LUNI-SOLAR PHASE (2) - Charles V, Holy Roman Emperor

 Charles V, Holy Roman Emperor 

- Luni -Solar phase

Astrologiae ratione and experientia refutatae liber ... by Hemminga, Sixtus (Antverpia, 1583) p. 29.

 Charle Quint
24 Feb 1500 JUL    CAL
monday JUL
radix theme | lat 51° 2' 59" | N 3°43' E E
- LMT -
---------------------------------
natal (bt) 13 h 30 min
raas-rams :23h 48' 9"
reckoned bt Lat --> lmt 4 h 0 min
tu 4h 15' 28"
tsn 14h 49' 16"
---------------------------------
timezone  : 0 
DST : 0 (-)
Equation of time 0h 14' 51"
ΔT 0h 3' 18"
---------------------------------

Luni-Solar phase

We find in the Primum mobile of Placidus the first article devoted to luni-solar progressions. The principle is exposed to Canon XL: Progressionibus and the first exemple is given : Index Exemplarum: Caroli V. Austriaci Imperatoris (pp. 59-63) in Tabulae Primi Mobilis etc. (Patavii Mdclvii). 

Here is the "modern" horoscope of Caroli V. I remind you that the aspects between planets and ASC are indicated directly in OA and those between planets and MC are indicated directly in AR. The aspects between planets are indicated in mundo (Regiomontanus).

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). We have redone the placidus calculations with the text below which is closer to its style: Note that Anthony Louis only gives the soli-lunar return at D0; Placidus continues the progression until end of process (i.e. the even). For example in the case of Charle Quint, if we take the date of 21 Sep 1558, we must first translate this date into 'life-year equivalent': we find :             ---------------------------------------             EVEN    58,5762012305913    58    Y                 6,91441476709571    6    M                27,4324430128712    27    D                10,3786323089089    10    H                                             22,72    M ---------------------------------------             The method of “embolismic lunations” as a predictive technique :   See : Tabulae Primi Mobilis,,, Placido De Titis, Patavii, MDCLVII              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 judgement 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 luni-solar 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).             We find in the literature another method which is similar to that of the solilunar phase: it is the tertiary directions. We find a critique of it in “Les Moyens de pronostic en Astrologie” by Max DUVAL [ed Traditionnelles, 1986, pp. 67-71] and a complete analysis in "A close look at tertiary progressions" by Elva Howson & Jack Nichols, [Considerations, vol XI-4, 1996; pp 3-12]- https://archive.org/details/considerations-21-1/considerations-11-4/page/n1/mode/2up             In the case of Charle Quint, we observe:                          SU radix = 344° 00' 1" (344° PIS)                          MO radix = 276° 56' 37"° (276,94° CAP)                          ∆ = |67° 3' 24"| (67,06° ) [ 5 tithi = ROUNDUP (∆/12)]                          Here is now the way in which Placidus would have proceeded: for 48 full years, 44 embolismic lunations are accomplished in 10 years after birth but with 33 days less, that is to say 11*4 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 24 Feb 1504, by removing 44 days, we arrive at 11 January 1504 [,,,] and then, the process is completed for 44 full years. Then, for the 10 other years elapsed during the twelve embolismic lunations, I arrive at 29 October 1504, for the remaining 9 months and 21 days. I compute the tithi (exact distance between SU and MO radix) for the last time : the date of Embolismic Progression J0 is : 2 November 1504 at 18h 42min tu. Thereafter, i add to this date 17,02 d corresponding to 6,914M [see EVEN] :                          JD Pr Emb = 6,91 x 30 / (365.24 /29.53) = 17,02 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                           trop days 365,242220375371 (1)                          syn month = 29,5305877633503 (2)                          where T = (JD-2451545)/36525                          In the present case JD = 2268986,5                          so, T = -4,99817932922656 (see formula 1 and 2)                          Finally, we find : date for J17,02D = 19 November 1504 at 19h 4min   local (19h 4min  TU).  Note that 1504 is a leap year ;  so we find the moon's longitude of Placidus by intercaling 1 supplementary day.                        ---------------------------------------             (1) exact value for number of tropical days is : 365,2421896698-0,00000615359*T-0,000000000729*T^2+0,000000000264*T³             (2) exact value for synodic month is : 29,5305888531+0,00000021621*T-0,000000000364*T^2             The outer circle (in red) represents the arrangement of the planets and houses during the lunisolar cycle; the inner circle (in gray) represents the natal horoscope.             Some choices (in this case difficulties) are available to us: 1)- Take the planets and longitude houses (zodiacal method) or in domitude (mundane method); 2)- Choose the date D0 (start of the luni-solar cycle) or the due date (here D18). It seemed more 'natural' to choose the zodiacal method; Experience leads to favouring D0 mode for chronic disease and rather the due date of the current cycle for an accident or acute disease potentially involving the vital prognosis. Only in-depth studies will be able to enlighten us on this ... We see here that we have choosen the D0 :   Charles V has been sick for many years (gout attacks) and had retired to the Yuste monastery, Caceres. In August 1558, Charles was taken seriously ill with what was diagnosed in the twenty-first century as malaria. He died in the early hours of the morning on 21 September 1558. we find the following aspects (R = radix): - {♀,☉} ☍ ♄R  ( ♄ being the alchocoden) - MC ◻ ♄R (mundane ◻ with lunar conjunction) - ♃ ◻ ♄R (♃ being the dominant -but weak - planet) We see here the progressions from Placidus (Primum mobile, p. 62) : with our result : We find at D18: - {♀♂} ◻ ☉R - ♃ ◻ ♄R (see D0) - ☉ ◻ ♃R The result to take in account is : ♂ ◻ ☉R. These results recall those we have highlighted for the previous theme.

