68°
---------------------------------
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 □MO) and the f point is a planet or an axis, (here SA)

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 [86,72°] / DM f [-81,79°])

Sa m / DM m =-1,06

and the angle x = SA f x DM m/SA m, so : SA f [107,55°] x DM m [-81,79°] / SA m [86,72°]

x = -101,44°

We find the direction by DM f - x, so : DM f [32,38°] ± x [-101,44°]
We must now have regard to the double ± sign of the last expression; in the case where m (□MO) and f (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 DM f and x. This is not the case here, so sign = (-)
---------------------------------
arc C =69,06°
---------------------------------
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 (SA) : cot DAP f = (cot de f x cot lat) / in DM f ± cot DM f, i,e, :  cot (DAP f) = (Cot dec f[16,89°] x Cot Lat [44,8°]) /sin DM f [32,38°] ± cot DM f  [32,38°]

DAPf = 7,33°

We find the pole of f (SA) by formula : tan(pole f) = sin (DAP f) x cot (dec f) i,e, tan(pole f) = tan f [7,33°] x cot f [16,89°]

pole SA regio  =22,81°

(1) We need now the DAP of m (□MO) under the pole of f, sin (DAP m) = tan (pole f) x tan (DEC m), i,e, : (SA) : sin (DAPm/f) = tan [22,8°] x tan [-3,3°]

DAP m/f = -1,39°

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 SA = 145,56° and AO m = AR m ± DAP m ; idem for sign ; so  AO m□MO = 189,03°

---------------------------------
arc D Regio = -58,13°
---------------------------------
We are now going to compute the converse Regiomontanus direction corresponding to the arc  f SA / p □MO

First, compute the ascensional difference under m (□MO) : cot DAPm = (cot dec m x cot lat)/sin DM m ± cot DM m, i,e, :  Cot(DAP m) = (Cot decm[-3,3°] x Cot Lat [44,8°]) / Sin DM f [81,79°] ± Cot DM m [81,79°]

DAP m = 176,73°

We find the pole of m (□MO) by formula : Tan(pole m) = Sin (DAP m) x Cot (dec m) i,e, Tan(pole m) = Sin m [176,73°] x Cot m [-3,3°]

pole □MO regio  =-44,7°

We need now the DAP of f (SA) under the pole of m, Sin (DAP f) = Tan (pole m) x Tan (DEC f), i,e, : (□MO) : Sin (DAP f/m) = Tan[44,69°] x Tan [16,89°]

DAP f/m = 17,48°

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 □MO = 191° and AO f = AR f ± DAP f ; idem for sign ; so  AO f SA = 155,71°

---------------------------------
arc C Regio = -70,17°
---------------------------------
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 [16,89°] / cos DM f [32,38°]

A = 19,78°

Then : B = Lat [44,8°] + A [-19,78°]

B = 25,02°

And, Tang C = Cot DM f [32,38°] x Cos B [25,02°] / Cos A [-19,78°]

C = 56,63°

Then, we have Sin pole f = Cos C [56,63°] x  Sin LG [44,8°]
---------------------------------
So, pole SA regio = 22,8°
---------------------------------
Now go back to (1)

For m □MO; we have : A => Tan m = tan dec m [-3,3°] / cos DM m [81,79°]

A = -21,99°

Then : B = Lat [44,8°] + A [21,99°]

B = 66,79°

And, Tang C = Cot DM m [81,79°] x Cos B [66,79°] / Cos A [21,99°]

C = -3,51°

Then, we have Sin pole m = Cos C [-3,51°] x  Sin LG [44,8°]
---------------------------------
So, pole □MO regio = 44,69°
---------------------------------
Now go back to (1)

ARMILLARY SPHERAE

This armillary sphere presents us with a true stereographic projection of the :
---------------------------------
DIRECTION : □MO conj SA
---------------------------------
We see the superior meridian upper the pole 44,8° 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 45,2° and the prime vertical
 - the horizon with ecliptic inclination of 68° and the ecliptic pole at 22°
 - 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 SA is = sin DA = -tan(lat [44,8]) x tan(dec f [16,89])
---------------------------------
so DA f SA = 17,55°
---------------------------------
 - Ascensional difference (DA) for m □MO is = sin DA = -tan(lat [44,8]) x tan(dec f [-3,3])
---------------------------------
so DA m □MO = 3,28°
---------------------------------
 - You see  also an almucantar circle for the mundane primary directions : actually the altitude of f SA = 3,42° ; it is therefore almost equal to the altitude of the su and therefore m and f are in mundane conjunction because Δ alt <2° (-3,47°), This altitude corresponds to that of point f SA (alt f = 51,09), 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 □MO with dashed line (between equator and equinoctial colure) to design the m DA (see above) ; for point f SA (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]

