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

Of interest :
The astral origin of the Soul
A Neoplatonic myth in the iconography of a few cards of the Triumphs
By Andrea VITALi
Translation from the Italian by Michael S. Howard, June 2013

In addition to Andrea VITALI's essay, further inquiry on
The Astral Journey of the Soul
Porphyry and Plutarch in the context of the medieval cosmograph
By Michael S. Howard ... Biographie

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

Hi Alain.

First my congratulations on your publishment with „Andrea VITALI“ Alain.

I've read through 2 of your works there:

Like you I believe that „Tessellation“ is the key to Tarot – but with a rather different and more practical/pragmatic approach. ... ot-com-pdf



Furthermore the „Golden Rectangle“ is obviously a key ingredient of Tarot (here demonstrated with Jean Noblet's Tarot):


So I was exited to see the „Fibonacci Sequence“ (for example!) between your thoughts which brought the „Golden Rectangle“ as the key to/of life with a very simple formula into the Christian minds of the west.

But I wondered why you would tie Tessellation in the flow of your texts to Christian mythology (and so Tarot too) when the Arabs (the former „Saracens“) had made all the practical developments from Pythagorean wisdom centuries before Leonardo of Pisa especially with tiles and kilim rugs?

Practically all science that developed here was rooted in „Saracen“ minds somehow.

Additionally my approach to The NUMERALS is totally different to yours because the 1st Tarots (Visconti etc.) had none – but you know that.

So – again – delighted to see Tessellation included in your thoughts!


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

Hello again Alain.

Going over your model again ...


... I was asking myself - and now you - where every card would be EXACTLY?

Since the tetraktys ...


... is in it's essential form arranged like this - an observer would be able to identify any term (1-2-3-4-5-6-7-8-9-10) with reference to his own reading habits (from left to right - or right to left) anytime he looks at it and every term (number) was assigned a special esoteric complexity.

When you now - like you did - extrapolated on that to arrive at your model where would the 78 unique terms (numbers) be situated in your model to be tied to a similar unique card?

What esoteric complexity would you assign to everyone of those 78 terms and based on what philosophy?
Where would be the congruency between your assigned 78 esoteric complexities concerning the assumed modern meanings (that may not be always correct and/or complete - but COMPLEX they are) of those 78 cards be so that a feasible model would be achieved?

As of now it (your model) seems to me much more like a mental exercise in grouping than a model for the 78 Tarot cards - because for example the 4 sets of the 10 number cards are totally interchangeable and divided from their specific court and the 22 Great Secrets are at the lowest levels whereas the glory (because for Pythagoras 1 was the greatest TERM of all ...
For example, the number one was the generator of all numbers; two represented opinion; three, harmony; four, justice; five, marriage; six, creation; seven, the seven planets or “wandering stars” ...
... and all that come after 2-3-4- ... 78 should have special assignments too) belongs to the 16 of the courts all together in one group without any specification of who is who and where at - what all doesn't align with the meaning they bare due to rumors published for ages to give Tarot some meanings men could thrive on. I believe that you came by such books too which sparkled your interest in Tarot but I cannot find that reflected in your grouped model - but maybe I over read that and you can point me to the solution in your work.


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

Re-bonjour Alain.

Since I went over your "arithmological sequence" >> 1+4+7+10 = 22 << which should be an "arithmetic sequence" I suppose by the standards of math...
An arithmetic sequence is a sequence of numbers in which two consecutive terms always have the same difference.
In general, the terms of an arithmetic sequence with the first term a0 and common difference d, have the form
an = dn+a0 (n=0,1,2,...).

Examples of arithmetic sequence:

1, 7, 13, 19, 25, 31, 37, ...

5, 11, 17, 23, 29, 35, 41, ... ... cans13.htm
... your "core model" for the 22 doesn't fit those standards in a formal way because adding "3" to every term beginning with 1 and ending with 10 would make the sequence "closed". So 22 won't be a part of the sequence.

