Re: Le Tarot arithmologique - la séquence 1+4+7+10 = 22

#551
mikeh wrote: I am not sure that Etteilla was a practicing astrologer. Holbronn says his "astrology" bears no relation to anyone else's. He did know about the 7 planets, 12 zodiacal signs, and parts of fortune. Whether he knew about epicycles I don't know, but probably so, why not? I will check the 4th cahier.
I made a presumption based upon the fact that horoscopes were among the services he advertised - he also knew other technical aspects, such as formula for Arabic parts, or at least the Part of Fortune, which he included on his cards - and his integration of tarot and (horary) astrology generally* -- I don't have the fourth cahier (or the others) any longer, and hadn't really had the chance / time to look over it closely when I did have it, since the fire destroyed all my hard-drive backups -- ***
That's great about your anonymous gift.
Yes - several AT members have been tremendously generous and kindly sent some decks (and in this instance a book) after hearing about the loss of my collection in the fire --

SteveM

*Elizabeth Hazel & James W. Revak at one time had an article, with examples, on Etteilla's astrological integration and method -- I can no longer find it online -- but there is a Spanish translation of their article with illustrations here:

http://www.clubedotaro.com.br/site/p52_3Etteilla_1.asp

SteveM

Oh - the fourth Cahier is at google !?

Image


An astrological chart applied to the reading of Tarot, derived from the book of Etteilla, Manière
De se récréer avec le jeu de cartes nommées tarots (1785).


https://books.google.com.tr/books?id=7Y ... &q&f=false

In terms of translation, looks pretty straight forward (I am pretty au fait with astrology, so perhaps that is why it seems easier to follow than some of his other works), at least in comparison with the first cahier (in which I find the numerical references very confusing and hard to follow!)
Immature poets imitate; mature poets steal; bad poets deface what they take, and good poets make it into something better, or at least something different.
T. S. Eliot

Re: Le Tarot arithmologique - la séquence 1+4+7+10 = 22

#552
My feeling about Numbers and pythagorism in Tarot

Etteilla and disciple's pythagorism is indeed of interest.
Yet I am quite sure that they did rely on what I would call an elementary pythagorism at best reduced to the Decade and to triangular figurated numbers such as 78 = 1+2+3+5 +6 +7+8+9+10+11+12
They had no intuition of pentagonal numbers and their figurate expression.

The Arithmological Tarot - though it still remains alike an "invisible" matrix, only because there is, yet, no evidence discovered of it in the times of the standardisation of the deck and related to it, remains as a clear reference to Triangular, Square and Pentagonal figurate numbers in a "whole".

On one part , a Tetractys game with 4 Tetractys of Numerals and 4 Tetrads of Honours (counted possibly as 1 2 3 4) in 4 Emblems.
On the other part, 22 allegorical figures expanded as :
1+4+7+10 = 22

The modern attempts are in the spirit of Etteilla's pythagorism.
They finally reduce the Pentagonal 22 to 2 Decades +2,
This is an elementary Pythagorism,
It is orthodox because it views the expansion of numbers as an arithmetical succession of Decades. This is in conformity with Nicolas de Cuse.
But is does not take in account the figurate pentagonal expansion of Number 22 and simplifies this Pentagonal figurate geometrical expansion of Number 22 to an elementary Pythagorism of a Decimal Numeroly(10+10+2)

We know from the philosophers game that Pythagorean proportions were in use as a strategy to win a game.
These notions of Harmonia were far more complex than the very simple arithmology of the Pentagonal 22;
1 Unity
4 Tetrad
7 Septenaire
10 Decade

So if I understand that Occultists or Moderns do not understand or find too complex pentagonals figurate numbers, I m not sure at all, that in the time and space of the birth of Tarot, close to learned people aware of Pythagorism or close to the Platonician Medicean Academy, these notions would have been unknowned or seemed far fetched ...

Boethius « De institutione arithmetica »

#553
Boethius and the pentagonal generation of Number 22

Writing for posterity ... :D
Well maybe not - if Mikeh or Steve would be kind enough to translate... :ympray:

I had in a recent time posted about BOETHIUS "arithmology" (arithmetic and harmonies) related to the "philosopher's game" in late medieval times and Italian Renaissance

Anne E. MOYER, The Philosopher's game, Rithmomachia in Renaissance and Medieval Europe, University of Michigan Press, 2001
viewtopic.php?f=11&t=1102&p=18487#p18487


I had found some specific data about Pentagonal Number 22 as the arithmetic serie 1,5,12,22 [gnomons : 1+4+7+10]
Boece « De institutione arithmetica » edition 1867
https://archive.org/details/aniciimanliitor01friegoog

Image


https://ia802607.us.archive.org/BookRea ... 4&rotate=0



Comments and Images : :ymapplause: (still a little late but pretty explicit - an edition incunable 1499)
Surely there are prior editions with digitalized views available today ...there have been before so many since IXth century...
Auteurs : Association des Professeurs de Mathématiques de l'Enseignement public
http://www.apmep.fr/IMG/pdf/03_Eclairs_ ... -Age_I.pdf

Image

Image

Image


In French sorry.

