CAMPANELLA Tommaso |
| 05 Sep 1568 JUL CAL |
| sunday JUL |
| | lat 38° 29' 0" | N 16°28' E |
| 0 |
| --------------------------------- |
| natal (bt) 15 h 27 min |
| raas-rams :0h 5' 0" |
| reckoned bt Lat --> lmt 6 h 16 min |
| tu 6h 16' 10" |
| tsn 5h 52' 38" |
| --------------------------------- |
| timezone : 0 |
| DST : 0 (-) |
| Equation of time 0h 5' 0" |
| ΔT 0h 2' 18" |
| --------------------------------- |
Italian philosopher, theologian, astrologer, and poet.
Accused of leading a conspiracy against the Spanish rule in his hometown of Stilo, Campanella was captured and incarcerated in Naples (1599), where he was tortured seven times and then, crippled and ill, was sentenced to life imprisonment. Campanella spent twenty-seven years imprisoned there, often in the worst conditions. During his detention, he wrote his most important works including his most famous piece, The City of the Sun (originally written in Italian in 1602; published in Latin in Frankfurt (1623) and later in Paris (1638). He defended Galileo Galilei in his first trial with his work The Defense of Galileo (written in 1616, published in 1622). Campanella was finally released from prison in 1626, and was restored to full liberty in 1629. We note a whole series of trials against him between 1591 and 1594. That of 1599 earned him 26 years of captivity. Another plot almost succeeded in 1634.
He died on 21 May 1639 in the convent of Saint-Honoré in Paris, France.
source : "Una Nativita manoscritta di Campanella", Germana Ernst - Giuseppe Bezza, Bruniana & Campanelliana anno XIII, 2007/2, p. 711-716
Birth took place in Italy, in Stilo. The style is therefore italic: it is stipulated 12 6 HOR, that is to say about 6.16 (Sunset) + 12.6, at 6:26 pm, September 4. We must therefore count on September 5.
| sunset 6,18 → [18,28] |
| italic : D-1 [pm: 6h 16' 42"] |
For dates back to the 18th century, the day began at 0h of a real local solar time when the sun passed to the meridian of the place, which is close to the actual noon. We must therefore add 12 hours to find on this theme (and the many others which appear in this blog) our current civil time.
THEME
SU is P with a [-11] score
MO is Fa with a [-1] score
VE is F cb with a [-4] score
JU is Ru with a [-5] score
MA is D with a [-8] score
SA is te - T with a [18] score
Moreover, SA is in mutual reception by exaltation with ME which is an unfortunate circumstance (cf, Morin de Villefranche, Astrologia gallica, book XVII, cap VII, 39-51, La Haye, 1636)
Last, ME is besieged (<13° between MA and SA) that is another unfortunate circumstance.
we see below the list of aspects :
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JU 90 SU Or MA 120 MO Oc JU 90 VE Or
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The best aspect is [best :ma 0° (0,63) me] and the worst aspect is [worst :mo 120° (-0,03) ma]
The traditional almuten (Omar, Ibn Ezra) is JU
we see below the list of dignities for JU :
---------------------------------------
[ term 4 tri 0 rul 2 exn 0 fac 4 ]
[ su 2 mo 0 asc 3 syg 0 pof 2 ]
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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 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)
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Ω 165,41 /
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We note that Algol (bêta Persei) is conjuct (in mundo) with cusp of IX house... and TRINE to SA, conjuct to ASC. Unfortunately, this did not prevent accidents and severe injuries. Antares is conjuct (in mundo) with JU : "Great religious zeal, real or pretended, ecclesiastical preferment, a tendency to hypocrisy, benefits through relatives" [Fixed Stars and Constellations in Astrology, Vivian E. Robson, 1923, p.136, 234].
HYLEG - ALCHOCODEN
ZODIACAL – MUNDANE
In our research, we hypothesized 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 CAMPANELLA Tommaso 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 CAMPANELLA Tommaso, it is .
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 [-7],
But, when we look for the dignities that appear in the zodiacal inscription of ASC, we find none.
we find at least one aspect to match with the dignities
We'll see later what we get when we search for mundane dignities.
Now that we doubt to take SU as hyleg, we are left with MO but we don't find any aspect to match with the dignities,,,
Now that we doubt to take MO as hyleg, we are left with the choice of ASC and that of POF. It is the way in which is laid out MO which will indicate the choice to us. If MO is waxing, we take ASC for hyleg ; if MO is waning, we take POF for hyleg,
It turns out that MO is waxing; so we will take ASC,
Now we must look for the alchocoden: it is the planet which has the maximum dignity with regard to the hyleg and which exchanges a Ptolemaic aspect with the hyleg.
if we consider the MUNDANE system, we observe a conjunction aspect of SA.
At the same time, it appears that SA has dignity of TERM over ASC.
So we have two possibilities with our hypothesis : first choose ASC for hyleg ; second choose the MUNDANE system and try to find another couple of hyleg/alchocoden,
If we choose now ASC we must know that Dorotheus, Al Qabisi, and Ptolemy, agree with this choice
In case of ASC is the Hyleg, there is then one candidate to be the alchocoden:SA
First, we have to see which candidate has the most dignity: here, SA has candidate alcho dignities referring to ASC : [TERM]
First, SA is linked with ASC by a [conjunction] aspect and a [TERM] dignity,
However, SA is [te - T] and has a power of [3], SA has a Kadkhudah score of [1]
SA is located at 179,21 °at more than 5° from [Δ degrees cups sup [XII] : 29,41° (330)] and has a domitude regio of : [359,41] for a latitude of [2,13°]
So, HYLEG = ASC and ALCHOCODEN = SA.
