Francisco Gómez
28 Mar 1552 JUL CAL
monday JUL
| lat 41° 17' 59" | N 4°55' W
0
---------------------------------
natal (bt) 15 h 27 min
raas-rams :23h 57' 48"
reckoned bt Lat --> lmt 7 h 40 min
tu 7h 40' 3"
tsn 20h 20' 48"
---------------------------------
timezone : 0
DST : 0 (-)
Equation of time -0h 2' 11"
ΔT 0h 2' 30"
---------------------------------
We see the direction of square VE conj SA in mundo. All the data are hereunder and the REGIOMONTANUS and PLACIDUS arcs.
HYLEG = MO
ALCHOCODEN = VE
ALMUTEN = SA
THEME
SU is E with a [6] score
MO is E with a [5] score
VE is E with a [11] score
JU is te - T with a [5] score
MA is T with a [7] score
SA is T with a [11] score
we see below the list of aspects :
---------------------------------------
VE 60 MO Oc SA 60 MO Oc MA 0 ME Or SA 0 VE Oc
---------------------------------------
The best aspect is [best :ve 0° (0,79) sa] and the worst aspect is [worst :mo 60° (-0,88) sa]
The traditionnal almuten (Omar, Ibn Ezra) is ME
we see below the list of dignities for ME :
---------------------------------------
[ term 3 tri 0 rul 1 exn 0 fac 3 ]
[ su 2 mo 0 asc 0 syg 2 pof 1 ]
---------------------------------------
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, Nativities, 101) – almuten = al-mu’tazz (arabic term) [7] As for the governor which is the <planet> predominating (al-mubtazz) over the birth from which one indicates the conditions of the native after the haylāğ and the kadhudāh,n it is the planet having the most leadership in the ascendant, the position<s> of the two luminaries, the position of the Lot of Fortune and the position of the degree of the conjunction or opposition which precedes the birth. When a planet has mastery over two, three or four positions by the abundance of its shares in them, it is the governor and the predominant <planet> (al-mubtazz) and the indicator after the haylāğ and the kadhudāh. From it one indicates the conditions of the native. Some people use it instead of the kadhudāh in giving life. [Al-Qabisi , Charles Burnett, Keji Yamamoto, Michio Yano, The Introduction to Astrology, IV, 7, p, 117, Warburg, 2004]
Note 2 : There are at least 4 systems for determining the almuten depending on whether the combinations of triplicities and terms are used: the Ptolemaic almuten (followed by Lilly) with Ptolemaic terms ; the same with Egyptian terms; the almuten of Dorotheus with Ptolemaic terms ; the same with Egyptian terms, knowing that one can embellish the whole thing with different weighting system (like Lilly or not using weights like Montanus) [cf. Temperament: Astrology's Forgotten Key, p. 79, Dorian Gieseler Greenbaum 2005]
The Lilly (Ptolemaïc) almuten is SA
In our experience, it seems that Ptolemy's almuten allows one to first appreciate the static side of the natal chart and that the Lilly-type elaboration allows one to deepen the more ‘temporary’ or ‘dynamic ‘ relationships (cf, Shlomo Sela, Ibn Ezra, on Nativities and Continuous Horoscopy, appendix 6, quot 2 ; Horary astrology p, 458, Brill, 2014)
---------------------------------------
Ω 186,66 / -11,25
---------------------------------------
DIRECTION : □VE conj SA
--------------------------------------------------------------------------------------------------------------
PARAMETERS |
28 Mar 1552 | JUL | |
house = rgo |
DIRECTION |
PROMISSOR |
SIGNIFICATOR |
□ VE C SA |
□ VE |
C SA |
long |
268,51 N W |
330,35 N E |
lat |
0,000 |
-1,393 |
☊ (***) |
|
|
AR |
268,37 |
332,94 |
dec |
-23,49 |
-12,68 |
h |
16,77 |
30,26 |
OA |
290,81 |
344,33 |
Dom Campa |
207,69 |
312,02 |
Dom Regio |
214,93 |