 ---------------------------------

RUDOLF II Emperor

18 Jul 1552 JUL    CAL
monday JUL
 | lat 48° 13' 0" | N 16°22' E
Vienna, Austria
---------------------------------
natal 19h 0' 0"
lmt 17h 54' 31"
tu 17h 54' 31"
tsn 15h 24' 52"
---------------------------------
timezone
Equation of time 0h 5' 35"
ΔT 0h 2' 28"
---------------------------------
source = https://www.astro.com/astro-databank/Rudolf_II,_Holy_Roman_Emperor

Pierre Brind’Amour, Nostradamus astrophile (Ottawa, n.d.), pp.377–80, 452 [Nostradamus astrophile. Les astres et l’astrologie dans la vie et l’œuvre de Nostradamus, Paris, Klincksieck, 1993 in chapter 11, note 1, the Magic Circle of Rudolf II, Peter Marshall, Bloomsbury, 2006]. The German manuscript of Rudolf’s horoscope, completed in 1564, is held at the Kungliga Biblioteke, Stockholm, v., J.1695 ; In the central cartouche of the horoscope drawing [fol. 2r] the time is given as “H. VI. M. XLV” (6 hours, 45 minutes) [http://nostredame.chez-alice.fr/nerg1.html#ref3]
Note : Tycho Brahe indicates the day of birth: July 18 (but not the time of birth) in Opera omnia, tome 3, edidit I.L.E. Dreyer, p. 382, 1913

Rudolf II (18 July 1552 – 20 January 1612) was Holy Roman Emperor (1576–1612), King of Hungary and Croatia (as Rudolf I, 1572–1608), King of Bohemia (1575–1608/1611) and Archduke of Austria (1576–1608). He was a member of the House of Habsburg.
Rudolf died in 1612, nine months after he had been stripped of all effective power by his younger brother, except the empty title of Holy Roman Emperor, to which Matthias was elected five months later.

Natal chart

THEME

SU is Ru with a [14] score
MO is Ru with a [7] score
VE is P  with a [-11] score
JU is Fa cb with a [1] score

MA is Fa with a [-1] score

SA is Fa with a [-6] score


we see below the list of ZODIACAL aspects :
---------------------------------------
                                     SA 120 MO Oc                                JU 60 MA Or        
---------------------------------------
The best aspect is  [best :mo 120° (5,9) sa]  and the worst aspect is  [worst :ma 60° (0,38) ju]


The traditionnel almuten (Omar, Ibn Ezra) is MA
we see below the list of dignities for MA :
---------------------------------------
[ term 1 tri 0 rul 0 exn 2 fac 1 ]
[ su 0 mo 2 asc 1 syg 1 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 MA

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

It is rare that in a theme we immediately find the figure of the hyleg. It is also rare that one does not have the choice between several possibilities. Precisely, in this theme which turns out to be complex in this respect, there are three possibilities which are offered. We will analyse them.

1)- hyleg = SA, dominante planet and MO alchocoden in ZODIACAL system

The search for the ruling planet is explained by Ptolemy in Tetrabiblos III,10. This planet must have at least three dignities out of five [cf Ptolemy, Tetrabiblos, tr. Robbins F.E., Heinemann, London, 1940, p. 277]

The table below gives the synthesis of all the elements in our possession.

DOMINANCE	Diurnal (*)	Nocturnal (*)	House (**)		aspect D	aspect N	Σ D		score Lilly	dignities (***)
	0	2	6	0	2	1	2	ME	1	Fa -- r
SA	2	2	6	0	0	0	2	VE	4	P --
	2	3	5	0	0	0	2	MA	13	Fa --
	2	2	7	1	0	0	3	JU	0	Fa cb --
	4	2	1	1	0	1	5	SA	6	Fa -- r

(*) if diurnal, dignities for SU, ASC, sygyzy ; if nocturnal, dignities for MO, POF, sygyzy
(**) houses : 1, 7, 9, 10
(***) (P)eregrine – (D)etrimental – (F)all – (Ru)ler – (E)xalt – (Ori)entation – (R)etrograde - (T)rip - (Fa)ce – (te)rm

JU is combust ; JU and SA are FA ; SA is r.