DIRECTIONS AT DEATH
DIRECTIO DIRECTA (m) □ ♄ ☌ ☽
---------------------------------------------------------------------------------------------------------------------
| DP REGIOMONTANUS | DP REGIO-CAMPA D | DP REGIO-CAMPA C | ||||
| A2 □SA | A1 MO | A1 MO | A2 □SA | A2 □SA | A1 MO | |
| Tan A | tan dec/cos dm | -18,29 | -23,48 | |||
| B (1) | +LG-A or -LG+A | 20,19 | 15,00 | |||
| Tan C | cot DM.cos B/cos A | -18,35 | 89,80 | |||
| Sin pole | Cos C.sin LG | 36,20 | 0,13 | |||
| Sin DA (2) | Tan pole A1.Tan Dec A2 Tan pole A2. Tan Dec A1 |
DAP | -4,41 | -18,54 | -0,06 | -0,01 |
| AO (3) | AO ± DA | 335,20 | 249,84 | 268,32 | 339,60 | |
| arc | AO1 – AO2 | 85,36 | 71,28 | |||
| DIRECT | CONVERS |
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| DP PLACIDUS | ||
| METHOD CHOISNARD | ||
| Plac direct | Plac conv | |
| sa1/dm1 | 524,81 | 1,33 |
| sa2 | 94,80 | 110,21 |
| x | 0,18 | 83,06 |
| dm² | 71,45 | 0,21 |
| sign | -1 | -1 |
| ------------------------------------------------------------------- | ||
| arc | 71,27 | -82,85 |
| ------------------------------------------------------------------- | ||
| X = sa2.dm1/sa1 | ||
| sign : if the two points are on either side of the meridian, take +1 ; otherwise -1 | ||
| Arc = dm2 ±sign.x |
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We note a whole series of trials against him between 1591 and 1594. That of 1599 earned him 26 years of captivity.
'At Naples. however, suspicions and allegations regarding the young friar were also taking shape. In 1592, the ‘first trial’ took place, an event that was still obscure and uncertain in the treatment of Amabile and then later took on more precise contours in the studies of Giovanni Gentile and Luigi Firpo. In the month of May, Campanella was imprisoned in the convent of San Domenico, on the allegation that his extraordinary knowledge had a demonic origin and that he had scoffed at excommunication. But the real issue, as would later be verified from the text of the condemnation, was adherence to the doctrines of Telesio.' [Germania Ernst, Tommaso Campanella: The Book and the Body of Nature, p. 19, Springer, 2010]
DIRECTIO CONVERSA : [c] (m) □ ♄ ☌ ♂
This direction may seem paradoxical because it involves the two malecient planets. However, let us not forget that SA is alchocoden, in close conjunction with ASC. What we observe is a singular ballet of arcs engaging the square of Saturn: one with a direct direction to MO, the other with a converse direction to MA (which will have had the last word in this epic battle of a life!).
| speculum | Lat | Dec | AR | MD | SA | HA |
| MA | -0,07 S | -10,59 S | 205,28 | 62,88 N | 98,55 N | 35,67 E |
| □SA | 0 S | -23,48 S | 268,37 | 0,21 N | 110,21 N | 110 W |
– MD = meridian distance (from MC if SA f [MA] is diurnal or IC if Sa f is nocturnal)
– SA = semi-arc (if f is diurnal, SA f [MA] 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 [MA] and m □SA)
under bracket [] the fixed point, (here MA)
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| DP REGIOMONTANUS | DP REGIO-CAMPA C | DP REGIO-CAMPA D | ||||
| A2 □SA | A1 MA | A1 MA | A2 □SA | A2 □SA | A1 MA | |
| Tan A | tan dec/cos dm | -22,30 | -23,48 | |||
| B (1) | +LG-A or -LG+A | 16,18 | 15,00 | |||
| Tan C | cot DM.cos B/cos A | -28,00 | 89,80 | |||
| Sin pole (2) | Cos C.sin LG | -33,33 | -0,13 | |||
| Sin DA (3) | Tan pole A1.Tan Dec A2 Tan pole A2. Tan Dec A1 |
DAP | 7,06 | 16,60 | 0,06 | 0,02 |
| AO (4) | AO ± DA | 212,34 | 284,97 | 268,32 | 205,26 | |
| arc | AO1 – AO2 | -72,63 | 63,06 | |||
| CONVERS | DIRECT |
(1) B must be < ε
(2) sign of pole has the same sens of LG for DA Here, DA = DA/pole A
(3) [+] sign if pole A and Dec have the same sign; sign [-] if pole and Dec have the opposite sign
(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
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| directio conversa | (AR C MA – AR fc) – HD□ SA x Temp HC MA | (AR □ SA – AR fc) – HDC MA x Temp H□ SA |
| -1 | ||
| Al-Battani, adapted from Nallino, Opus astronomicum, pp, 315-317 |
□ SA [S W] | C MA [S E] |
| ar signif | 268,37 | 205,28 |
| meridian : □ SA [IC | C MA [IC] |
88,16 | 88,16 |
| 1 | 0,21 | 117,12 |
| Dec | -23,48 | -10,59 |
| dAR | -20,21 | -8,55 |
| hd prom | 3,83 | 0,01 |
| temp H signif | 18,37 | 16,42 |
| arc | 70,54 | -63,07 |
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The arc is 70.54 Y (the Placidus key gives 72.7 Y).
| Hd prom=6.MD prom/SA prom | Hd sign=6.MD sign/SA sign | ||
| 3,83 | 0,01 | ||
| Temp H prom = (90-dAR prom) | Temp H sign = (90-dAR sign) | ||
| 18,37 | 16,42 | ||
| pm placidus | |||
| 0,18 | 57,43 | ||
| dom | dom | ||
| 90,18 | 32,57 |
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DIRECTION FOR MAY 1592
We see a # SU conj MA. It is the first of a whole series of trials against him between 1591 and 1594. That of 1599 earned him 26 years of captivity.It is the first in a series of counter-parallels related to the stellium of SU with [ME VE SA] which frames the ASC. Moreover, we see that MA is besieged (see Bonattus, Decem continens tractatus astronomie in Liber Astronomiae, part III, trad Robert Hand, cap XXI, pp. 96-97, Project Hindsight, vol XI, 1995).
