Affichage des articles dont le libellé est Lune-Saturne. Afficher tous les articles
Affichage des articles dont le libellé est Lune-Saturne. Afficher tous les articles

jeudi 2 juillet 2026

WAGNER Wieland - luni-solar phase (5)

 Wieland WAGNER

January 5 1917 - 9h15 (AM) - Bayreuth, Germany, 49n57, 11e35 - Timezone : MET h1e
source : [https://www.astro.com/astro-databank/Wagner,_Wieland]

German opera director.
Wieland was the elder of two sons of Siegfried and Winifred Wagner, grandson of composer Richard Wagner, and great-grandson of composer Franz Liszt through Wieland's paternal grandmother.
Wieland Wagner is credited as an initiator of Regietheater through ushering in a new modern style to Wagnerian opera as a stage director and designer, substituting a symbolic for a naturalist staging and focusing on the psychology of the drama. [https://en.wikipedia.org/wiki/Wieland_Wagner]

recall : the aspects between planets and ASC are plotted directly in OA and those between planets and MC are indicated directly in AR. The aspects between planets are indicated in mundo (for the actual domification, i.e. Regio).


ZODIACAL – MUNDANE

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

SU is P and therefore seems weak, with a dignity score of [-10],
But, when we look for the dignities that appear in the zodiacal inscription of ASC, we find none.
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 but we don't find any aspect to match with the dignities,,,

Now that we doubt to take MO 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 consider the MUNDANE system, we observe an opposition aspect of SA.
At the same time, it appears that SA has  dignity of TRI 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 no trad authority agree with this choice
In case of ASC is the Hyleg, there is then two candidates to be alchocoden:  and 
First, we have to see which candidate has the most dignity: here, ME has candidate alcho dignities referring to ASC : [TERM and FAC] : weak dignities
SA is linked with ASC by an [opposition] aspect and a [TRI + RUL] dignity,
However, SA is [D] and has a power of [-19], and so SA has a bad Kadkhudah score of [7]
SA is located at 118,15° at more than 5° from [Δ degrees cups sup [VI] : 27,28° (150)] and has a domitude Regio of : [177,28] for a latitude of [0,18°]
Ultimately, ASC can be considered HYL, and SA as ALCHO.

Wieland Wagner, who was a heavy smoker, died of lung cancer on October 17, 1966.

I. Primary directions

☽ ☌ ♄

speculum Lat Dec AR MD SA HA
SA 0,18 N 20,72 N 120,29 60,57 N 63,26 N 2,69 W
CMO 0 S 25,44 N 69,60 9,89 N 55,53 N 45,64 W


DP PLACIDUS Plac direct Plac conv
sa1/dm1 5,61 1,04
sa2 63,26 55,53
x 11,27 53,17
dm² 60,57 9,89
sign -1 -1
orient SA and DM N
arc 49,30 -43,28


FOMALHAUT-CHOISNARD
X = sa2.dm1/sa1 = and the angle x = SAm x DM f/SA f, so : SA m [ 63,26°] x DM f [ 9,89°]/SA f [ 55,53°]
sign : if the two points are on either side of the meridian, take +1 ; otherwise -1
Arc = dm2 ± sign.x We find the direction by DMm - x, so : DM m [ 9,89°] ± x [11,27]
important note: the SA and DM of the two points are always counted as daytime if the first point A1 (promissor) is above the horizon, even if the second is below. They are all counted as nighttime if the first point A1 (promissor) is below the horizon, regardless of the position of the second point A2 (significator). In present case SA et DA are all quoted N (see Choisnard, 'Langage Astral, p, 152, Ed, Trad,, 1963

DIRECTION : CMO conj SA    17 10 1966                
---------------------------------                    
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. But we have to take care of a fact : when we have a countra parallel or an aspect, the quadrant is not the same and the declination is different ; so the sign is also different.                    
                    
sin(DA) = -tan(φ)tan(δ)                    
φ = latitude 49,95 N                    
δ SA = 20,72 +                    
DA-SA = 26,74°                     
δ CMO =25,44 +                    
DA-CMO =34,47°                     
                    
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 SA is -1,43°. 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.                    
                    
nocturnal meridian MC = 59,72°                    
AR SA = 120,29°                    
AR CMO = 69,6°                    
                    
