Affichage des articles dont le libellé est oblique ascension. Afficher tous les articles
Affichage des articles dont le libellé est oblique ascension. Afficher tous les articles

vendredi 11 octobre 2024

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.

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