"Dès le IXème siècle nombreuses étaient les copies de son « De institutione arithmetica » dont les spécialistes, même s’ils s’accordent à la trouver inspirée de Nicomaque (mathématicien du Ier siècle, originaire de Palestine),
reconnaissent que Boèce a su y pousser à l’extrême sa science des nombres.

Nous reproduisons des extraits d’un incunable de 1499. L’influence de Boèce était restée
telle, un millénaire après sa mort, que son œuvre fut parmi les tout premiers textes imprimés"

Link with Pentagonal Number 22
Serie :
1,5,12,22
Gnomons or "différences"
1+4+7+10
{b]Images Link : [/b]
https://docs.google.com/document/d/1bh7 ... sp=sharing

Boethius 's understanding on the progression of Pentagonal Number 22 is in absolute conformity with the editions of Theon de Smyrna and Iamblicus presentaion of figurate numbers
Image

"The manuscripts and editions of the Introduction to Arithmetic of Nicomachus lack these figures here; but they are found in the edition of the Commentary of Iamblichus and in both editions of the Arithmetic of Theon of Smyrna." (Th. Henri MARTIN, op. cit.)

Conclusion
The 22 subjects of the standard Tarot ; an "arithmétique théologique"
- an iconografical progression or mystical stair - Christian
- a numerical progession or a "mystical arithmetic" : Pythagorean
and vice-versa :


The Arithmological Tarot http://letarot.it/page.aspx?id=603&lng=ENG
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Re: Le Tarot arithmologique - la séquence 1+4+7+10 = 22

#555
I'll be away a little time...

Meanwhile, i ll share my actual intuition .

I am looking for a Christian learned Pythagorean aware of figurate numbers and interested in games in the last quarter of the XVth centuy or the very beginning of the XVIth in Italy - circa the period of Cardinat of Cardinalat of Giuliano della Rovere Pope 1503 as Jules II (correction added 14/02)- and from there exploring his relations.

For the moment, I have found Fra Luca di Paccioli related to Leon_Battista_Alberti in 1471 (1496 he meets Leonardo da Vinci)
Image


Luca di Borgo : birth 1445 in Borgo Sansepolcro Toscane - death1517 in Rome
https://fr.wikipedia.org/wiki/Luca_Pacioli

Pythagorean essay :
De divina proportione (written Milan 1496-1498 and published Venise 1509)

The games he wrote about were :
A (lost) Treaty on Chess rediscovered 2006
De ludo scacchorum
Times online : Renaissance chess master and the Da Vinci decode mystery
New York Times : Checkmate again for Leonardo? Chess book's diagrams are linked to artist

Magic trick cards
De viribus quantitatis, (1496-1508)
Mathknow: Mathematics, Applied Science and Real Life (Sous la direction de Michele Emmer et Alfio M. Quarteroni) page 193 (Editions Springer)

Maybe also the Treaty on Abacus was related to Boethius ?
Never published -Vatican Library codice Vaticano Urbinate 3129

Nota
A "Golden" curiosity ?
BtW the 78 cards can also be divided in two series :
56 the Tetractys Game with 2 series of 2 "suits" (?) that is 56 = 2x (14x2=28)
22 the Pentagonal pogression of the iconographical figures.
56 and 22 are not in a Golden Ratio.
But are these numbers really random?
No. These Numbers (22) and (56 as 28x2) are nevertheless related to the square root of PHI .

56/2 ) = 28 divided by 22 = Square Root of PHI

PS : Square root of PHI (also called Golden Number) = 1,272 with PHI as 1.16179 circa real value as 1.618
Reminder : PHi also called Golden number : (1 + square root of 5) divided by 2 = circa 1.618

Hmmmm....

Re: Le Tarot arithmologique - la séquence 1+4+7+10 = 22

#557
BOUGEAREL Alain wrote:I'll be away a little time...

Meanwhile, i ll share my actual intuition .

I am looking for a Christian learned Pythagorean aware of figurate numbers and interested in games in the last quarter of the XVth centuy or the very beginning of the XVIth in Italy - circa the period of Cardinat of Jules II de Medicis - and from there exploring his relations.

For the moment, I have found Fra Luca di Paccioli related to Leon_Battista_Alberti in 1471 (1496 he meets Leonardo da Vinci)
Image


Luca di Borgo : birth 1445 in Borgo Sansepolcro Toscane - death1517 in Rome
https://fr.wikipedia.org/wiki/Luca_Pacioli

Pythagorean essay :
De divina proportione (written Milan 1496-1498 and published Venise 1509)

The games he wrote about were :
A (lost) Treaty on Chess rediscovered 2006
De ludo scacchorum
Times online : Renaissance chess master and the Da Vinci decode mystery
New York Times : Checkmate again for Leonardo? Chess book's diagrams are linked to artist

Magic trick cards
De viribus quantitatis, (1496-1508)
Mathknow: Mathematics, Applied Science and Real Life (Sous la direction de Michele Emmer et Alfio M. Quarteroni) page 193 (Editions Springer)