'The greatest debility, which can happen to a pianet, is combustion, although both retrogradation and several other (conditions] are very much wont to impede other planets, as you will plainly see in what follows. The combustion of the planets is recognised by moiety of their orbs. And indeed when they are distant from the Sun less then the moiety of their orbs, or precisely that much before and after, the
[condition] is called combust and a complete weakness of power. This is the moiety of orb; SA & JU 9 degrees; MA 8 VE9 & ME, 7 degrees; MO 12 degrees: SU 15 degrees.'

[Schoner, Joannis Schoneri Carolostadii 'Opusculum astrologicum', Canon XVII, The Second Part of the Introduction Treats Compendiously of Astrology., tr Robert Hand, Project Hindsight, p. 13]

We highlight that the planet which has the most dignities is VE, VE which is peregrine... There is a kind of paradox there, like Rudolf II who was not made to be an emperor but an alchemist or an astrologer ... In the same vein we find JU combust even though SU is in his domicile but "only" in house VII; VE is in house VI as well as MO also in his domicile (VE and MO are both cadent). Sa is the true ruling planet in house I, in zodiacal trine with MO.

Anyway, only SA is likely to fulfil the conditions to represent the ruling planet. The table below is the summary of hyleg and alchocoden validation :

A word about continuity correction regarding MO, having to do with being within 5° (in the mundane REGIOMONTANUS system) of the nearest cusp (cadent).

To do this, the procedure is not unequivocal but one of the most logical seems to me to be the one mentioned by Auger Ferrier in 'Jugements astronomiques sur les nativités', Rouen, 1583 (pp, 39-51 and notably pp, 43-48)
the years of life are identified for the cad and succ houses relative to the alchocoden.
cad = 25
ang = 66
we take the difference = -41
take the 1/5 of this difference = -8,2
then take the difference between 5 and the actual position of the point = -23,4 (28,4)
take the rule of three = -38,38
Then we add the cad Y 25 and -38,38 = 63,38
We must add [1-(dom MO (151,6) - cusp (150)/5)]/ x [ cusp ang (25) - cusp succ 66) ]
So, we add to Y : Δ = 27,88

Note that this Δ changes according to the used system of houses. With CAMPANUS, Δ = 0 (MO in VI > 5°), and with PLACIDUS, there is a zodiacal conjunction between the cusp of VI and MO (Mo in V > 5°).

2)- now, we can try SU as hyleg and MA as alchocoden (in MUNDANE system).

Unlike the previous chart, here we see the MUNDANE aspects. They are marked by the presence of a sextil between SU and MA. We note that in this particular case, MA has no dignity over SU; it is SU which has two proper dignities over itself (TRI and RUL).

As I have observed many times before, the MUNDANE system alternative looks interesting; the main problem comes from the fact that the different results according to the house systems oblige to make a choice which must be maintained over a long series of chart ; I consider that the REGIOMONTANUS system represents a middle choice between the CAMPANUS system and the PLACIDUS system.

Primary directions

1)- SU conj square SA (true converse)

	Lat	Dec	AR	MD	SA	HA
SU	-	19 N	127,62	103,61 D	112,67 D	9,06 W
□SA	0 S	21,69 N	66,21	-165 D	116,43 D	281,43 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 □SA)    

DIRECTION : □SA conj SU
---------------------------------
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 48,22 N
δ SU = 19 +
DA-SU = 22,67°
δ □SA =21,69 +
DA-□SA =26,43°

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 SU is 5,42°. important note: the SA and DM of the two points are always counted diurnal if the first point (here SU) is above the horizon even if the second is below. They are counted nightly if the first point (SU) 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 SU is diurnal, and from the nocturnal meridian if it is nocturnal.

diurnal meridian MC = 231,22°
AR SU = 127,61°
AR □SA = 66,21°

SA D (d+) SU=112,67°
DM D  SU=283,61°

For the  significator  □SA altitude (h) =-18,81°. so :

SA D (δ+) □SA=116,43°
DM D □SA=-165°

Then we compute Saf/DMf (so : SA f [112,67°] / DM f [283,61°])