 = 55,53°                    
DM N  CMO = 9,89°                     9,89°
                    
For the  significator  CMO altitude (h) =-14,1°. so :                9    
                    
 = 63,26°                    
DM N  SA = 9,89°                    
            2        
Then we compute Saf/DMf (so : SA f [ 55,53°] / DM f [ 9,89°])                    
                    
Sa f / DM f =5,61                    
                    
and the angle x = SAm x DM f/SA f, so : SA m [ 63,26°] x DM f [ 9,89°]/SA f [ 55,53°]                    
                    
 x = 11,27°                    
                    
We find the direction by DMm - x, so : DM m [ 9,89°] ± x [11,27]                    
We must now have regard to the double ± sign of the last expression; in the case where f (SA) and m (CMO) 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 =49,3°                    
---------------------------------                    
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 CMO) 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 [116,74] / DM m [119,43])                    
                    
Sa m / DM m =1,04                    
                    
and the angle x = SA f x DM m/SA m, so : SA f [ 55,53°] x DM m [119,43] / SA m [116,74]                    
                    
x = 53,17°                    
                    
We find the direction by DM f - x, so : DM f [ 9,89°] ± x [53,17°]                    
We must now have regard to the double ± sign of the last expression; in the case where m (CMO) 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 =43,28°                    
---------------------------------

REGIOMONTANUS

We must first determine the respective ascensional differences under the pole (DAP). The ascensional difference (DA) is the difference between right ascension and oblique ascension. The difficulty in calculating oblique ascensions lies in determining the correct ± sign to use; the following table makes it easier to navigate and allows for the adjustment of the values ​​found in the subsequent table: it provides the adjusted oblique ascension values ​​required to calculate primary directions according to the Regiomontanus method.

point quadrant DEC TABLE of AO and DO AO DO DO AO 0




1 2 3 4 -1


20,72 A1 SA

+

SA 3 + AO ±

-



25,44 A2 CMO

+

CMO 3 + AO ±

-
± DAP | □
SA -1
DO SA

147
[+]
CMO -1
DO MO / pole SA

104.02
[+]



DO MO

81.99
[+]



DO SA / pole MO

130.11
[+]










AR-DA 120,29 26,74 AO DO DO AO

AR+DA


AR+DA AR-DA

Thus, we see that the significant points lie in the DO zone (3)—corresponding to the third sector situated between DS and FC—which is a zone of oblique descent rather than ascent. The ± sign is determined by the declination of the significant point, resulting in two formulas: DO = AR + DA if the declination is + (N), or DO = AR - DA if the declination is - (S).

DP REGIOMONTANUS (5)

3 quadrant 3


h -1,43
-14,10
DIRECTIO RECTA ☽ ☌ ♄ dec 20,72
25,44



DP REGIO-CAMPA D
DP REGIO-CAMPA C

A2 CMO A1 SA A1 SA A2 CMO A2 CMO A1 SA
Tan A tan dec/cos dm
37,59
25,77
B (1) +LG-A or -LG+A 49,95 87,54
75,72
Tan C cot DM.cos B/cos A
-1,75
57,52
Sin pole (2) Cos C.sin LG
49,92
24,27
Sin DA (3) Tan pole A1.Tan Dec A2
Tan pole A2. Tan Dec A1
DAP (6) 26,71 34,42 12,39 9,82
AO (4) AR ± DA
147,00 104,02 81,99 130,11
Arc (7) AO1 – AO2

42,97
48,12




DIRECT
CONVERS

1    (1) B must be treated as positive number (< LG)                         
2    (2) sign of pole has the same sens of LG for DA Here, DA = DA/pole A                        
3    (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    (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    (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    (6) ascensional difference under own pole (cf. https://mediocielo.org/risorse/prometheus-video-guide/37-testi-e-file/54-tavole-del-primo-mobile.html)                        
7    (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

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[20,72°] x Cot Lat [49,95°]) /sin DM f [60,57°] ± cot DM f  [60,57°]

DAPf = 17,79°

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 [26,71°] x cot f [20,72°]

pole SA regio  =49,92°

(1) We need now the DAP of m (CMO) under the pole of f, sin (DAP m) = tan (pole f) x tan (DEC m), i,e, : (SA) : sin (DAPm/f) = tan [49,92°] x tan [25,44°]

DAP m/f = 34,42°

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 = 147° and AO m = AR m ± DAP m ; idem for sign ; so  AO mCMO = 104,03°