DIRECTIO CONVERSA ♯ ☉ ☌ ♂
We must take into account an important element: the ascensional difference (DA). This is the difference between Right Ascension (AR) and Oblique Ascension (OA). DA is always calculated in absolute value |DA| and it is added or subtracted from 90° (SA = 90° corresponds to a point on the equator cut by the horizon; depending on whether a star approaches or moves away from the line of horizon, SA is > 90° or < 90°, i,e, (+) depending on whether it is diurnal and northern ; or nocturnal and southern ; (-) depending on whether it is diurnal and southern ; or nocturnal and northern. But we have to take care of a fact : when we have a counter parallel or an aspect, the quadrant is not the same and the declination is different ; so the sign is also different.
sin(DA) = -tan(φ)tan(δ)
φ = latitude 38,48 N
δ MA = -10,59 -
DA-MA = 8,55°
δ (m) #SU =-2,37 -
DA-(m) #SU =1,89°
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| converse direction | Lat | Dec | AR | MD | SA | HA |
| MA | -0,07 S | -10,59 S | 205,28 | 63,63 N | 98,55 N | 34,92 E |
| (m) #SU | 0,00 | -2,37 S | 185,46 | 83,45 N | 91,89 N | 8,44 E |
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– MD = meridian distance (from MC if SA f [MA] is diurnal or IC if Sa f is nocturnal)
– SA = semi-arc (if f is diurnal, SA f [MA] 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 [MA] and m (m) #SU)
under bracket [] the fixed point, (here MA)
| DP REGIOMONTANUS | DP REGIO-CAMPA C | DP REGIO-CAMPA D | ||||
| A2 (m) #SU | A1 MA | A1 MA | A2 (m) #SU | A2 (m) #SU | A1 MA | |
| Tan A | tan dec/cos dm | -22,83 | -19,94 | |||
| B (1) | +LG-A or -LG+A | 61,31 | 58,42 | |||
| Tan C | cot DM.cos B/cos A | -14,48 | 3,66 | |||
| Sin pole | Cos C.sin LG | 37,05 | 38,39 | |||
| Sin DA (2) | Tan pole A1.Tan Dec A2 Tan pole A2. Tan Dec A1 |
DAP | -8,11 | -1,79 | -1,88 | -8,52 |
| AO (3) | AO ± DA | 213,40 | 187,25 | 187,34 | 213,80 | |
| arc | AO1 – AO2 | 26,14 | 26,46 | |||
| CONVERS | DIRECT |
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 (MA) : cot DAP f = (cot de f x cot lat) / in DM f ± cot DM f, i,e, : cot (DAP f) = (Cot dec f[-10,59°] x Cot Lat [38,48°]) /sin DM f [63,63°] ± cot DM f [63,63°]
DAPf = 171,89°
We find the pole of f (MA) by formula : tan(pole f) = sin (DAP f) x cot (dec f) i,e, tan(pole f) = tan f [8,11°] x cot f [-10,59°]
pole MA regio =-37,05°
(1) We need now the DAP of m ((m) #SU) under the pole of f, sin (DAP m) = tan (pole f) x tan (DEC m), i,e, : (MA) : sin (DAPm/f) = tan [37,05°] x tan [-2,37°]
DAP m/f = -1,79°
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 MA = 213,4° and AO m = AR m ± DAP m ; idem for sign ; so AO m(m) #SU = 187,25°
---------------------------------
arc D Regio = 26,14°
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We are now going to compute the converse Regiomontanus direction corresponding to the arc f MA / p (m) #SU
First, compute the ascensional difference under m ((m) #SU) : cot DAPm = (cot dec m x cot lat)/sin DM m ± cot DM m, i,e, : Cot(DAP m) = (Cot decm[-2,37°] x Cot Lat [38,48°]) / Sin DM f [83,45°] ± Cot DM m [83,45°]
DAP m = 178,12°
We find the pole of m ((m) #SU) by formula : Tan(pole m) = Sin (DAP m) x Cot (dec m) i,e, Tan(pole m) = Sin m [178,12°] x Cot m [-2,37°]
pole (m) #SU regio =-38,39°
We need now the DAP of f (MA) under the pole of m, Sin (DAP f) = Tan (pole m) x Tan (DEC f), i,e, : ((m) #SU) : Sin (DAP f/m) = Tan[38,39°] x Tan [-10,59°]
DAP f/m = -8,52°
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 (m) #SU = 187° and AO f = AR f ± DAP f ; idem for sign ; so AO f MA = 213,8°
---------------------------------
arc C Regio = 26,46°
---------------------------------
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 [-10,59°] / cos DM f [63,63°]
A = -22,83°
Then : B = Lat [38,48°] + A [-22,83°]
B = 61,31°
And, Tang C = Cot DM f [63,63°] x Cos B [61,31°] / Cos A [-22,83°]
C = -14,48°
Then, we have Sin pole f = Cos C [-14,48°] x Sin LG [38,48°]
---------------------------------
So, pole MA regio = 37,05°
---------------------------------
Now go back to (1)
For m (m) #SU; we have : A => Tan m = tan dec m [-2,37°] / cos DM m [83,45°]
A = -19,94°
Then : B = Lat [38,48°] + A [-19,94°]
B = 58,42°
And, Tang C = Cot DM m [-263,45°] x Cos B [58,42°] / Cos A [-19,94°]
C = 3,66°
Then, we have Sin pole m = Cos C [3,66°] x Sin LG [38,48°]
---------------------------------
So, pole (m) #SU regio = 38,39°
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| DP PLACIDUS | Plac direct | Plac conv |