The addition of the 4 terms 1-4-7-10 is a step that belongs not to "sequencing" - or does it?
Well of course you could make a special rule for that step too - like you did.

But when you do that and create a new closed sequence of 78 with 6 separate clusters with 1 of them the 1-4-7-10 core sequence at least the "sequential(?) law(s)" for the other 5 (sequences? No - can not be by their defined numerical nature taken from Tarot) clusters should be defined too - because you put them in a closed grouped model. You instead seem to understand them (the 56) as pure variables in a non defined mathematical way - so you should define them all to add some logic to the model of 78.

Furthermore if you impose the "tetraktys" model on the whole 78 in your triangle it is only fully present (of course) in the 4 clusters with the 10 number cards because the tetraktys consists of 10 points. You may even be able to explain the 16 court variables in your model as the tetraktys mirrored in a way. But still you would have to define what court card is where between those 16 points.

For the 22 core model - that is the outcome of the added 4 terms of the closed 1-4-7-10 sequence - the tetraktys doesn't really apply.

You arranged those 22 dots just in a "pseudo tetraktical" way that throws all that you WANTED to BE in the mix.

When the tetraktys is composed of 10 points that symbolize the whole Universe it is per se complete.
You did arrange 3 teraktyses (? :) ) in an overlapping manner without defining the specific overlapping dots - just to make your sequential idea fit an ancient model of renown that would be totally destroyed to it's core by your idea.

Of course 3 teraktyses (? :) ) would add up to 30 dots with 2 GAPS between them - but that wouldn't fit your sequential idea - so you MADE it fit!

Obviously this is all said out of the top of the mind of a layman and I do not share "Andrea VITALI's" elusive standards that urged him to publish your work ...
Le Tarot Arithmologique
... and since you seem not to be keen on replying in a topic that you opened I'll leave it at that.

:ymparty: Adrian

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

Dear Alain

even when you are not in the mood to reply right now to my well meant stimuli – I love you anyway!

Because you reminded me that I've touched on the Tetraktys and Tessellation matter concerning Tarot here only so far in the above mentioned links.

So I decided to come back here once more to share the following model with you.
A new topic will be created for this matter and I'll keep you informed here.

„Tetraktys – Tessellation – Tarotée > TAROT“ will be the title and a link will follow in some days.

Subject will be the further Tessellation of the following model below and The REVERSED MAN from the PMB will offer his kind assistance to reconstruct The BOARD on the WALL(s) of the Visconti-Sforza Palaces where the PMB was hung for education.

Back to your beginnings now:

You did work on the „Tetraktys“ of Pythagoras which is a closed concept of 10 dots who represent the Universe and it's creation in this specific configuration:


Tessellation has rules and 3 different types.
Below you will see REGULAR Tessellation that is the only type that occurs to govern the tableaus.


1 device to create a regular tessallation is an axis of symmetry.
And the trick here is to know the correct defining space between the 2 Tetraktys proxies.
The Tetraktys itself will tell you WHERE to draw the LINE.

The axis of symmetry here is where the 2 RED DOTS WOULD be IF the Tetraktys COULD get enlarged (your 78 dots in your model).


The next item on agenda to solve would be the WHOLE space the now correctly tessellated Tetraktys WILL occupy – so you (I) need a border – an naturally occurring one.

The DOTS that WOULD be there IF the Tetraktys COULD be enlarged to DEFINE your (my) model.


Now the CORE Model of the tessellated Tetraktys for the tableaus of Tarot is complete – and no other use will be made of it to define anything concerning Tarot – what you surely won't believe.

2 more ESSENTIAL DEFINITIONS - concerning the Tarot de Marseille especially - is contained in this model that you perhaps did not notice so far.

The 2 RED DOTS which are not REALLY a part of the Tetraktys(es?) shown here in close proximity - BUT DEFINING for the tessellated model.