---------------------------------
arc D Regio = 42,97°
---------------------------------
We are now going to compute the converse Regiomontanus direction corresponding to the arc  f SA / p CMO

First, compute the ascensional difference under m (CMO) : cot DAPm = (cot dec m x cot lat)/sin DM m ± cot DM m, i,e, :  Cot(DAP m) = (Cot decm[25,44°] x Cot Lat [49,95°]) / Sin DM f [9,89°] ± Cot DM m [9,89°]

DAP m = 3,57°

We find the pole of m (CMO) by formula : Tan(pole m) = Sin (DAP m) x Cot (dec m) i,e, Tan(pole m) = Sin m [12,39°] x Cot m [25,44°]

pole CMO regio  =24,28°

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, : (CMO) : Sin (DAP f/m) = Tan[24,28°] x Tan [20,72°]

DAP f/m = 9,82°

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 CMO = 82° and AO f = AR f ± DAP f ; idem for sign ; so  AO f SA = 130,11°

---------------------------------
arc C Regio = 48,12°
---------------------------------
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 is the method of Henri Selva (La domification, Vigot, 1917, reprint Lacour 1992)
It 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 [20,72°] / cos DM f [60,57°]

A = 37,59°

Then : B = Lat [49,95°] + A [37,59°]

B = 87,54°

And, Tang C = Cot DM f [60,57°] x Cos B [87,54°] / Cos A [37,59°]

C = -1,75°

Then, we have Sin pole f = Cos C [-1,75°] x  Sin LG [49,95°]
---------------------------------
So, pole SA regio = 49,92°
---------------------------------
Now go back to (1)

For m CMO; we have : A => Tan m = tan dec m [25,44°] / cos DM m [9,89°]

A = 25,77°

Then : B = Lat [49,95°] + A [25,77°]

B = 75,72°

And, Tang C = Cot DM m [-189,89°] x Cos B [75,72°] / Cos A [25,77°]

C = 57,52°

Then, we have Sin pole m = Cos C [57,52°] x  Sin LG [49,95°]
---------------------------------
So, pole CMO regio = 24,27°
---------------------------------
Now go back to (1) and see also the Regiomontanus table.

II. 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. even). For example in the case of Wagner, Wieland, if we take the date of 17 Oct 1966, we must first translate this date into 'life-year equivalent': we find :            
---------------------------------------            
EVEN    49,7820364521361    49    Y
0    9,38443742563351    9    M
    11,5331227690052    11    D
    12,7949464561252    12    H
        47,7    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 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).            
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. But here, I want to try to demonstrate the particular method advocated by Placidus. So:            
In the case of Wagner, Wieland, we observe:            
            
SU radix = 284° 27' 5" (284,45° CAP)            
            
MO radix = 71° 37' 30"° (71,63° GEM)            
            
∆ = |212° 49' 35"| (212,83° ) [ 17 tithi = ROUNDUP (∆/12)]            
            
Here is now the way in which Placidus would have proceeded: for 48 full years, 44 embolismic lunations are accomplished in 4 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 5 Ja 1921, by removing 44 days, we arrive at 22 November 1921 [,,,] and then, the process is completed for 44 full years. Then, for the 1 other years elapsed during the twelve embolismic lunations, I arrive at 21 December 1921, for the remaining 0 months and 23,09 days (i,e, 23 days and 5,4 hours). I compute the tithi (exact distance between SU and MO radix) for the last time : the date of Embolismic Progression J0 is : 21 December 1921 at 13h 21min tu. Thereafter, i add to this date 23,09 d corresponding to 9,384M [see EVEN] :            
            
JD Pr Emb = 9,38 x 30 / (365.24 /29.53) = 23,09 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 365,242194775911 (1)            
            
syn month = 29,5305886734202 (2)            
            
where T = (JD-2451545)/36525            
            
In the present case JD = 2421233,5            
            
so, T = -0,829883641341547 (see formula 1 and 2)            
            
Finally, we find : date for J23,09D = 13 January 1922 at 16h 36min   local (15h 36min  TU).    