304,10 |
Dom Placidus |
220,93 |
301,76 |
Pôle Regio |
35,76 |
26,22 |
Pôle Campa |
35,76 |
26,22 |
Pôle Placidus |
26,00 |
17,32 |
DM D|N |
D |36,831- N |143,169 |
D |27,735- N |152,27 |
DA pole D|N (Placidus) |
D |12,235- N |28,575 |
D |4,022- N |17,116 |
DA pole Regio-Campa (under pole □ VE | C SA) |
-18,24 | -12,36 |
-9,32 | -6,36 |
DA |
22,44 |
11,40 |
SA D|N |
D |67,56- N |112,44 |
D |78,6- N |101,4 |
D Horiz (SA-DM) (min E W) |
30,73 (W) |
50,87 (E) |
temporal hour (*) □ VE (HTn) | C SA (HTn) |
11,26 |
13,10 |
horary distance (**) |
3,27 |
2,12 |
house regio <postdir> |
8 |
11 |
quadrant dir □ | C : diff HD [+] |
3 |
4 |
horary angle (TS – AR) from midnight (W from S) |
36,83 |
332,27 |
Azimuth (0-360 W from S) |
35,04 |
328,29 |
ARMC | TSN |
305° 12' 2" |
20h 20' 48" |
latgeo, |
41,30 |
Equ time |
ecliptic |
23,50 |
+ 359° 27' 9" |
Length SU |
0,98 |
Luna motion |
Length MO |
11,78 |
2,35 (for y time + key EQU) |
Birth year |
1 552,24 |
y time PTO for 1625,38 |
Event year |
1 625,38 |
-4,931 h = (73,13 Y) |
--------------------------------------------------------------------------------------------------------------
speculum
| converse direction | Lat | Dec | AR | MD | SA | HA |
| SA | -1,39 S | -12,68 S | 332,94 | 27,73 D | 78,6 D | 50,87 E |
| □VE | 0 S | -23,49 S | 268,37 | 36,83 D | 67,56 D | 30,73 W |
MD = meridian distance (from MC if SA f [SA] is diurnal or IC if Sa f is nocturnal)
– SA = semi-arc (if f is diurnal, SA f [SA] 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 [SA] and m □VE)
under bracket [] the fixed point, (here SA)
--------------------------------------------------------------------------------------------------------------
DP REGIO |
|
|
DP REGIO-CAMPA D |
|
DP REGIO-CAMPA C |
|
|
A2 □VE |
A1 SA |
A1 SA |
A2 □VE |
A2 □VE |
A1 SA |
Tan A |
tan dec/cos dm |
|
-14,26 |
|
28,50 |
|
B (1) |
+LG-A or -LG+A |
|
55,56 |
|
69,80 |
|
Tan C |
cot DM.cos B/cos A |
|
47,98 |
|
-27,68 |
|
Sin pole |
Cos C.sin LG |
|
26,22 |
|
35,76 |
|
Sin DA (2) |
Tan pole A1.Tan DecA2 Tan pole A2. Tan DecA1 |
|
-6,36 |
-12,36 |
-18,24 |
-9,33 |
AO (3) |
AO ± DA |
|
339,30 |
280,73 |
250,13 |
323,61 |
arc |
AO1 – AO2 |
|
|
58,57 |
|
73,48 |
(1) B depends on sign Tan A
(2) 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
(3) [+] sign if LG and Dec have the Opposite sign; sign [-] if LG and Dec have the same sign
--------------------------------------------------------------------------------------------------------------
DP PLACIDUS |
|
|
METHOD CHOISNARD |
|
|
|
|
|
|
Plac direct |
Plac conv |
sa1/dm1 |
1,83 |
2,83 |
sa2 |
78,60 |
67,56 |
x |
42,85 |
23,84 |
dm² |
27,73 |
36,83 |
sign |
1 |
1 |
|
|
|
arc |
70,58 |
60,67 |
|
|
|
--------------------------------------------------------------------------------------------------------------
---------------------------------
We must take into account an important element: the ascensional difference (DA); it can be observed on the graph in a dotted line (measured between the horizon and the axis of the pole). This is the difference between Right Ascension (AR) and Oblique Ascension (OA). This is the difference between Right Ascension (AR) and Oblique Ascension (OA). DA is always calculated in absolute value |DA| and it is added or subtracted from 90° (SA = 90° corresponds to a point on the equator cut by the horizon; depending on whether a star approaches or moves away from the line of horizon, SA is > 90° or < 90°, i,e, (+) depending on whether it is diurnal and northern ; or nocturnal and southern ; (-) depending on whether it is diurnal and southern ; or nocturnal and northern.