Maybe also the Treaty on Abacus was related to Boethius ?
Never published -Vatican Library codice Vaticano Urbinate 3129

About Paccioli Isabelle d'Este and chess :
paccioligames1.PNG
(136.73 KiB) Not downloaded yet
paccioligames2.PNG
(66.72 KiB) Not downloaded yet
paccioligames3.PNG
(127.98 KiB) Not downloaded yet
The Merels Board Enigma. With the worldwide census
Marisa Uberti,30 nov. 2012
https://books.google.fr/books?id=plPhAg ... navlinks_s

Re: Le Tarot arithmologique - la séquence 1+4+7+10 = 22

#558
Corrections 14/02 underlined

For the moment , appearently nothing about Pentagonal numbers as 22 in Tarot. But, we have a high learned Pythagorician (maybe the best), Paccioli, interested in games such as chess in a Pythagorean approach, fan of card magic tricks, with Isabelle 'Este in Mantoua linked to cards and trionfi, in 1500 under Cardinalat of Giuliano della Rovere ., five years before the apparition of the word "tarocchi" (D'Este) or "taraux" in Avignon ....
[BtW why do I speak about the Cardinalat of Giuliano della Rovere : because this englobes his first cardinat in Avignon also...another thread of interest still at work - may well become of interest to understand the simultaneity of the appearance of tarrochi (Este) and taraux (Avignon) two years after his nomination to Pontificat in 1 Novembre 1503 as Jules II)
https://fr.wikipedia.org/wiki/Jules_II
viewtopic.php?f=11&t=691&hilit=bougearel

Hmmmm!
Right time, right place, right persons ...of interest for sure! No?
At least, it legitimates a deeper inquiry, i believe.
Paccioli did not write a manuscript a about Tarot like he did about Chess.
But he knew about cards.
Did he or close relatives influence for a Pythagorean standardisation to 22 for the Iconografical figures?

Introducing
Suggested links to understand the period and the relations between Mantoua and Este via François II de Gonzague and isabelle d' Este, his wife wedding 12 février 1490 Isabelle d'Este (1474-1539):
http://autourdelombreduconnetable.com/b ... ur-durbin/

François II de Mantoue dit de Gonzague
https://fr.wikipedia.org/wiki/Fran%C3%A ... de_Mantoue
Image

Isabelle d'Este
https://fr.wikipedia.org/wiki/Isabelle_d%27Este

Nota bene : before 1500

Emilia PIA and Timoteo Viti
Another interesting link with many informations : Castigione at the service of the Marquisat of Mantoua and specifically his long lasting "relation" (until death) with Isabelle d'Este and also the description of the Court's games at the Court of Urbino conducted by Emilia PIA.
http://autourdelombreduconnetable.com/b ... ur-durbin/


Connection Boiardo / Viti as well as the Urban court via Emilia PIA.
(Young Pietro Bembo is already there debating with Emila PIA. He'll have as teacher in 1492 the long living Byzantin Constantin Lascaris (1434-1501), the preceptor of Francisco Sforza in Milan and close to Bessarion )

Rappel : Constantin Lascaris
https://fr.wikipedia.org/wiki/Constantin_Lascaris


The "overlooked" figure of Emilia PIA - she first appears in an still obscur for me connection with Boiardo and VIti : Huck had found the information but I ve lost the link and she appears after close to Isabelle d'Este and becomes the confident of the Lady of Urbino.
viewtopic.php?f=11&t=1102&hilit=emilia+ ... 270#p17505

Timoteo VITI
viewtopic.php?f=11&t=1102&p=17504&hilit ... ens#p17504
He come back from Bolona to the Urban Cour t in 1495 and would have been the master of Raphael.
Raphael's later School of Athens ...
https://en.wikipedia.org/wiki/The_School_of_Athens

Re: Le Tarot arithmologique - la séquence 1+4+7+10 = 22

#559
Alain wrote,
About Paccioli Isabelle d'Este and chess :
paccioligames1.PNG
paccioligames2.PNG
paccioligames3.PNG
Where is this from?

The question is, were Pentagonal Numbers part of the standard quadrivium of the time or not? If so, anybody could have applied the numbers connected with them to the cards.

What is then important is the number 5, for pentagonal. It is for the fifth suit, the one that shows the way to God, an especially sacred number, of the Pope card and of the various sacred associations to the number that made it particularly holy. For example Augustine: the five wise virgins, who have abstained from unlawful use of the five senses (http://www.newadvent.org/fathers/160343.htm); the "five books of Moses", the "five porches containing the sick folk", the "five loaves feeding the five thousand" (https://books.google.com/books?id=wIp0A ... ve&f=false), and the five stigmata of Christ, the same repeated for Francis of Asissi (https://en.wikipedia.org/wiki/Stigmata).

But perhaps some author emphasized pentagonal numbers for some reason. If so, the relevant passage needs to be found.

One thing: Julius was not a Medici; he was a della Rovere (https://en.wikipedia.org/wiki/Pope_Julius_II). The Medici popes were after him.

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