LUNI-SOLAR PHASE (1) - Felipe III Rex Hispania

 LUNISOLAR PHASE (1)

---------------------------------
Felipe III
06 Sep 1581 JUL    CAL
wednesday JUL
 | lat 40° 23' 59" | N 3°41' W
0
---------------------------------
natal (bt) 13 h 30 min
raas-rams :0h 5' 14"
reckoned bt Lat --> lmt 1 h 50 min
tu 2h 4' 44"
tsn 1h 27' 9"
---------------------------------
timezone  : 0
DST : 0 (-)
Equation of time 0h 5' 14"
ΔT 0h 2' 10"
---------------------------------

source : Andrea Argoli, De diebus criticis et aegrorum Decubitu, p. 166, Patavii, MDCLII (Padua, Pauli Frambotti, 1653)

Placidus writes in his Primum mobile that Philip III died on March 31, 1621, aged 42 years and 11 months [in fact he died at the age of 40, exactly 39.56, born 1581.68, died 1621.25]. We note - as is quite common with Placidus - a discrepancy between the times he gives and those of his colleagues: in Placidus, the time of birth is 14:47 PM; in Argoli 14:21 PM.

Here is the "modern" horoscope of Felipe III. I remind you that the aspects between planets and ASC are indicated directly in OA and those between planets and MC are indicated directly in AR. The aspects between planets are indicated in mundo (Regiomontanus).

LUNI-SOLAR 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 end of process (i.e. the even). For example in the case of Felipe III, if we take the date of 31 Mar 1621, we must first translate this date into 'life-year equivalent': we find :            
---------------------------------------            
EVEN    42,9605353483002    42    Y
                11,5264241796021    11    M
                15,7927253880635    15    D
                19,0254093135241    19    H
                                                   1,52    M
---------------------------------------            
The method of “embolismic lunations” as a predictive technique :  
See : Tabulae Primi Mobilis,,, Placido De Titis, Patavii, MDCLVII  
            
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 judgement 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 luni-solar 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).            
We find in the literature another method which is similar to that of the soli-lunar phase: it is the tertiary directions. We find a critique of it in “Les Moyens de pronostic en Astrologie” by Max DUVAL [ed Traditionnelles, 1986, pp. 67-71] and a complete analysis in "A close look at tertiary progressions" by Elva Howson & Jack Nichols, [Considerations, vol XI-4, 1996; pp 3-12]- https://archive.org/details/considerations-21-1/considerations-11-4/page/n1/mode/2up        
In the case of Felipe III, we observe:            
            
SU radix = 172° 56' 25" (172,94° VIR)            
            
MO radix = 262° 05' 2"° (262,08° SAG)            
            
∆ = |89° 8' 36"| (89,14° ) [ 7 tithi = ROUNDUP (∆/12)]            
            