sin(DA) = -tan(φ)tan(δ)
φ = latitude 41,3 N
δ SA = -12,68 -
DA-SA = 11,4°
δ □VE =-23,49 -
DA-□VE =22,44°
We will first use the Placidus system of mundane directions. The simplest system is that of Choisnard-Fomalhaut. First you need to retrieve the data from the SA (semi-arc) and the DM (meridian distance) of the diurnal point because the altitude of SA is 30,26°. important note: the SA and DM of the two points are always counted diurnal if the first point (here SA) is above the horizon even if the second is below. They are counted nightly if the first point (SA) is below the horizon regardless of the position of the second point.
For DMs, they are counted in AR from the diurnal meridian if the fixed point SA is diurnal, and from the nocturnal meridian if it is nocturnal.
diurnal meridian MC = 305,2°
AR SA = 332,94°
AR □VE = 268,37°
SA D (δ-) □VE=67,56°
DM D □VE=36,83°
For the significator □VE altitude (h) =16,77°. so :
=78,6°
DM D SA=36,83°
Then we compute Saf/DMf (so : SA f [67,56°] / DM f [36,83°])
Sa f / DM f =1,83
and the angle x = SAm x DM f/SA f, so : SA m [78,6°] x DM f [36,83°]/SA f [67,56°]
x = 42,85°
We find the direction by DMm - x, so : DM m [36,83°] ± x [42,85]
We must now have regard to the double ± sign of the last expression; in the case where f (SA) and m (□VE) are on either side of the meridian, the direction arc is obtained by taking the sum (instead of the difference) of the two quantities DMm and x. this is the case here so sign = (-)
the computation of the arc requires, depending on the case, a reduction of 360° (so arc modulo 360°)
---------------------------------
arc D =70,58°
---------------------------------
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 □VE) 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 judgement on this.
That time, we compute Sa m / DM m (so : SA m [101,4] / DM m [152,27])
Sa m / DM m =2,83
and the angle x = SA f x DM m/SA m, so : SA f [67,56°] x DM m [152,27] / SA m [101,4]
x = 23,84°
We find the direction by DM f - x, so : DM f [36,83°] ± x [23,84°]
We must now have regard to the double ± sign of the last expression; in the case where m (□VE) 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 the case here : so, signe = (+)
---------------------------------
arc C =60,67°
---------------------------------
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[-12,68°] x Cot Lat [41,3°]) /sin DM f [27,73°] ± cot DM f [27,73°]
DAPf = 173,64°
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 [6,36°] x cot f [-12,68°]
pole SA regio =-26,21°
(1) We need now the DAP of m (□VE) under the pole of f, sin (DAP m) = tan (pole f) x tan (DEC m), i,e, : (SA) : sin (DAPm/f) = tan [26,22°] x tan [-23,49°]
DAP m/f = -12,36°
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 = 339,3° and AO m = AR m ± DAP m ; idem for sign ; so AO m□VE = 280,73°
---------------------------------
arc D Regio = 58,57°
---------------------------------
We are now going to compute the converse Regiomontanus direction corresponding to the arc f SA / p □VE
First, compute the ascensional difference under m (□VE) : cot DAPm = (cot dec m x cot lat)/sin DM m ± cot DM m, i,e, : Cot(DAP m) = (Cot decm[-23,49°] x Cot Lat [41,3°]) / Sin DM f [36,83°] ± Cot DM m [36,83°]
DAP m = 161,76°
We find the pole of m (□VE) by formula : Tan(pole m) = Sin (DAP m) x Cot (dec m) i,e, Tan(pole m) = Sin m [161,76°] x Cot m [-23,49°]
pole □VE regio =-35,76°
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, : (□VE) : Sin (DAP f/m) = Tan[35,76°] x Tan [-12,68°]
