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

ATTERSALL James

ATTERSALL James

01 Oct 1817 GREG    CAL
wednesday GREG
 | lat 53° 15' 0" | N 0°33' W
LONDON
---------------------------------
natal (bt) 19 h 45 min
raas-rams :0h 10' 18"
reckoned bt Lat --> lmt 16 h 34 min
tu 16h 36' 11"
tsn 17h 14' 11"
---------------------------------
timezone  : 0
DST : 0 (-)
Equation of time 0h 10' 18"
ΔT 0h 0' 14"
---------------------------------

 This topic was discussed in the forum

https://skyscript.co.uk/forums/viewtopic.php?p=125144#p125144

and it comes from a collection of 30 themes by John Worsdale, contained in the 'Celestial Philosophy' (Longman, 1828), with a large discussion [pp 35-37], the square theme appearing on p. 19.

 

Born October 1st, 1817, 4:45 P.M. in London.

In the forum cited above, we can read:

'On the day of Death, the Child went into the Street unobserved by any one, and immediately accompanied several other Children who were playing very near a Horse that was feeding a short distance from the Door, near the side of the River. The Horse was always considered to be a very quiet Animal, but in the fatal Hour, he kicked at the Children, yet none were injured, except the unfortunate Child, who received the stroke in its forehead, which proved instantly mortal; his Death happened on the 22nd of September, 1819, near three o’clock in the Afternoon, Age one Year, eleven Months, and twenty days.' [...] 

 and i add this extract from Worsdale :

'The Astral causes that produced the sudden and violent Death of this Child, are plainly visible; the Ascendant is afflicted by the body of Saturn, and Square of the Moon, and Mars in Mundo; the Moon is conjoined with Mars among evil Stars in the Northern Angle, approaching the Terms of Saturn, without any relief, and that Luminary is applying- to the Mundane Square of Saturn, by direct motion. The Part of Fortune is afflicted by the opposition of the Moon and Mars; but I judged the work of Mortality to arise chiefly from the uninterrupted communication of those violent rays of Mars and the Moon from the Imum Celi, to the Sun, who is the true Apheta, or giver of Life, particularly because the Hyleg is near the Body of Mercury, and Rapt Parallel of Saturn ; and I shall here observe that Mercury is of the nature of the enemies in the Celestial constitution.'

Celestial philosophy, p. 36-37

 Now, I give the theme in a more modern form: 

 
Aspects are computed from the mundane version of the theme; the blue triangle is the mark of the hyleg (SU) and the red triangle, that of the alchocoden (ME).
If we look at the possibilities for the hyleg, we find SU (which has an aspect with ME) and ME has a TERM-like dignity; moreover the theme is diurnal. MO does not have a Ptolemaic type aspect. ASC is the 2nd candidate to be the hyleg with an aspect of VE (and two dignities, TERM and EXN, I pass on FAC which is only mentioned for the record). However, ASC cannot be retained in principle because the moon is preventional (WANING type).
The fourth point to examine is POF since the theme is conjunctional. But there is no dignity.
The last point is the dominant of the theme: VE. VE is in opposition to ASC and SA. It is in dignity of TERM with SA.
If we want to make a synthesis, it is essential to respect the order of succession of the different possibilities offered: here there is no need to hesitate. The hyleg is SU and the alchocoden can only be ME, even if ME appears, as Worsdale clearly saw it as problematic.

ME is retrograde, peregrine and also occidental. SU is in fall [LIB].

The dominance table :

We see that VE and SA (score >= 5) are 'effective'.

The disposition of the stars (I am only talking about the group of Behenian stars here) shows:
- conjunction cusp of XII and Algol (β Per) in Regio domitude at 331.36
- conjunction of ASC and Deneb algedi (δ Cap) at 359.76 (Regio domitude)

The primary directions  :

1)- DIRECTION : □MA conj ASC
---------------------------------
For a direction between ASC and any planet or aspect (zodiacal or mundane),  we must compute ASC OA and m OA (here □MA) ; the inner circle contains the AR (right ascension) values of ASC and MA or SA.  The outer circle contains the values of the same elements in OA (oblique ascent). Natal ASC is always indicated with a round symbol (o) and the natal significator (MA or SA) with a cross (x). The direction is simulated  by a segment of a circle that ends counter-clockwise at the value in OA. A symbol reflects either a conjunction aspect or a quadrature aspect.

OA ASC = 348,55°
OA □ MA progr = 353,59

 D= 1,01°

1)- DIRECTION : CSA conj ASC
---------------------------------
For a direction between ASC and any planet or aspect (zodiacal or mundane),  we must compute ASC OA and m OA (here CSA) ; the inner circle contains the AR (right ascension) values of ASC and MA or SA.  The outer circle contains the values of the same elements in OA (oblique ascent). Natal ASC is always indicated with a round symbol (o) and the natal significator (MA or SA) with a cross (x). The direction is simulated  by a segment of a circle that ends counter-clockwise at the value in OA. A symbol reflects either a conjunction aspect or a quadrature aspect.