| sa1/dm1 | 1,10 | 1,55 |
| sa2 | 98,55 | 91,89 |
| x | 89,50 | 59,33 |
| dm² | 63,63 | 83,45 |
| sign | -1 | -1 |
| ------------------------------------------------------------------- | ||
| arc | -25,87 | 24,12 |
| ------------------------------------------------------------------- | ||
| FOMALHAUT-CHOISNARD | ||
| X = sa2.dm1/sa1 | ||
| sign : if the two points are on either side of the meridian, take +1 ; otherwise -1 | ||
| Arc = dm2 ±sign.x |
We will now use the Placidus system of mundane directions. The simplest system is that of Choisnard-Fomalhaut. First you need to retrieve the data from the SA (semi-arc) and the DM (meridian distance) of the nocturnal point because the altitude of MA is -27,14°. important note: the SA and DM of the two points are always counted diurnal if the first point (here MA) is above the horizon even if the second is below. They are counted nightly if the first point (MA) 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 MA is diurnal, and from the nocturnal meridian if it is nocturnal.
nocturnal meridian MC = 268,91°
AR MA = 205,28°
AR (m) #SU = 185,46°
SA N (δ-) (m) #SU = 91,89°
DM N (m) #SU = 83,45°
For the significator (m) #SU altitude (h) =-6,6°. so :
SA D (δ-) (m) #SU = 98,55°
DM N MA = 83,45°
Then we compute Saf/DMf (so : SA f [ 91,89°] / DM f [ 83,45°])
Sa f / DM f =1,1
and the angle x = SAm x DM f/SA f, so : SA m [ 98,55°] x DM f [ 83,45°]/SA f [ 91,89°]
x = 89,5°
We find the direction by DMm - x, so : DM m [ 83,45°] ± x [89,5]
We must now have regard to the double ± sign of the last expression; in the case where f (MA) and m ((m) #SU) are on either side of the meridian, the direction arc is obtained by taking the sum (instead of the difference) of the two quantities DMm and x. This is not the case here, so sign = (+)
the computation of the arc requires, depending on the case, a reduction of 360° (so arc modulo 360°)
---------------------------------
arc D =-25,87°
---------------------------------
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 (m) #SU) and the f point is a planet or an axis, (here MA)
We can now compute the converse direction : point f is directed towards point m, i.e. the star is directed towards the aspect. This is where the problem of the orientation of the primum mobile arises because it is not concevable to rotate the local sphere in both directions… It does not seem convenient to postulate that the arc of direction is counted in the order of the signs of the zodiac (when it is direct, i.e. when one directs a promissor towards a significator): indeed, the ecliptic has nothing to do with a direction since this one depends only on the diurnal movement ( primum mobile). It is therefore otherwise that we must pass judgment on this.
That time, we compute Sa m / DM m (so : SA m [81,45] / DM m [116,37])
Sa m / DM m =1,55
and the angle x = SA f x DM m/SA m, so : SA f [ 91,89°] x DM m [116,37] / SA m [81,45]
x = 59,33°
We find the direction by DM f - x, so : DM f [ 83,45°] ± x [59,33°]
We must now have regard to the double ± sign of the last expression; in the case where m ((m) #SU) and f (MA) are on either side of the meridian, the direction arc is obtained by taking the sum (instead of the difference) of the two quantities DM f and x. This is not the case here, so sign = (-)
---------------------------------
arc C =24,12°
---------------------------------
Below we will find two algorithms that we find in the Encyclopedia of Islam (vol IV, 1934) in the article tasyir and in the translation given by Carlo Alfonso Nallino of the opus astronomicum of Al-Battani (1903)
| Adapted from Schirmer, 1934 [al-Battani, al-Biruni] | directio conversa | ||
| AR (m) # SU - ARC MA | 1 | ||
| 19,82 | 19,82 | ||
| OA (m) # SU - OAC MA | |||
| 26,48 | 26,48 | ||
| dist C MA from FC | -63,63 | ||
| -63,63 | 83,45 | ||
| half night arc C MA (= SA) | -360 | ||
| 98,55 | 91,89 | ||
| tasyir degrees | |||
| 24,12 | 25,87 | ||
| 335,879 | 385,87 |
"According to the respective positions of the significator and promissor, two kinds of tasyir arc distinguished:
a. Direct tasyir (directio directa) when the significator precedes the promissor in the order of the signs of the zodiac. Here the significator is the place to be “directed”, the promissor regarded as fixed .
b. Indirect tasyir (directio conversa) when the significator precedes the promissor in the order of the daily motion of the celestial sphere. In this case the promissor is moved to the circle of position of the significator which is assumed to be fixed.