Here is now the way in which Placidus would have proceeded: for 36 full years, 33 embolismic lunations are accomplished in 6 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 14 APR 1581, by removing 33 days, we arrive at 13 March 1581 [,,,] and then, the process is completed for 33 full years. Then, for the 6 other years elapsed during the twelve embolismic lunations, I arrive at 3 September 1581, for the remaining 5 months and 24 days. I compute the tithi (exact distance between SU and MO radix) for the last time : the date of Embolismic Progression J0 is : 6 September 1581 at 2h 5min tu. Thereafter, i add to this date 28,37 d corresponding to 11,526M [see EVEN] :            
            
JD Pr Emb = 11,53 x 30 / (365.24 /29.53) = 28,37 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            
            
 trop days 365,242215585481 (1)            
            
syn month = 29,530587934914 (2)            
            
where T = (JD-2451545)/36525            
            
In the present case JD = 2298766,5            
            
so, T = -4,21679671457906 (see formula 1 and 2)            
            
Finally, we find : date for J28,37D = 4 October 1581 at 10h 36min  local (10h 51min  TU).

(1) exact value for number of tropical days is : 365,2421896698-0,00000615359*T-0,000000000729*T^2+0,000000000264*T³
(2) exact value for synodic month is : 29,5305888531+0,00000021621*T-0,000000000364*T^2

The outer circle (in red) represents the arrangement of the planets and houses during the luni-solar cycle; the inner circle (in gray) represents the natal horoscope.
There is a discrepancy between MO given by Placidus (27°29' ♐) and 6°72 ♑ taking into account the difference in years of Felipe's death (moreover he does not indicate the reason why he removes 24° from MO which he first calculates at 21° ♑...).

Anyway, we find the following aspects (R = radix):
- ♀ ◻ ♂R
- ♂ ☍ ♀R
- ♄ # ☉R

We give below the table of Placidus' positions (Primum mobile, op cit, p. 67, exemplum III) :

(for MO, we must read 27 19♐   and no 17 19♐).

Ebn Shemaya (Parkes David)

 Parkes David (Ebn Shemaya)

Author of a thick book, "the star, a system of theoretical and practical astrology" (Cornish, 1838) with the nativity of the author, p. 132.
bibliography : “A” Catalogue Raisonné of Works on the Occult Sciences, Volume 2, Astrological books, Frederick Leigh Gardner, 1911, p. 109

---------------------------------
Parkes David
14 Jul 1811 GREG    CAL
sunday GREG
 | lat 53° 23' 59" | N 0°10' W
0
---------------------------------
natal (bt) 13 h 30 min
raas-rams :23h 54' 36"
reckoned bt Lat --> lmt 22 h 30 min
tu 22h 30' 40"
tsn 17h 57' 20"
---------------------------------
timezone  : 0
DST : 0 (-)
Equation of time -0h 5' 23"
ΔT 0h 0' 13"
---------------------------------

THEME

SU is P with a [-10] score - house rgo 5
MO is E with a [6] score - house rgo 2
ME is T - FA with a [8] score - house rgo 4
VE is P  with a [-12] score - house rgo 3
JU is D with a [-5] score - house rgo 7
MA is Ru with a [10] score - house rgo 3
SA is Fa with a [-6] score - house rgo 9

no point in critical house
no point -
we see below the list of  aspects in mundo :
---------------------------------------
        SU[0,21 Occ 60]JU    MO[3,81 Or 90]ME                    VE[0,4  Or 120]MA          JU[0,37 Or 180]SA
---------------------------------------
The best aspect is  [best :su 60° (0,21) ju]  and the worst aspect is  [worst :ma 120° (0,16) ve]

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

The Lilly (Ptolemaïc) almuten is ME

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  57,41 /
---------------------------------------
the lot of Fortune has been computed according to Placidus's revised method (see 'Primary directions', A primer of calculation by Bob Makransky, 1988, cap X: the Arabian parts, pp. 98-103; see also Mario Fumagalli,  'Il calcolo delle sorti secondo Placido', Linguaggio Astrale 103, June 1996 and 'La sorte oraria, il vero oroscopo lunare.' (Phôs 2, giugno 2001) and Placidus, Coelestis philosophiae, 1675, Brunacci and Onorati ; see finally the english traduction of Placidus, Primum mobile, John Cooper, 1814, Canon of the Part of Fortune, pp, 308-318) ; help will be found also from: : Sepharial, directional astrology, cap XII, the part of fortune, pp, 81-85, 1921 and Oxley Thomas, The Gem of Astral Sciences, cap VII, of the part of fortune or lunar horoscope, pp,45 - 48, 1848)