We now return to the problem we faced: should the graphical results be expressed in zodiacal or mundane terms? Let us examine this:

With the mundane system, we find :

- At J23.09

♂☍♀
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mardi 23 avril 2024

More about Placidean circles of positions (under the pole) and Monteregio method

More about Regiomontanus directions


Let us take again the Primum mobile of Placidus. The 1st theme is that of Charles V (Quint) which we have already analyzed. Here we will consider the directions in a more traditional way using the direct teachings of Placidus and Magini. On Magini, we have in the History of Astronomy of the Middle Ages, an entire chapter devoted to the calculation proposed by Delambre, the complete details of which will be seen below on the example of the SA opp MO arc. I give again the theme of Charles V, according to the data of Placidus (Primum Mobile, pp. 59-61: Exemplum Primum Caroli V Austriaci Imperatoris).


For comments on the theme itself, see the following 3 posts:

https://primarydirections.blogspot.com/2017/04/charles-quint.html
https://primarydirections.blogspot.com/2017/09/carolus-v.html
https://primarydirections.blogspot.com/2018/02/carolus-v-3.html

IOANNIS ANTONII MAGINI  PRIMI MOBILIS LIBER NONUS QUI AGIT DE DIRECTIONIBUS pp, 214-232 PROBLEMA XVIII p, 230   

We take the direction : ꝏSA C MO.

1) - MAGINI    - REGIOMONTANUS


direct   
modified from [ Delambre, Hist Astron Moyen Âge, Magini, pp, 486-491 Paris 1819]   
    
    Eq for Fig 129 (pl 12)  see fig for location and explanation of spherical triangles

Figure 129 is mixed. It represents a state of the sky at the moment when star A' arrives in a situation similar to star A. The reference element for the observer is the horizon OBH. The arc OAA'H is the position circle (or incident horizon) whose pole is PR. PA is the hour angle counted from midnight. When A' reaches the arc OAA'H, A is no longer on the circle; we must therefore imagine its image on the incident circle. Furthermore, EBQ is the equator. T is the pole of RS (or of A'V') and ET the symmetry axis.
The time when opp SA is on the circle of position of MO is 7h 31 33 TU and the initial time is 3h 52 (corresponding to 58.57 Y for the date of death, the 12 September 1558 (OS), so : 1558.72.

    
    h (altitude of the promissor) - H (latitude of the observer) - D (declination of the promissor) –
    D' (declination of incident horizon = position circle of promissor) - PH=H - 

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

PARAMETERS

24 Fev 1500 | JUL |

house = pcd

DIRECTION

PROMISSOR

SIGNIFICATOR

ꝏ SA C MO

ꝏ SA

C MO

long

226,15 N E

279,12 S E

lat

2,023

-2,097

(***)

na

72,218

AR

224,27

280,09

dec

-14,78

-25,28

h

23,87

-4,26

OA

243,32

315,84

Dom Campa

286,71

5,27

Dom Regio

280,69

8,35

Dom Placidus

279,15

6,29

Pôle Regio

12,92

50,75

Pôle Campa

12,92

50,75

Pôle Placidus

7,30

49,26

DM D|N

D |7,216- N |172,784

D |63,03- N |116,97

DA pôle D|N (Placidus)

D |1,937- N |30,18

D |41,544- N |33,257

DA

19,05

35,75

SA D|N

D |70,95- N |109,05

D |54,25- N |125,75

D Horiz (SA-DM) (min E W)

63,74 (E)

8,78 (E)

temporal hour (*) ꝏ SA (HTn) | C MO (HTd)

11,83

9,04

horary distance (**)

0,61

5,58

horary angle (TS – AR) from midnight (W from S)

352,78

296,97

Azimuth (0-360 W from S)

352,37

306,09

ARMC | TSN

217° 3' 19"

14h 28' 13"

latgeo,

51,05

Equ time

ecliptic

23,51

+ 356° 55' 15"

Length SU

1,00

Luna motion

Length MO

14,61

2,34 (for y time + key EQU)

---------------------------------------------------------------------------------------------------------------------------
One can see hereunder : label of angles, left : value for each equation of angle and right formulas.    