A special form for application of the calculation of the tasyir (a kind of inversion of the process) was developed in choosing days in this way that the position of only one star was given and also a definite time or what is the same thing on account of the conversion of periods of time into degrees of the equator, a definite number of tasyir degrees. The problem is to find the degree which corresponds to the end point (the “goal”) of the tasvir arc. indicia could then be deduced from the conjunction of planets occurring at this degree." [Schirmer, in Encyclopaedia of Islam, vol IV, article :AL-TASYIR (in the west; atazir, atagir, athadr, directio, prorogatio, théorie aphétique, pp. 694-697, 1934),
| Al-Battani, adapted from Nallino, opus astronomicum, pp, 315-317 |
(AR C MA – AR fc) – HD(m) # SU x Temp HC MA | (AR (m) # SU – AR fc) – HDC MA x Temp H(m) # SU |
| ar signif | 185,46 | 205,28 |
| SU | MA | |
| ar cardine | 88,91 | 88,91 |
| 1 | 96,55 | 116,37 |
| Dec | -2,37 | -10,59 |
| dAR | -1,89 | -8,55 |
| hd prom | 3,87 | 5,45 |
| temp H signif | 15,31 | 16,42 |
| arc | 155,86 | 205,84 |
| 24,14 | -25,84 |
But there is another kind of direction which is entirely consistent with tradition; it consists of directing (in the direction of the signs of the zodiac) the planet to the aspect (or parallel). We practice this category of directions in mundo.
ANOTHER DIRECTIO # ♂ ☌ ☉
This direction is superimposed on the previous one: I call it an “echo” direction. This type of leadership often demonstrates lasting episodes.
DIRECTION FOR 1592
We find the two same with a smaller orb.
Much more serious was the Calabrian plot in 1599 : arrestation the 6 September 1599.
DIRECTION FOR SEPTEMBER 1599
We find a square MO to MC (diff AR 1.22°).
We note two counter parallels echo: # SA conj MA and # MA conj SA.
DIRECTIO #MA conj SA
This direction touches SA, the alchocoden. It is all the more important as SA is close to ASC (AO ASC = 179.16°) and AO SA = 178.32°. We note that AO # MA is 177.54°.
We find the arc with the method of MAGINI :
MAGINI – REGIOMONTANUS
direct
--------------------------------------------------------------------------------------------------------------------------
| speculum |
Lat | Dec | AR | MD | SA | HA |
| SA | 2,13 N | 2,27 N | 180,13 | 90,97 D | 91,81 D | 0,84 E |
| (m) #MA | -0,07 S | 10,97 N | 153,32 | 64,16 D | 98,86 D | 34,7 E |
-------------------------------------------------------------------------------------------------------------------------- – 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 (m) #MA)
under bracket [] the fixed point, (here SA)
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 -
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, which assumes the hour angle of the star and
its semidiurnal arc. With ET and H you will have the angle O of the
position circle with the meridian; you will compare this circle to that
of the significator and you will see if it differs from it. Problem
XVII. The significance being placed in
any angle, direct or lead him
to the promissor, following the order of the signs. He [Magini] calls,
following the usage of astrologers, significator, the one who holds the
first place in the zodiac, and promissor, the one who holds the second
place according to the order of the signs.
To direct means to seek
the arc of the equator which, by the movement of the sphere, while the
promissor will be transferred to the position of the first, that is to
say of the significator, will pass through the meridian or through the
horizon, if it is in one of these circles, or through the circle of
position of the significator, if it declines from one of these angles.
We have already seen that astrologers counted four angles; the angle of
the east and that of the west, that of the upper meridian and that of
the lower meridian; that is to say the two points of the ecliptic which
are on the horizon and the two which are at the meridian. The angle of
the upper meridian was also called the middle of the sky, that of the
lower meridian was still called the bottom of the sky. This problem,
quite complicated, depends only on the most ordinary rules of spherical
trigonometry. [DELAMBRE, Hist Astron Moyen-Âge
Extracted and adapted from pp, 486-491]
control pole (0,1) necessary to calibrate the type of direction.
P (horary angle, from midnight) 0
-64,16 || cosP = (sinh-sin Hsin D)/(cosHcosD)
295,84
PHA (HAO angle)
-62,84 || TanPHA = sinP/((sinD+cosP)cosH)
------------------------------------------
PR (pole HAO)
-33,619 || sinPR=sinPHsinPHA
ET (arc meridian/HAO)
123,24 || tanET=cosHtanPHA
------------------------------------------ MAGINI – PROBLEMA XVI
H' || H' (incident horizon = B50
33,62 || tanH'=sinETtanH
------------------------------------------
PAR (position angle)
34,33 || sinPAR=sinH'/cosD
QS, HPR (Az PR)
33,24 || cosQS=sinET
ΔAR' (DA/HAO)
7,40 || sinΔAR'=tanDtangH'
OTE, HTQ, ETH (equat/HAO angle)
56,38 || tanOTE=cotH/sinET
Problem XVIII. Wherever the signifier is, outside the angles from the
meridian and the horizon, lead him to any promissor, following the order
of the signs, by the rational path. The operation, says Magini, is very
painful. You must have right ascension and the distance to the
meridian, both of the significator and the promissor; their declinations
and the semi-diurnal or semi-nocturnal arc, depending on whether it is
above or below the horizon; it is necessary to find the elevation of the
pole on the position circle and the position arc. We reported the
necessary formulas for all these calculations. Then let S be the
signifier, R the promissor (fig. 130), RZN the parallel of the
promissor, OK the difference of
right ascensions; R will cross the
ASC position circle in Z; K.V will be the movement of the equator, which
will take R to point Z; the time interval will be therefore measured by
KV = KO — OT — TV = direction,
These
last problems bring the theory of directions into the greatest light !