OA ASC = 348,55°
OA C SA progr = 355,41

 D= 0,52°

It is notable that at birth we have respectively :

- for MA D = 2.55° and for SA D = 3.04°

2)- DIRECTION : □ VE conj MA

Problem XVI gives the means of finding if a star is in the same circle of position, with a planet or any significator. Find the arc position ET [3.21], which assumes the hour angle of the star and its semidiurnal arc. With ET and H [H' 4.29] you will have the angle O [5.36] of the position circle with the meridian; you will compare this circle to that of the signifier and you will see if it differs [adapted from Delambre, Histoire de l'Astronomie du Moyen Âge, p. 489, 1819]

2.1 MAGINI – REGIOMONTANUS   
---------------------------------
converse   
---------------------------------
If dir is converse,  change in [P] dec and h of [□ VE] for [C MA]  and in [ET], change DA of [□ VE] for [C MA]   
    
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
    
    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 -
---------------------------------   
P (horary angle, from midnight)    0
-178,58    ||  cosP = (sinh-sin Hsin D)/(cosHcosD)
    
PHA (HAO angle)   
5,36    ||  TanPHA = sinP/((sinD+cosP)cosH)
    
PR (pole HAO)   
4,289    ||  sinPR=sinPHsinPHA
    
ET (arc meridian/HAO)   
3,21    ||  tanET=cosHtanPHA
    
H'    ||  H' (incident horizon = B50
4,29    ||  tanH'=sinETtanH
    
PAR (position angle)   
4,67    ||  sinPAR=sinH'/cosD
    
QS, HPR (Az PR)   
86,79    ||  cosQS=sinET
    3,2104838638743
ΔAR' (DA/HAO)   
1,79    ||  sinΔAR'=tanDtangH'
    
OTE, HTQ, ETH (equat/HAO angle)   
85,71    ||  tanOTE=cotH/sinET
    
KO (≠AR □ VE C MA)    Eq for Fig 130 (pl 12) see fig for location and  Explanation of spherical triangles
0,45    ||  KO=AR□ VE - ARC MA
    
A (AET angle)    ||  EA = 90-H
5,36    ||  sinA=sinETsinOTE/sinEA
    
T (angle horizon/OTH)    ||  pole of PRS (=90-H')
85,71    ||  cosT=sinAETsinH
    
[+] TO ΔAR' □ VE    ||  D boreal --> sign [+] = switch for [-]
1,84    ||  sinTO=tanDcotT
-1   
[-] TV ΔAR' C MA    ||  D' boreal-> sign [-] = switch for [-]
1,79    ||  sinTV=tanVZcotT
1   
tasyir    ||  If OS (D) [+], TO ~ sign,  If RK (D') [-], TV ~ sign
0,41    ||  KV=KO – OT – TV
    
VZ    ||  D' (declin of C MA)
22,65   
    
OS    ||  D (declin of □ VE)
23,17   
    
ST    distance ST
23,24    ||  sinST=sinD/sinT
    
TZ    distance TZ
22,72    ||  sinTZ=sinD'/sinT
    
ZS    ≠dist
0,52    ||  If D/D'<0 [-]
    
EPA (EPV, EV) ± ΔAR'    horary angle of □ VE
5,00    ||  if d is [-] ~ ΔAR'
    
IOANNIS ANTONII MAGINI  PRIMI MOBILIS LIBER NONUS QUI AGIT DE DIRECTIONIBUS pp, 214-232 PROBLEMA XVIII p, 230   
    
KV = KO [+] TO [-] TV   
0,41    ||  KV = KO [+] TO ΔAR' □ VE [-] TV ΔAR' C MA
-0,05    ≠AR'
---------------------------------
DIRECTION = TASYIR = 0.41
---------------------------------

2.2 PLACIDUS - AL BIRUNI - AL BATTANI

PLACIDUS        □VE C MA
choose if  sign alt □ VE = sign alt C MA       
Actually, -13,58 / -14,09       
-------------------------------------------       
semiarc    □ VE    55,04
dm            □ VE    0,96
semiarc    C MA    56,03
second. Dist.    C MA    0,98
              
dist from MC or IC    C MA    1,42
 -------------------------------------------       
arc of dir    DIRECTIO DIRECTA    0,44
-------------------------------------------                
semiarc     C MA    56,03
dm            C MA    1,42
semiarc    □ VE    55,04
second. Dist.    □ VE    1,39
       
dist from MC or IC    □ VE    0,96
-------------------------------------------         
arc of dir    DIRECTIO CONVERSA    0,43
------------------------------------------- 

 
DP PLACIDUS        METHOD FOMALHAUD-CHOISNARD       

This is the method which appears in the work of Paul Choisnard "Langage Astral" (Editions Traditionnelles, reed 1963), pp. 149-173. Choisnard bases himself on Ptolemy's process (Tetrabiblos, III, 10 and IV, 11) which Neugebauer analyzes in his "History of Ancient Mathematical Astronomy", pp. 898-899 (see also : Neugebauer - Van Hoesen "Greek Horoscopes", p. 12 in the 'Starter' article where he gives a basic bibliography).

    Plac     direct    Plac conv
-------------------------------------------
sa1/dm1    57,33        39,46
sa2            56,03        55,04
x                0,98        1,39            (x = sa2.dm1 / sa1)
dm²            1,42        0,96
sign            -1        -1                   if the two points are on either side of the meridian, take + ; otherwise -
-------------------------------------------
arc            0,44        -0,43            arc = dm2 ± x
-------------------------------------------    

Perry Matthew

 Perry, Matthew

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

 THEME

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

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

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

Hyleg is ASC and alchocoden MA.

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

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

PRIMARY DIRECTIONS

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

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

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

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

This time, the orb is 1.88.

PROGRESSED (secondary progressions)

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

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

SOLI-LUNAR PHASE

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

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

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

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

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

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

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

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

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

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

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

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

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

In the case of Matthew Perry, we observe:

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

∆ = 71°28' (6 tithi = ROUNDUP(∆/12))

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

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

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

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

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

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

 

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

Solar return

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

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

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

We find : MA # MO (orb ≤ 2°).