PA (horary angle, from midnight)   
172,78    ||  cosP = (sinh-sin Hsin D)/(cosHcosD)
    
PHA (HAO angle)   
-16,71    ||  TanPHA = sinP/((sin(SAD-90)+cosP)cosH)
    
PR (pole HAO)   
-12,919    ||  sinPR=sinPHsinPHA
    
ET (arc meridian/HAO)   
169,31    ||  tanET=cosHtanPHA
    
H'    ||  H' (incident horizon = pole [ꝏ SA]
12,92    ||  tanH'=sinETtanH
    
PAR (position angle)   
13,37    ||  sinPAR=sinH'/cosD
    
QS, HPR (Az PR)   
79,31    ||  cosQS=sinET

ΔAR' (DA/HAO)   
-3,47    ||  sinΔAR'=tanDtangH'
    
OTE, HTQ, ETH (equat/HAO angle)   
77,08    ||  tanOTE=cotH/sinET
    

   Eq for Fig 130 (pl 12) see fig for location and explanation of spherical triangles

Figure 130 resembles a sagittal shot of the sky. The element of symmetry is the ETQ equator. Point S is the significator (point A in figure 129) and point R is the promissor (point A' in figure 129). Point Z is the image of point R at the instant when R reaches a position similar to S. AQC is the observer's horizon; ASZC is the position circle of S (incident horizon). PR, PZ and PS are arcs of position of the points R, Z and S. ZV is the boreal [+] declination of Z and OS the austral [-] declination of S. TO is the ascensional difference (AR) of S while TV is the ascensional  difference (AR') of Z. They allow the calculation of the distance OV which must be added or subtracted from the arc KO (difference of the right ascensions of S and Z) to obtain the arc of direction whose the common equation is:

KV = KO - OT - TV

If the OS declination is boreal, OT would change sign; if RK is austral, TV would change sign (adapted from Delambre, History of Astronomy of the Middle Ages, Magini article, p. 490, 1819).



KO (≠AR ꝏ SA C MO)
53,23    ||  KO=ARꝏ SA - ARC MO
    
A (AET angle)    ||  EA = 90-H
16,71    ||  sinA=sinETsinOTE/sinEA
    
T (angle horizon/OTH)    ||  pole of PRS (=90-H')
77,08    ||  cosT=sinAETsinH
    
[-] TO ΔAR' ꝏ SA    ||  D boreal --> sign [-] = switch for [+]
-3,47    ||  sinTO=tanDcotT
    
[+] TV ΔAR' C MO    ||  D' boreal-> sign [+] = switch for [-]
-6,26    ||  sinTV=tanVZcotT
-----------------------------------------------------------------   
tasyir    ||  If OS (D) [+], TO ~ sign,  If RK (D') [-], TV ~ sign
56,02    ||  KV=KO – OT – TV
-----------------------------------------------------------------   
VZ    ||  D' (declin of C MO)
-25,43   
    
OS    ||  D (declin of ꝏ SA)
-14,78   
    
ST    distance ST
-15,17    ||  sinST=sinD/sinT
    
TZ    distance TZ
-26,13    ||  sinTZ=sinD'/sinT
    
ZS    ≠dist
10,96    ||  If D/D'<0 [-]
    
EPA (EPV, EV) ± ΔAR'    horary angle of ꝏ SA
172,78    ||  if d is [-] ~ ΔAR'
    
So, the direction is tasyir = 56.02 (Regiomontanus).


we see superimposed the arc of direction with opp SA emanating from SA (at 46.27° ♉), arriving in conjunction with MO at 280° ♑.

2)- PLACIDUS 1558

Placidus calculates in his system thus:
 

 The direction of the Moon in the place of opposition of Saturn by converse motion is calculated as follows: the distance of Saturn counted from the IC (immum coeli) is 3.59° because its right ascension (RA) is 43.67°, the height at the pole of the 5th house and the 11th is 23.4°, the semi-nocturnal arc (SA N) of Saturn is 70.95° of which the third is 23.65°, that is for Saturn a polar height of almost 6° (in fact the pole is ≈ 4.92°). Note that the mundane position of the opposition of SA is PM = 8.36 (this is the ratio of 90° to the nocturnal semi-arc of 70.95° at the meridian distance of  6.69°). In any case, at this pole, the oblique ascension (OA) of the position opposite to SA is 224.97° (the ascensional difference DA of SA under the pole of MO is -1.3°) (Placidus finds for opposite to SA 227°21') and that of the MO at this same place is 279.99° (Placidus finds 280°19') ; by subtraction we obtain the arc of direction 55.02° (Placidus obtains 52°58'). To find the equivalence in years, we add to this arc of 55.02° (52°58') the right ascension of the SU of 345°39' and we obtain 42.88° (i.e. 12°52' ♉, on April 24, 1500), position where the SU, counting from the day and hour of birth, arrives in 59.5 days (Placidus finds 58 days) which means as many years. [adapted from Primum mobile, Placidus de Titis, trad John Cooper, 1814, p. 133]
The important point to consider is that the ascensional difference of the promissor as of the significator is taken under the pole of SA, i.e. of the promissor.