DAP f/m = -9,33°
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 □VE = 287° and AO f = AR f ± DAP f ; idem for sign ; so AO f SA = 342,26°
---------------------------------
arc C Regio = 73,48°
---------------------------------
H.J. Gouchon [l’Horoscope Annuel simplifié, Dervy, 1973, p, 181-182 and Dictionnaire astrologique, p, 277, 1937-1942, Gouchon ed., 1975, Dervy, but be careful because in DAP's equation, the double sign ± was mistakenly replaced by the sign (-) ] advises to avoid errors, to always place the star A1 (for us f, i.e. SU) in the eastern houses; in fact it is enough to change the registration number of the house based on the transformation (IV-V-VI) -> (X-XI-XII) and (VII-VIII-IX) -> (I-II-III ) to adapt the double sign ± in the calculation of DAP f or DAP m; moreover, this sign must be reversed if |DM| > 90°.
For the Regiomontanus directions, there is another mode of computing, mentioned by Gouchon (Dictionnaire astrologique, op. cit., p. 276) and especially Martin Gansten (Primary directions, pp. 155-157, the Wessex Astrologer, 2009)
This method consists at computing first 3 auxiliary angles before the pole. It then joins the other method. Contrary to what Gouchon says, I find it easier than the previous one because we avoid the double sign ± in the determination of DAP f.
So, initially, we have A => Tan f = tan dec f [-12,68°] / cos DM f [27,73°]
A = -14,26°
Then : B = Lat [41,3°] + A [-14,26°]
B = 55,56°
And, Tang C = Cot DM f [27,73°] x Cos B [55,56°] / Cos A [-14,26°]
C = 47,98°
Then, we have Sin pole f = Cos C [47,98°] x Sin LG [41,3°]
---------------------------------
So, pole SA regio = 26,22°
---------------------------------
Now go back to (1)
For m □VE; we have : A => Tan m = tan dec m [-23,49°] / cos DM m [36,83°]
A = -28,5°
Then : B = Lat [41,3°] + A [28,5°]
B = 69,8°
And, Tang C = Cot DM m [36,83°] x Cos B [69,8°] / Cos A [28,5°]
C = -27,68°
Then, we have Sin pole m = Cos C [-27,68°] x Sin LG [41,3°]
---------------------------------
So, pole □VE regio = 35,76°
---------------------------------
Now go back to (1)
Accuracy of measuring the placidus and regiomontanus directions
DIRECTIONS |
| 04h 55' 52" |
12h 18' 42" TU |
user |
promissor |
significator |
ZODIACAL |
□ VE |
C SA |
Long radix |
268,510 |
330,350 |
(m) square VE / □ VE =87,38 |
♐ |
♓ |
Event year / Y | MO motion |
1625,375 / 73 Y |
|
MUNDANE ASPECT |
0,610 |
[D] - □ VE SA |
ZODIACAL DIRECTION |
ZC Regio-Campa PTO orb -0,35 |
|
□ VE C SA |
ACTUAL |
INTENDED |
keyfactor |
key : PTO=1 |
EQU | arc =1,02 |
result ± 2 year |
73,135 |
74,7 | 1627 |
Lg D CONVERSED (-) |
□ VE |
C SA |
Regio-campa |
172,49 |
254,35 |
|
♍ |
♐ |
placidus |
182,260 |
254,430 |
Lg D PROGRESSED (+) |
♎ |
♐ |
Regio-campa |
330,96 |
67,05 |
placidus |
334,04 |
60,40 |
CONVERSED DIFF |
♓ |
♊ |
Arc regio-campa |
-157,86 |
14,16 |
Arc placidus |
-148,09 |
14,08 |
PROGRESSED DIFF |
|
|
Arc regio-campa |
0,61 |
201,45 |
Arc placidus |
3,69 |
208,11 |
We notice that the regio direction is between ± 2° (0.61). The placidus direction is less precise. The step used is that in degrees of equator (EQU); some use the PLACIDUS step which is based on the movements in AR in the days following the birth: for example, in the present case, we find that SU reached the required longitude (86.82°) on June 8, 1552 at 11:18 a.m., with: 71.7 Y (i.e. November 28, 1623). The EQU step gives 74.72 Y. The theoretical age is 73.13 Y (corresponding to May 17, 1625, or 1625.38).