This theory belongs exclusively to the Middle Ages. No one has exposed
it as completely as Magini. [DELAMBRE, Hist Astron Moyen-Âge Extracted and adapted from pp, 486-491]
------------------------------------------ MAGINI – PROBLEMA XVII
KO (≠AR (m) # MA C SA) Eq for Fig 130 (pl 12) see fig for location and Explanation of spherical triangles
26,81 || KO=AR(m) # MA - ARC SA
------------------------------------------
A (AET angle) || EA = 90-H
62,84 || sinA=sinETsinOTE/sinEA
MAGINI – PROBLEMA XVIII
T (angle horizon/OTH) || pole of PRS (=90-H')
56,38 || cosT=sinAETsinH
[+] TO ΔAR' (m) # MA || D boreal --> sign OT [+]
7,40 || sinTO=tanDcotT
1 +
[-] TV ΔAR' C SA || D' boreal-> sign TV [-]
1,51 || sinTV=tanVZcotT
-1 -
tasyir || If OS (D) [+], TO ~ sign, If RK (D') [-], TV ~ sign
32,70 || KV=KO – OT – TV
VZ || D' (declin of C SA)
2,27
OS || D (declin of (m) # MA)
10,97
ST distance ST
13,21 || sinST=sinD/sinT
TZ distance TZ
2,73 || sinTZ=sinD'/sinT
ZS ≠dist
10,48 || If D/D'<0 [-]
EPA (EPV, EV) ± ΔAR' horary angle of (m) # MA
130,65 || if d is [-] ~ ΔAR'
IOANNIS ANTONII MAGINI PRIMI MOBILIS LIBER NONUS QUI AGIT DE DIRECTIONIBUS pp, 214-232 PROBLEMA XVI p, 229 – PROBLEMA XVII p,229 PROBLEMA XVIII p, 230 Venezia: Damiano Zenaro. 1604
So, we see that arc = 32.7 Y.
| (AR C SA – AR mc) – HD(m) # MA x Temp HC SA | (AR (m) # MA – AR mc) – HDC SA x Temp H(m) # MA | |
| Al-Battani, adapted from Nallino, Opus astronomicum, pp, 315-317 |
(m) # MA [N E] | C SA [N E] |
| ar signif | 153,32 | 180,13 |
| meridian : (m) # MA MC] | C SA [MC] |
89,16 | 89,16 |
| 1 | 64,16 | 90,97 |
| Dec | 10,97 | 2,27 |
| dAR | -8,86 | -1,81 |
| hd prom | 5,95 | 3,89 |
| temp H signif | 16,48 | 15,30 |
| arc | -33,81 | 31,39 |
| Hd prom=6.MD prom/SA prom | Hd sign=6.MD sign/SA sign | ||
| -5,95 | 3,89 | ||
| Temp H prom = (90-dAR prom) | Temp H sign = (90-dAR sign) | ||
| 16,48 | 15,30 | ||
| pm=90*DM/SA | |||
| 58,41 | -89,18 | ||
| domitude placidus=(3±dm/sa)*90 | (3±dm/sa)*90 | ||
| 328,41 | 359,18 |
the formula for domitude varies if h>0 or h<0 (± modulo 360 and take dm and sa for the correct quadrant). Max Duval (la domification et les transits, Ed Traditionnelles, 1984) gives an incomplete formula for domitude, only the formula of pm).
If h<0, dom placidus = (1+dm/sa)*90
If h>0, dom placidus = (3+dm/sa)*90
For #MA, dom pla = 90*(3+dm/sa) and for SA, dom pla= 90*(3-dm/sa) ; here take dm from mc for both and diurnal semi-arc for both.
Take the arc = 31.39 Y for directio directa. The placidus key gives : 32.3 Y.
LIBERATION : MAY 1626
DIRECTIO (m) ∆ ♀ ☌ ☽
----------------------------------------------------------------------------------------------------------------------
| speculum | Lat | Dec | AR | MD | SA | HA |
| MO | 2,41 N | -5,99 S | 339,65 | 72,26 N | 94,21 N | 21,95 W |
| *VE | 1,42 N | -21,18 S | 286,60 | 17,44 N | 107,94 N | 90,5 W |
----------------------------------------------------------------------------------------------------------------------
| DP REGIOMONTANUS | DP REGIO-CAMPA C | DP REGIO-CAMPA D | ||||
| A2 *VE | A1 MO | A1 MO | A2 *VE | A2 *VE | A1 MO | |
| Tan A | tan dec/cos dm | -16,87 | -22,10 | |||
| B (1) | +LG-A or -LG+A | 21,61 | 16,38 | |||
| Tan C | cot DM.cos B/cos A | -17,27 | 73,12 | |||
| Sin pole | Cos C.sin LG | 36,45 | 10,41 | |||
| Sin DA (2) | Tan pole A1.Tan Dec A2 Tan pole A2. Tan Dec A1 |
DAP | -3,91 | -16,63 | -4,08 | -0,97 |
| AO (3) | AO ± DA | 337,50 | 269,97 | 282,52 | 340,45 | |
| arc | AO1 – AO2 | 67,53 | 57,92 | |||
| CONVERS | DIRECT |
(1) B must be < ε
(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 pole A1 and Dec A1 have the same sign; sign [-] if pole A2 and Dec A2 have the opposite sign
----------------------------------------------------------------------------------------------------------------------
The direct arc is 57.92 Y and the EQU key gives 59.03 Y.
| (AR C MO – AR fc) – HD* VE x Temp HC MO | (AR * VE – AR fc) – HDC MO x Temp H* VE | |
| Al-Battani, adapted from Nallino, Opus astronomicum, pp, 315-317 |
* VE [S W] | C MO [S W] |
| ar signif | 286,60 | 341,42 |
| meridian : * VE [IC | C MO [IC] |
89,16 | 89,16 |
| 1 | 17,44 | 72,26 |
| Dec | -21,18 | -5,28 |
| dAR | -17,94 | -4,21 |
| hd prom | 4,60 | 0,97 |
| temp H signif | 17,99 | 15,70 |
| arc | -65,34 | 57,03 |
With Placidus method, the direct arc is 57.03 Y.