SIN(DA♄) = TAN(p♄)*TAN(𝛅♄) and SIN(DA ☌☽) = TAN(p♄)*TAN(𝛅☽)

with p♄ = 4.97° and 𝛅♄ = -14.78°

Then, Placidus retains the date of 1519 which coincides with the coronation of Charles V (June 28, 1519) :

'In his 19th year, when he was chosen emperor, the MO had arrived at the cusp of the twelfth, and VE at the second ; therefore the medium coeli was directed to the * of the MO and TRI of VE, and they were both in parallel by rapt motion: the MO also came to the * of VE in zodiac, near 26° CAP, and to the quintile in the world [mundane quintile] by converse motion. But the most important was, the SU to parallel of JU in the zodiac, near 25° of ARI, where he acquires the same declination as JU' [Primum mobile, op cit, p. 134]

We note that Placidus does not hesitate to mix zodiacal and mundane directions, which considerably (and mistakenly) amplifies the chances of success...

In 1519, in mundo, we find this direction which coincides with the event:

directio conversa : [C] ∆☽ ☌☉


speculum Lat Dec AR MD SA HA
SU - -6,26 S 345,40 54,69 N 97,8 N 43,11 W
∆MO -2,12 S 5,92 N 19,36 20,72 N 82,63 N 61,91 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 ∆MO)
under bracket [] the fixed point, (here SU)
- Lat ∆MO -2,12 S and lat MO : -2° 7' 4"

3)- PLACIDUS 1519
Below we see an old method of obtaining position circles, practically contemporary with Placidus. It can be used to illustrate the writings of Placidus and contemporary authors such as Argoli and Coley (see bibliography)


CUSPAL DIST
∆ MO SU PLAC DIR – POLE

OA ASC 310,08 signif promissor

OA ∆ MO 26,73



dist horiz 61,91



house ∆ MO 3 ∆ MO [SU] 97,8 N


horary time 13,77 82,63 90 pole ∆ MO

double ht 27,54 20,72 22,57 17,28
houses
32,55 DM PM
3 0,33 10,85


4 0,00 0,00
DA SU / ∆ MO OA SU / ∆ MO

pole 3 23,40 23,40 4,11 15,25

dec ∆ MO 5,92

OA MO

DA ∆ MO /3 2,57 2,57 -4,35 349,75

RA ∆ MO 19,36
1,29 334,50

OA 21,93 21,93
25,50

dist ∆ MO cusp / 3 4,80 22,75
dir

after Sepharial (Walter Gorn Old), cuspal distances, debatable ground, the horoscope, 2, 5, 19-23, Oct 1903 and Sepharial, directional astrology, p, 72,1921

The direction of the SU in the place of  ∆ MO by converse motion is calculated as follows:
the distance of ∆ MO counted from the IC (Immum Coeli) is 20,72° ; because its right ascension (RA) is 19,36°, the height at the pole of the III house and the IX is 23,4°, the semi-nocturnal arc (SA N) of ∆ MO is 82,63° of which ⅓ (double horary time) is 27,54°, that is for ∆ MO a polar height of ≈ 17,28°
Note that the mundane position of the ∆ MO is PM = 22,57 (this is the ratio of 90° to the nocturnal semi-arc of 82,63° at the meridian distance of  20,72°).
If we wanted to determine the Placidus domitude, it would be sufficient, depending on the height h (actual h =-30,31), to compute : (h<0) 270-PM or (h>0) 90-PM, or in the present case dom = 67,43, or : 7,43 [ d, III ],
In any case, at this pole, the oblique ascension (OA) of the position ∆ MO is 349,75° (the ascensional difference DA of ∆ MO under the pole of SU is DA = -4,35°) and that of the SU at this same place is OA [SU] = 15,25 ° with its own declination ; by subtraction we obtain the arc of direction |-25,5|°.