[Brunacci : 271,84°] the Fumagalli method is the so called horary method from Brunacci and Onorati : we find it in 'De Parte Fortunae Ptolemaica', pp, 8-14 ex libro iii, cap i, in Physiomathematica sive Coelestis Philosophia, Milano, 1675; Cursino Francobacci et Africano Scirata are anagrams for Francesco Brunacci and Francesco Maria Onorati,

HYLEG – ALCHOCODEN – domification ,

In our research, we hypothesised that the mundane chart alone should be considered; also we must base on the aspects taken in the semiarcs the research of the degrees likely to be considered in the duration of the life.
In the case of Parkes David 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 Parkes David, it is NOCTURNAL.
In this case, the first point to check is SU. If  SU is well disposed, it can claim 1st stage to be HYLEG.

SU is P and therefore seems weak, with a dignity score of [-2],
Moreover, when we look for the dignities that appear in the zodiacal inscription of MO, 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 know that we cannot consider SU as hyleg, we are left with MO we find aspect to match with the dignities.

If we consider the MUNDANE system, we observe a conjunction aspect of MO.
At the same time, it appears that MO has  dignity of EXN over POF.
So we have two possibilities with our hypothesis : first choose MO for hyleg ; second choose the MUNDANE system and try to find another couple of hyleg/alchocoden,
If we choose now MO we must know that no trad authority agree with this choice
In case of MO is the Hyleg, there is then one candidate to be the alchocoden: MO
First, we have to see which candidate has the most dignity: here, ME has candidate alcho dignities referring to MO : [EXN]
First, MO is linked with MO by a [conjunction] aspect and a [EXN] dignity,
However, MO is [E] and has a power of [8], and so MO has a good Kadkhudah score of [2]
MO is located at 46,54° at 0° (°) from the next (cad) cusp
Now, we have to take account of the radix zodiacal aspects,
------------------------------------------------------
  ME 90 MO: 6,67      minus alcho dy (0)
------------------------------------------------------
Without any change, we find with MO as Kadhkhudah : Y = 66 as a result of MO SUCCEDENT years
But as MO is EXN, following William Lilly in Christian astrology, p, 115 (London, 1647) on his table of Fortitudes and debilities, we remove 1/5 of his value, as dignity for MO is    E     Or  (ie 0)
------------------------------------------------------
So, zodiacal Y =80,31

Primary direction at death (1906)

David Parkes died at a very advanced age (95 years) for his time. The factors found are: MO in CAN (EXN), VE in lower culmination.

We find two directions :

1) a converse direction from SU to SA, in REGIO.

speculum	Lat	Dec	AR	MD	SA	HA
SU	-	21,74 N	113,23	156,11 D	122,48 D	-33,63 W
CSA	-2,37 S	-21,9 S	260,67	8,66 D	57,22 D	48,56 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 CSA)
under bracket [] the fixed point, (here SU)
- Lat CSA -2,37 S and lat SA : 1° 16' 41"

TABLE of AO and DO	AO	DO	AO	DO
	1	2	3	4
A1 SU			+
AO ±			-
A2 CSA		+
AO ±		-
AO SU			136,36
DO SA / pole SU		237,34
DO SA		250,72
AO SU / pole SA			123,10
	AO	DO	AO	DO
		AR-DA	AR-DA

The only tricky point to take into account is to highlight whether the key points (SU and SA) should be considered in OA (oblique ascension) or OD (oblique descension). The values ​​of AO and DO will be obtained from the RA and the DA of the star, applying the following formulas:

for a star with positive declination (North)
AO = RA - DA
DO = RA + DA
for a star with negative declination (South)
AO = RA + DA
DO = RA - DA

You also see that the rule is double and does not include the sign of DA (ascensional difference). The table above summarises these observations.