Sa f / DM f =0,4

and the angle x = SAm x DM f/SA f, so : SA m [116,43°] x DM f [283,61°]/SA f [112,67°]

 x = 107,08°

We find the direction by DMm - x, so : DM m [-165°] ± x [107,08]
We must now have regard to the double ± sign of the last expression; in the case where f (SU) 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 =57,92°
---------------------------------
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 SU)

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 [116,43°] / DM f [-165°])

Sa m / DM m =4,24

and the angle x = SA f x DM m/SA m, so : SA f [112,67°] x DM m [-165°] / SA m [116,43°]

x = 15,88°

We find the direction by DM f - x, so : DM f [283,61°] ± x [15,88°]
We must now have regard to the double ± sign of the last expression; in the case where m (□SA) and f (SU) 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 =60,5°
---------------------------------
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 (SU) : cot DAP f = (cot de f x cot lat) / in DM f ± cot DM f, i,e, :  cot (DAP f) = (Cot dec f[19°] x Cot Lat [48,22°]) /sin DM f [283,61°] ± cot DM f  [283,61°]

DAPf = 161,05°

We find the pole of f (SU) by formula : tan(pole f) = sin (DAP f) x cot (dec f) i,e, tan(pole f) = tan f [22,39°] x cot f [19°]

pole SU regio  =47,89°

(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, : (SU) : sin (DAPm/f) = tan [47,88°] x tan [21,69°]

DAP m/f = 26,1°

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 SU = 150° and AO m = AR m ± DAP m ; idem for sign ; so  AO m□SA = 92,32°

---------------------------------
arc D Regio = 57,68°
---------------------------------
We are now going to compute the converse Regiomontanus direction corresponding to the arc  f SU / 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[21,69°] x Cot Lat [48,22°]) / Sin DM f [15°] ± Cot DM m [15°]

DAP m = 4,61°

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 [168,58°] x Cot m [21,69°]

pole □SA regio  =26,47°

We need now the DAP of f (SU) under the pole of m, Sin (DAP f) = Tan (pole m) x Tan (DEC f), i,e, : (□SA) : Sin (DAP f/m) = Tan[26,47°] x Tan [19°]

DAP f/m = 9,87°

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 □SA = 78° and AO f = AR f ± DAP f ; idem for sign ; so  AO f SU = 137,48°

---------------------------------
arc C Regio = 59,84°
---------------------------------
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 [19°] / cos DM f [-103,61°]

A = 124,35°

Then : B = Lat [48,22°] + A [-124,35°]

B = -76,13°

And, Tang C = Cot DM f [-103,61°] x Cos B [-76,13°] / Cos A [-124,35°]

C = 174,13°

Then, we have Sin pole f = Cos C [174,13°] x  Sin LG [48,22°]
---------------------------------
So, pole SU regio = -47,88°
---------------------------------
Now go back to (1)

For m □SA; we have : A => Tan m = tan dec m [21,69°] / cos DM m [15°]

A = 22,38°

Then : B = Lat [48,22°] + A [-22,38°]

B = 70,6°

And, Tang C = Cot DM m [-165°] x Cos B [70,6°] / Cos A [-22,38°]

C = 53,29°

Then, we have Sin pole m = Cos C [53,29°] x  Sin LG [48,22°]
---------------------------------
So, pole □SA regio = 26,47°
---------------------------------
Now go back to (1)

2) SA conj MA

This direction between the two 'mali and infortunae' may seem surprising to consider; however, I remind you that if we consider SA as Hyleg (see above) or MA as alchocoden, there is nothing illogical.

	Lat	Dec	AR	MD	SA	HA
MA	-0,11 S	22,46 N	72,94	21,72 N	62,44 N	40,72 W
CSA	-1,78 S	-12,32 S	334,99	-76,23 N	104,15 N	180,38 E

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 □SA) 

DIRECTION : CSA conj MA
---------------------------------
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 48,22 N
δ MA = 22,46 +
DA-MA = 27,56°
δ CSA =-12,32 -
DA-CSA =14,15°

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 MA is -16,69°. important note: the SA and DM of the two points are always counted diurnal if the first point (here MA) is above the horizon even if the second is below. They are counted nightly if the first point (MA) 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 MA is diurnal, and from the nocturnal meridian if it is nocturnal.