Bob Makransky provides an algorithm in 'Primary directions, a primer of calculation' (part 1, pp. 29-30, 1988) but which does not allow calculation before 1900. We find an algorithm (EXC_SUNJJ) at the following link which fills this gap:
https://icalendrier.fr/calendriers-saga/etudes-thematiques/formules-calcul
It allows you to obtain the Julian day from a position of the sun (Daniel LACROZE-MARTY). Please note, it is designed with EXCEL but can easily be converted for CALC (LIBREOFFICE).
DIRECTION (m) # SA conj SU
speculum
--------------------------------------------------------------------------------------------------------------
converse direction |
Lat |
Dec |
AR |
MD |
SA |
HA |
SU |
- |
6,81 N |
15,95 |
109,26 N |
83,98 N |
-25,28 E |
(m) #SA |
-1,39 S |
21,56 N |
103,00 |
22,2 N |
69,69 N |
47,49 E |
- MD = meridian distance (from MC if SA f [SU] is diurnal or IC if Sa f is nocturnal)
– SA = semi-arc (if f is diurnal, SA f [SU] is D and all MD’s and SA’s are D, otherwise N
– HA = horizontal distance (from the nearest horizon W or E for f [SU] and m (m) #SA)
under bracket [] the fixed point, (here SU)
--------------------------------------------------------------------------------------------------------------
DP REGIOMONTANUS |
|
|
DP REGIO-CAMPA D |
|
DP REGIO-CAMPA C |
|
|
A2 (m) #SA |
A1 SU |
A1 SU |
A2 (m) #SA |
A2 (m) #SA |
A1 SU |
Tan A |
tan dec/cos dm |
|
19,90 |
|
23,11 |
|
B (1) |
+LG-A or -LG+A |
|
21,40 |
|
64,41 |
|
Tan C |
cot DM.cos B/cos A |
|
-19,08 |
|
49,01 |
|
Sin pole |
Cos C.sin LG |
|
38,59 |
|
25,65 |
|
Sin DA (2) |
Tan pole A1.Tan Dec A2 Tan pole A2. Tan Dec A1 |
DAP |
5,47 |
18,38 |
10,94 |
3,29 |
AO (3) |
AO ± DA |
|
10,47 |
84,62 |
92,06 |
12,66 |
arc |
AO1 – AO2 |
|
|
-74,15 |
|
-79,41 |
|
|
|
|
DIRECT |
|
CONVERS |
--------------------------------------------------------------------------------------------------------------
DP PLACIDUS |
|
|
METHOD CHOISNARD |
|
|
|
|
|
|
Plac direct |
Plac conv |
sa1/dm1 |
3,14 |
1,36 |
sa2 |
83,98 |
110,31 |
x |
26,75 |
81,27 |
dm² |
109,26 |
157,80 |
sign |
-1 |
-1 |
|
|
|
arc |
82,51 |
76,53 |
|
|
--------------------------------------------------------------------------------------------------------------
X = sa2.dm1/sa1
sign : if the two points are on either side of the meridian, take +1 ; otherwise -1
Arc = dm2 ±sign.x