DP REGIOMONTANUS (5)			DP REGIO-CAMPA D		DP REGIO-CAMPA C
DIRECTIO CONVERSA	A2 CSA	A1 SU	A1 SU	A2 CSA	A2 CSA	A1 SU
Tan A	tan dec/cos dm		23,56		-22,13
B (1)	+LG-A or -LG+A		-76,96		75,53
Tan C	cot DM.cos B/cos A		-29,06		-60,54
Sin pole (2)	Cos C.sin LG		44,57		23,26
Sin DA (3)	Tan pole A1.Tan Dec A2 Tan pole A2. Tan Dec A1	DAP (6)	23,13	-23,33	-9,95	9,87
AO (4)	AR ± DA		136,35	237,34	250,72	123,09
Arc (7)	AO1 – AO2			-100,99		127,63
				DIRECT		CONVERS

(1) B must be treated as positive number
(2) sign of pole has the same sens of LG for DA Here, DA = DA/pole A
(3) sign [-] if pole and Dec have the opposite sign – sign [+] if planet located in western half, sign [-] if planet located in eastern half ; Signs [+] and [-] must be reversed for births in the southern hemisphere
(4) to find AO of a star A2 under the pole of A1, we calculate the  DA of A2 under the pole A1 ex: tan pôleA1.tan DecA2=sin DA A2/poleA1
(5) algorithm and lessons from : a)- Gouchon (‘Dictionnaire astrologique’, Dervy, 1946, 1975, p, 276, attributed to H. Selva) ; b)- Martin Gansten (‘Primary directions’, pp, 155-157, 2009, Wessex Astrologer) - instructions for use only appear in Gansten – c)- Astrologia gallica, Morin de Villefranche, trad Holden (appendix 5, pp, 151-153) ; d)- Henry Coley, Clavis astrologiae elimata, 1676, pp. 609-648 ; e)- Henri Selva, La domification, Vigot, 1917, reprint Lacour 1992, p, 25 and 131
(6) ascensional difference under own pole
(7) if the 0° point of the equator (viz 0° trop ARI) should fall between one of the two points, 360° must be added to arc

The clearest and most complete exposition I know can be read in:
- Delambre (about Magni)
- Selva (about the regiomontanus directions)

arc = 100.99 (regio)
conversion for key BRAHE : even (94.92) x 1.048 = 99.5
diff = 1.49

We can also use the formula from 'Casting the horoscope' from Alan Leo (but I doubt he is the author) :

REGIOMONTANUS	C SA	SU
(a)	8,03	22,10	Sina = cos dec x sin MD
(b)	-247,87	113,57	tan b (b') = cot dec x cos MD (***)
(c)	0,56	-1,80	X = tan a x cosec (latgeo +b (b'))
PM	18,62	47,04	Tan PM regio = tan(X x cos(latgeo))
(mod ∟)	251,38	137,04	dom regio
house	9	5
	11,38 [ d, IX ]	17,04 [ d, V ]	domitude
(**)	23,26	44,58	pole regio
A	cosA=tanp/tanλ	42,96	∠ meridian↑ p/λ
B	66,66	cosB=-tanp tanδm	SA D C SA / pole 44,58
Arm	260,67		AR C SA
TS	269,334		AR MC
3|Occ	100,95	B+A±(TS-Arm)	pf Occ N - pm Occ D
quadrant SU	arc	formula (mod 360°)	orient pf – pm
even	94,92
EQU | arc =1,048	99,50		DA [C SA] with δ C SU 23,14
≠ PLACIDUS	-22,05		DA [C SU] with δ C SA -23,34
≠ REGIO	-1,45		SA D prom [C SU] with δ C SA 66,66

(*) Sepharial (Walter Gorn Old), cuspal distances, debatable ground, the horoscope, 2, 5, 19-23, Oct 1903
directional astrology, p, 72, Sepharial, 1921
(**) according to Max Duval, ''Les Moyens de pronostic en astrologie', pp 11-15, direct zodiacal directions, Ed Traditionnelles, 1986
(***) if 0<b<90;b=b' ; if 180<b<90; b'=180-b (use sign of b)
cf, Alan Leo, Casting the horoscope, (Astrology for all, II,, appendix, pp 180-183, L. N. Fowler & Co., London, 1912)

We see that the interest of this last method is that it allows to place in a first time the PM (in mundo positions) and therefore, to determine the Regio domitudes (and Campanus not noted here). We use in a second time the formulas given by Max Duval. The poles are determined from the PM.