nocturnal meridian MC = 51,22°
AR MA = 72,94°
AR CSA = 334,99°

SA N (d+) MA = 62,44°
DM N  MA = -21,72°

For the  significator  CSA altitude (h) =-18,3°. so :

 = 104,15°
DM N  CSA = -76,23°

Then we compute Saf/DMf (so : SA f [ 62,44°] / DM f [ -21,72°])

Sa f / DM f =2,87

and the angle x = SAm x DM f/SA f, so : SA m [ 104,15°] x DM f [ -21,72°]/SA f [ 62,44°]

 x = 36,23°

We find the direction by DMm - x, so : DM m [ -76,23°] ± x [36,23]
We must now have regard to the double ± sign of the last expression; in the case where f (MA) and m (CSA) 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 =112,46°
---------------------------------
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 CSA) and the f point is a planet or an axis, (here MA)

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 [ 104,15°] / DM f [ -76,23°])

Sa m / DM m =1

and the angle x = SA f x DM m/SA m, so : SA f [ 62,44°] x DM m [ -76,23°] / SA m [ 104,15°]

x = -45,7°

We find the direction by DM f - x, so : DM f [ -21,72°] ± x [-45,7°]
We must now have regard to the double ± sign of the last expression; in the case where m (CSA) and f (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 DM f and x. this is the case here : so, signe = (+)
---------------------------------
arc C =67,43°
---------------------------------
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 (MA) : cot DAP f = (cot de f x cot lat) / in DM f ± cot DM f, i,e, :  cot (DAP f) = (Cot dec f[22,46°] x Cot Lat [48,22°]) /sin DM f [21,72°] ± cot DM f  [21,72°]

DAPf = 6,83°

We find the pole of f (MA) by formula : tan(pole f) = sin (DAP f) x cot (dec f) i,e, tan(pole f) = tan f [163,28°] x cot f [22,46°]

pole MA regio  =34,83°

(1) We need now the DAP of m (CSA) under the pole of f, sin (DAP m) = tan (pole f) x tan (DEC m), i,e, : (MA) : sin (DAPm/f) = tan [34,83°] x tan [-12,32°]

DAP m/f = -8,74°

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 MA = 89,66° and AO m = AR m ± DAP m ; idem for sign ; so  AO mCSA = 343,73°

---------------------------------
arc D Regio = 123,41°
---------------------------------
We are now going to compute the converse Regiomontanus direction corresponding to the arc  f MA / p CSA

First, compute the ascensional difference under m (CSA) : cot DAPm = (cot dec m x cot lat)/sin DM m ± cot DM m, i,e, :  Cot(DAP m) = (Cot decm[-12,32°] x Cot Lat [48,22°]) / Sin DM f [103,77°] ± Cot DM m [283,77°]

DAP m = 14,15°

We find the pole of m (CSA) by formula : Tan(pole m) = Sin (DAP m) x Cot (dec m) i,e, Tan(pole m) = Sin m [167,36°] x Cot m [-12,32°]

pole CSA regio  =-45,06°

We need now the DAP of f (MA) under the pole of m, Sin (DAP f) = Tan (pole m) x Tan (DEC f), i,e, : (CSA) : Sin (DAP f/m) = Tan[45,06°] x Tan [22,46°]

DAP f/m = 24,48°

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 CSA = 348° and AO f = AR f ± DAP f ; idem for sign ; so  AO f MA = 97,42°

---------------------------------
arc C Regio = 60,83°
---------------------------------
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 [22,46°] / cos DM f [21,72°]

A = 23,99°

Then : B = Lat [48,22°] + A [-23,99°]

B = 72,21°

And, Tang C = Cot DM f [21,72°] x Cos B [72,21°] / Cos A [-23,99°]

C = -40,01°

Then, we have Sin pole f = Cos C [-40,01°] x  Sin LG [48,22°]
---------------------------------
So, pole MA regio = 34,83°
---------------------------------
Now go back to (1)

For m CSA; we have : A => Tan m = tan dec m [-12,32°] / cos DM m [283,77°]

A = -42,53°

Then : B = Lat [48,22°] + A [42,53°]

B = 5,69°

And, Tang C = Cot DM m [-76,23°] x Cos B [5,69°] / Cos A [42,53°]

C = -18,31°

Then, we have Sin pole m = Cos C [-18,31°] x  Sin LG [48,22°]
---------------------------------
So, pole CSA regio = 45,07°
---------------------------------
Now go back to (1)