Accuracy of measuring the placidus and regiomontanus directions
--------------------------------------------------------------------------------------------------------------
DIRECTIONS |
| 04h 55' 52" |
12h 18' 42" TU |
user |
promissor |
significator |
ZODIACAL |
(m) # SA |
C SU |
Long radix |
102,080 |
17,300 |
(m) square SA / □ SA = |
CAN |
ARI |
Event year / Y | MO motion |
1625,375 / 73 Y |
|
MUNDANE ASPECT |
1,530 |
[C] - (m) # SA SU |
ZODIACAL DIRECTION |
ZC Regio-Campa AR orb 0,47 |
|
(m) # SA C SU |
ACTUAL |
INTENDED |
keyfactor |
key : 1/Equ=1,02 |
EQU | arc =1,02 |
result ± 2 year |
74,716 |
74,7 | 1627 |
Lg D CONVERSED (-) |
(m) # SA |
C SU |
Regio-campa |
25,66 |
275,12 |
|
ARI |
CAP |
placidus |
208,970 |
279,720 |
Lg D PROGRESSED (+) |
LIB |
CAP |
Regio-campa |
168,09 |
103,61 |
placidus |
171,61 |
101,21 |
CONVERSED DIFF |
VIR |
CAN |
Arc regio-campa |
8,36 |
-173,04 |
Arc placidus |
191,67 |
-177,64 |
PROGRESSED DIFF |
|
|
Arc regio-campa |
150,79 |
-1,53 |
Arc placidus |
154,31 |
0,87 |
--------------------------------------------------------------------------------------------------------------
Here, we have precision both with PLACIDUS and REGIOMONTANUS (0.87 and -1.53 respectively).
DIRECTION MC
JU TRI MC : Created cardinal priest in the consistory of March 26, 1618; with dispensation for having a nephew in the Sacred College of Cardinals.
ANGLE DIRECTION |
AR
JU DIR |
AR
MC RADIX |
arc TRI |
1618 |
183,50 |
305,20 |
121,70 |
DIRECTION MC
SU conj MC
ANGLE DIRECTION |
AR SU |
AR MC |
MC |
1622 |
87,46 |
305,20 |
217,74 |
12h 23' 2" TU (-) |
15,94 |
16,71 |
0,77 |
year 71,47 EQU+ |
orb_ray |
|
70,74 |
The arc is SU (15.94-16.71) = 0.77 YEAR 70.74 (71.47 EQU).
The placidus key indicates 71.70 Y. (for the 8 june 1552 at 14h54).
DIRECTION # SU conj MA
Lerma was deposed by a palace intrigue carried out by his own son, Cristóbal de Sandoval, Duke of Uceda, manipulated by Olivares. It is probable that he would never have lost the confidence of Philip III, who divided his life between festivals and prayers, if not for the domestic treachery of his son, who allied himself with the king's confessor, Aliaga, whom Lerma had introduced. After a long intrigue in which the king remained silent and passive, Lerma was at last compelled to leave the court, on 4 October 1618. [see wikipedia].