----------------------------------------------------------------------------------------------------------------------
| Hd prom=6.MD prom/SA prom | Hd sign=6.MD sign/SA sign | |
| 4,60 | 0,97 | |
| Temp H prom = (90-dAR prom) | Temp H sign = (90-dAR sign) | |
| 17,99 | 15,70 | |
| pm | ||
| 14,54 | 69,03 | |
| domitude placidus = (1+dm/sa)*90 |
domitude placidus = (1+dm/sa)*90 | |
| 104,54 | 159,03 |
----------------------------------------------------------------------------------------------------------------------
DIRECTIO CONVERSA ECHO (m) ∆ ☽ ☌ ♀
It is a converse direction as VE enters into conjunction with the trine of MO.
----------------------------------------------------------------------------------------------------------------------
| speculum | Lat | Dec | AR | MD | SA | HA |
| VE | 1,42 N | 6,84 N | 167,67 | 101,49 N | 84,52 N | -16,97 E |
| ∆MO | 2,42 N | -9,86 S | 210,47 | 58,7 N | 97,94 N | 39,24 E |
----------------------------------------------------------------------------------------------------------------------
– MD = meridian distance (from MC if SA f [VE] is diurnal or IC if Sa f is nocturnal)
– SA = semi-arc (if f is diurnal, SA f [VE] 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 [VE] and m ∆MO)
under bracket [] the fixed point, (here VE)
----------------------------------------------------------------------------------------------------------------------
| DP REGIOMONTANUS | DP REGIO-CAMPA C | DP REGIO-CAMPA D | ||||
| A2 ∆MO | A1 VE | A1 VE | A2 ∆MO | A2 ∆MO | A1 VE | |
| Tan A | tan dec/cos dm | 31,05 | -18,50 | |||
| B (1) | +LG-A or -LG+A | 7,43 | 19,98 | |||
| Tan C | cot DM.cos B/cos A | 13,24 | 31,07 | |||
| Sin pole (2) |
Cos C.sin LG | 37,28 | -32,21 | |||
| Sin DA (3) | Tan pole A1.Tan Dec A2 Tan pole A2. Tan Dec A1 |
DAP | 5,24 | -7,60 | 6,29 | -4,33 |
| AO (4) | AO ± DA | 162,43 | 218,07 | 216,75 | 163,34 | |
| arc | AO1 – AO2 | -55,64 | -53,41 | |||
| CONVERS | DIRECT |
----------------------------------------------------------------------------------------------------------------------
(1) B must be < ε
(2) sign of pole has the same sens of LG for DA. Here, DA = DAP
(3) [+] sign if pole A and Dec have the same sign; sign [-] if pole and Dec have the opposite sign
(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
the converse arc is 55.64 Y.
Explication :
----------------------------------------------------------------------------------------------------------------------
----------------------------------------------------------------------------------------------------------------------
VE progressed longitude is 213.75° and TRI MO radix is 211.79°. So the diff is -1.96° and that corresponds to an arc of 55.64 Y (key EQU : 56.86 Y so diff : 56.86-57.77 <2°). 57.77=1568.68 (birth) - 1626.45 (even). Don't forget that it is a true directio conversa.
-----------------------------------------------------------------------------------------------------
| DP PLACIDUS | Plac direct | Plac conv |
| sa1/dm1 | 1,67 | 1,22 |
| sa2 | 84,52 | 82,06 |
| x | 50,66 | 67,48 |
| dm² | 101,49 | 121,30 |
| sign | -1 | -1 |
| ------------------------------------------------------------------- | ||
| arc | 50,83 | 53,82 |
| ------------------------------------------------------------------- | ||
| FOMALHAUT-CHOISNARD | ||
| X = sa2.dm1/sa1 | ||
| sign : if the two points are on either side of the meridian, take +1 ; otherwise -1 | ||
| Arc = dm2 ±sign.x |
-------------------------------------------------------------------------------------------------------
On July 8, 1626, the philosopher exchanged his prison in Naples for that of the Inquisition in Rome. It is true that from July or August 1628, he was authorized to live in the palace of the Holy Office “loco carceris”. — But it was not until April 6, 1629 that he was definitively pardoned and left in complete freedom. To this was limited the alleged benevolence of Urban VIII towards him, painfully won by Campanella after his arrival in Rome, and moreover, as we will see, quickly lost.
DIRECTION APRIL 1629
We find a (m) [c] conj MO TRI VE but the orb is at 2.36°.
New accusation against Campanella in 1634 : In 1634, an event of real gravity suddenly set things on fire. In April, the viceroy of Naples, Monterey, charged Campanella and his family with participation in a plot attempted against the Spanish authorities of that city by one of his disciples: Tommaso Pignatelli. e cette ville par un de ses disciples : Tommaso Pignatelli, and he tried to obtain his extradition from the Vatican. His request was not accepted, and Pignatelli, who had previously denounced his master, retracted before dying. However, Campanella understands that the provisions of the Secretary of State towards him are only half reassuring, and fearing new prosecutions from the Spaniards who persist in accusing him, he takes refuge with the French ambassador, Count de Noailles.