REGIOMONTANUS 1519

DP REGIOMONTANUS (5)

DP REGIO-CAMPA D
DP REGIO-CAMPA C

DIRECTIO CONVERSA A2 ∆MO A1 SU A1 SU A2 ∆MO A2 ∆MO A1 SU
Tan A tan dec/cos dm
-10,75
6,33

B (1) +LG-A or -LG+A
-40,30
57,38

Tan C cot DM.cos B/cos A
28,80
55,11

Sin pole (2) Cos C.sin LG
42,96
26,42

Sin DA (3) Tan pole A1.Tan Dec A2
Tan pole A2. Tan Dec A1
DAP (6) -5,86 5,54 2,95 -3,12
AO (4) AR ± DA
351,25 13,82 16,41 348,51
arc AO1 – AO2

-22,57
27,90




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

arc = 22.57 Y.

and this direction we must add two others : *☉ ☌☽ and *♃☌☽ which are "directio directa".


speculum Lat Dec AR MD SA HA
MO -2,12 S -25,43 S 277,79 57,71 D 53,97 D -3,74 W
*SU 0,00 -23,25 S 261,06 40,97 D 57,89 D 16,92 W

– MD = meridian distance (from MC if SA f [MO]  is diurnal or IC if Sa f  is nocturnal)
– SA = semi-arc (if f is diurnal, SA f [MO] is D and all MD’s and SA’s are D, otherwise N
– HA = horizontal distance (from the nearest horizon W or E for f [MO] and m *SU)
under bracket [] the fixed point, (here MO)
- Lat *SU 0 and lat SU : 0° 0' 0"

------------------------------------------------------------------------
PLACIDUS


CUSPAL DIST
(*)
2/3 SU MO PLAC DIR – POLE

OA ASC 310,08 signif promissor 2/3 SU [E] | MO [E]

OA 2/3 SU 228,95 OD OA asc or desc

dist horiz 81,14 1 4 2/3 SU above earth |
MO under earth

house 2/3 SU 12 2/3 SU [MO 126,03 N]


horary time (ht) 9,65 57,89 90 pole 2/3 SU

double ht 19,30 40,97 63,69 41,96
houses
32,55 DM PM
12 0,67 21,70


1 1,00 32,55
DA MO / 2/3 SU OD MO / 2/3 SU

pole 12 40,37 51,05 -31,05 292,10

dec 2/3 SU -23,25

OA MO

DA 2/3 SU /12 -21,42 -32,11 -34,81 312,60

RA 2/3 SU 261,06
17,40 20,50

OA 239,63 228,95
dir

dist 2/3 SU cusp / 1 10,68 8,61

(*) 2/3 means sextil or *

The direction of the MO in the place of  2/3 SU by converse motion is calculated as follows:
the distance of 2/3 SU counted from the MC (medium coeli) is 40,97° ; because its right ascension (RA) is 261,06°, the height at the pole of the XII house and the I is 40,37°, the semi-diurnal arc (SA D) of 2/3 SU is 57,89° of which ⅓ (double horary time) is 19,3°, that is for 2/3 SU a polar height of ≈ 41,96°
Note that the mundane position of the 2/3 SU is PM = 63,69 (this is the ratio of 90° to the diurnal semi-arc of 57,89° at the meridian distance of  40,97°).
If we wanted to determine the Placidus domitude, it would be sufficient, depending on the height h (actual h =7,42), to compute : (h<0) 270-PM or (h>0) 90-PM, or in the present case dom = 333,69, or : 3,69 [ d, XII ],
In any case, at this pole, the oblique descension (OD) of the position 2/3 SU is 312,6° (the ascensional difference DA of 2/3 SU under the pole of MO is DA = -34,81°) and that of the MO at this same place is OA [MO] = 292,1 ° with its own declination ; by subtraction we obtain the arc of direction |20,5|°,

REGIOMONTANUS


2/3 SU MO

37,04 49,77

-60,36 131,67

-4,67 -24,88

-71,17 -86,34 PM

341,17 3,66 dom regio

12 1

11,17 [ d, XII ] 3,66 [ d, I ] domitude

49,50 50,99 pole regio
A coA=tanp/tanλ 3,66 ∠ meridian↑ p/λ
B 57,97 cosB=-tanp tanδm SA D 2/3 SU / pole 50,99
Arm 261,06
AR 2/3 SU
TS 220,084
AR MC
4 -20,65 (ARm-TS) ± A-B pf Or D








quadrant MO arc
orient pf

arc = 20.26 Y