--------------------------------------------------------------------------------------------------------------
speculum
converse direction |
Lat |
Dec |
AR |
MD |
SA |
HA |
MA |
-1,1 S |
-4,16 S |
353,16 |
132,04 N |
93,66 N |
-38,38 E |
(m) #SU |
0,00 |
23,17 N |
79,89 |
45,31 N |
67,92 N |
22,61 E |
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DP PLACIDUS |
|
|
METHOD CHOISNARD |
|
|
|
|
|
|
Plac direct |
Plac conv |
sa1/dm1 |
1,50 |
1,80 |
sa2 |
93,66 |
112,08 |
x |
62,48 |
62,26 |
dm² |
132,04 |
134,69 |
sign |
-1 |
-1 |
|
|
|
arc |
69,56 |
72,43 |
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DP REGIO |
|
|
DP REGIO-CAMPA D |
|
DP REGIO-CAMPA C |
|
|
A2 (m) #SU |
A1 MA |
A1 MA |
A2 (m) #SU |
A2 (m) #SU |
A1 MA |
Tan A |
tan dec/cos dm |
|
-6,20 |
|
31,32 |
|
B (1) |
+LG-A or -LG+A |
|
47,50 |
|
72,62 |
|
Tan C |
cot DM.cos B/cos A |
|
31,50 |
|
19,08 |
|
Sin pole |
Cos C.sin LG |
|
34,25 |
|
38,59 |
|
Sin DA (2) |
Tan pole A1.Tan Dec A2 Tan pole A2. Tan Dec A1 |
DAP |
-2,84 |
16,94 |
19,97 |
-3,33 |
AO (3) |
AO ± DA |
|
356,00 |
62,95 |
59,92 |
356,48 |
arc |
AO1
– AO2 (modulo 360) |
|
|
-66,96 |
|
-63,44 |
|
|
|
|
DIRECT |
|
CONVERS |
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SOLI-LUNAR PROGRESSION
This technique is described in the PRIMUM MOBILE from PLACIDUS. I give here an interpretation in mundane theme for the death of Francisco GOMEZ (17 may 1625).
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. true date of even). For example in the case of Francisco Gómez, if we take the date of 17 May 1625, we must first translate this date into 'life-year equivalent': we find :
---------------------------------------
EVEN |
73,1377720195744 |
73 |
Y |
|
1,6532642348933 |
1 |
M |
|
19,597927046799 |
19 |
D |
|
14,3502491231757 |
14 |
H |
|
|
21,01 |
M |
---------------------------------------
The method of “embolismic lunations” as a predictive technique :
An embolismic lunation, correctly termed an embolismic month, is an intercalary month, inserted in some calendars, such as the Jewish, when the 11-days' annual excess over twelve lunar months adds up to 30. An arbitrary application of this was used by Placidus, who applied the term Embolismic Lunation, to a Figure cast for the moment of the Moon's return to the same relation to the Sun that it occupied at birth. It was made the basis for judgment concerning the affairs and conditions of the ensuing year of life.' [https://astrologysoftware.com/community/learn/dictionary/lunation.html]
The solar year does not have a whole number of lunar months (it is about 365/29.5 = 12.37 lunations), so a 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).
In the case of Francisco Gómez, we observe:
SU radix = 327° 30' 12" (327,5° AQU)
MO radix = 54° 55' 51"° (54,93° TAU)
∆ = |272° 34' 21"| (272,57° ) [ 22 tithi = ROUNDUP (∆/12)]
Here is now the way in which Placidus would have proceeded: for 60 full years, 55 embolismic lunations are accomplished in 13 years after birth but with 33 days less, that is to say 11*5 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 28 Ma 1557, by removing 55 days, we arrive at 2 February 1557 [,,,] and then, the process is completed for 55 full years. Then, for the 13 other years elapsed during the twelve embolistic lunations, I arrive at 20 February 1557, for the remaining 0 months and 18 days. I compute the tithi (exact distance between SU and MO radix) for the last time : the date of Embolistic Progression J0 is : 2 February 1557at 8h 10min TU. Thereafter, i add to this date 4,07 d corresponding to 1,653M [see EVEN] :
JD Pr Emb = 1,65 x 30 / (365.24 /29.53) = 4,07 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 365,242217182812 (1)
syn month = 29,5305878777714 (2)
where T = (JD-2451545)/36525
In the present case JD = 2289788,5
so, T = -4,4772758384668 (see formula 1 and 2)
Finally, we find : date for J4,07D = 6 February 1557 at 9h 28min local (9h 49min 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
We have another date : After a long intrigue in which the king remained silent and passive, Lerma was at last compelled to leave the court, on 4 October 1618.
Here, we find opp VE-SA to SU.
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