We then find two directions: [c] conj JU square MA and # VE conj JU. The first of these directions is converse and once again involves MA.
DIRECTIO CONVERSA : [c] ☌ ♃ ☐ ♂
| speculum | Lat | Dec | AR | MD | SA | HA |
| JU | 0,48 N | -20,47 S | 241,75 | 26,41 N | 107,26 N | 80,85 E |
| □MA | 0 S | -18,22 S | 310,79 | 42,63 N | 105,17 N | 62,54 W |
– MD = meridian distance (from MC if SA f [JU] is diurnal or IC if Sa f is nocturnal)
– SA = semi-arc (if f is diurnal, SA f [JU] 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 [JU] and m □MA)
under bracket [] the fixed point, (here JU)
----------------------------------------------------------------------------------------------------------------------
| DP REGIOMONTANUS | DP REGIO-CAMPA C | DP REGIO-CAMPA D | ||||
| A2 □MA | A1 JU | A1 JU | A2 □MA | A2 □MA | A1 JU | |
| Tan A | tan dec/cos dm | -22,62 | -24,10 | |||
| B (1) | +LG-A or -LG+A | 15,86 | 14,38 | |||
| Tan C | cot DM.cos B/cos A | -64,52 | 49,06 | |||
| Sin pole (2) | Cos C.sin LG | -15,53 | -24,06 | |||
| Sin DA (3) | Tan pole A1.Tan Dec A2 Tan pole A2. Tan Dec A1 |
DAP | 5,95 | 5,25 | 8,45 | 9,60 |
| AO (4) | AO ± DA | 247,71 | 316,04 | 302,34 | 232,16 | |
| arc | AO1 – AO2 | -68,33 | 70,18 | |||
| CONVERS | DIRECT |
(1) B must be < ε
(2) sign of pole has the same sens of LG for DA Here, DA = DA/pole A
(3) [+] sign if pole A and Dec have the same sign; sign [-] if pole and Dec have the opposite sign
(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
----------------------------------------------------------------------------------------------------------------------
the arc is convers : -68.33 Y (true converse direction).
| directio conversa | (AR C JU – AR fc) – HD□ MA x Temp HC JU | (AR □ MA – AR fc) – HDC JU x Temp H□ MA |
| -1 | ||
| Al-Battani, adapted from Nallino, Opus astronomicum, pp, 315-317 |
□ MA [S W] | C JU [S E] |
| ar signif | 310,79 | 241,75 |
| meridian : □ MA [IC | C JU [IC] |
88,16 | 88,16 |
| 1 | 42,63 | 153,59 |
| Dec | -18,22 | -20,47 |
| dAR | -15,17 | -17,26 |
| hd prom | 1,48 | 2,43 |
| temp H signif | 17,53 | 17,88 |
| arc | 68,52 | -69,89 |
----------------------------------------------------------------------------------------------------------------------
| Hd prom=6.MD prom/SA prom | Hd sign=6.MD sign/SA sign |
| 1,48 | 2,43 |
| Temp H prom = (90-dAR prom) | Temp H sign = (90-dAR sign) |
| 17,53 | 17,88 |
| pm placidus | |
| 36,48 | 22,16 |
| domitude placidus | |
| 126,48 | 67,84 |
----------------------------------------------------------------------------------------------------------------------
The placidus arc is : 68.52 Y. (the Placidus key provides a value of 70.7 Y).
'The kind words of Louis XIII, the kind welcome of Richelieu, who consulted the king on Italian affairs, the liberalism of the Sorbonne towards him and the reputation acquired among the lords of the Court and scholars are for him probably so many signs of the times, and confirm in his mind the astrological forecasts according to which the eldest daughter of the Church is ready, according to her request, to take in hand the great cause of religious unity and theocracy universal. This hope, expressed many times in the dedications of his works to Chancellor Séguier, to the superintendent of finances Bullion, to Louis XIII, and especially to Cardinal Richelieu, to whom he proposed to found the City of the Sun, became for Campanella a certainty after the birth of the dauphin, the future Louis XIV, from whom he himself draws the horoscope. The day this prodigious event occurred, unexpected by everyone, but announced by astrology
The horoscope is not flattering; in some ways it is prophetic. Campanella pulled him out after examining the young dolphin naked, twice. He had been called to the Palace by Richelieu, at the request of Anne of Austria who wanted to know the future of her son (Amabile, Cast., t. II, p. 132-136). He would have said: “Erit puer ille luxuriosus, sicut Henricus quartus, et valde superbus. Regnabit diu, sed dur, tamen congratulate; desinet misery and in fine erit confusio magna in Religione et in Imperio”. This horoscope was copied by Barrière (Unpublished Memoirs of Louis Henry de Loménie, Count of Brienne, 2 vols., Paris, 1828, vol. I, p. 346, note c), on a print from 1638, preserved in the Library National in Paris (Cabinet des Estampes, volume for the year 1638-1639). — Previously the philosopher would have foreseen the unexpected birth of Louis XIV, which he calls a “portentosam nativitatem”: “In France he performed several acts as an astrologer; consulted by Cardinal Richelieu if Monsieur would ascend the throne, he replied: Imperium non gustabit in aeternum”. ' (Naudaeana, Paris, Florentin and Delaulne, 1701, p. 4 and b). [Campanella à Rome et à Paris, pp. 63-64, Léon Blanchet, 1920, Alcan]