Tarot (the later TdMs) contains 22 Great Secrets.
The Tetraktys bears 10 dots – tessellated like here 20 dots for 2 proxies.

The Tetractys itself is part of a dualistic philosophy - so creating an „underworld“ with it's own 10 dots should be fine.

But both proxies are part of The WORLD who contains both without being visible and being herself designated XXI (and so NO part of the Tetraktys(es?)) in her similar shaped and bound garland.

About this you can glean a IDEA of the WHY when you know about the PELASGIANS and their CREATION MYTH (which sadly today is only available in the form of a recreation by Robert von Ranke Graves. But you can get an IDEA).

So XXI is 1 red dot.

Now you may think: „Wow – surely Le MAT must be the other red dot being „0“!

Yes - of course – the red dot symbolizes Le MAT – BUT Le MAT is NOT ZERO.
He can not be because Pythagoras did not refer to anything like it.
1 is the Beginning of ALL.

Euclid did 300 years later define a vaguely similar allegorical term for his calculations – but in Pythagorean models no ZERO is present.

There is a solution for this in classical sequences for the PLACEMENT of Le MAT.
EL and AEW rescued this ONLY working sequence for Tarot for your lifetime and it puts Le MAT BETWEEN XX & XXI what makes Le MAT factually (having himself NO numeral) by counting from 1 up to his place in the sequence) Nr. 21 so that SHE can keep her XXI and still be 22.

So this was incorporated in this model from the beginning.
From their works it can not be concluded that both knew about this – but from their bios you could glean where they contacted a messenger with a very reduced version of this.

You can work with that when you want now – or don't.


I – lke I said - will demonstrate what was done with this model in a week or so and leave you a link Alain.


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

I had to translate Alain's essay in order to read it, so here it is, in English, a very literal translation which I hope has not introduced new confusions. Most of it was easy to follow; however the parts in brackets beginning "would lack" (Alain's brackets--I did not use any) I did not quite understand and just translated literally. The beginning and end are in Italian, obviously written by Andrea. The original is at Whatever its historical validity--certainly, Pythagoreanism was fashionable in the late 15th to 18th centuries--it is a nice way of seeing the Tarot, bringing out some aspects, otherwise obscure, that might have been treasured by some. I may add a few comments in another post, to defend that position.

The Arithmological Tarot

by Alain Bougearel

We have received and, with great pleasure, publish, even in French, this essay by Alain Bougearel, referring the reader, for further study, to his essays in Italian, “ Tarocchi e Neopitagorismo”, ... 83&lng=ITA and “Numero d'Oro e i Tarocchi", ... 43&lng=ITA, by the same author.


At a moment in the history of the Tarot,

the number of cards finished by being fixed at 78: 22 + 40 + 16.
(see at link

The arithmological disposition of the 22 allegorical subjects of the Tarot is:



It is included in the global Pythagorean disposition of the 78:

The methodology requires that the Trumps be arranged as if one ignored their iconographic or ludic value by taking into account (only) their ordinal value i.e. from the first to the twenty-second position

- 1

- 2+3+4+5

- 6+7+8+9+10+11+12

- 13+14+15+16+17+18+19+20+21+22

The problem of the Order of the Trumps renders complex and delicate the replacement of the ordinal numbers of the pentagonal Number 22 by the corresponding allegorical subject in the sequence of the triumphs.

I am indebted to Michael Hurst, in his "critical examination" of my theory of the sequence of Trumps + 4 + 7 + 10 = 22, for drawing my attention to the work of Michael Dummett [The Game of Tarot and the 1985 FMR article Tarot Triumphant] and to the analysis of the "Problem of the Order of the Trumps” by Thierry Depaulis in "Tarot Jeu et Magie:

"His analyses [those of Mr. Dummett], particularly that published in "The Game of Tarot "are not so different from the analysis you present here. (The differences are just your odd placement of the Fool; and your segregation of the Bateleur). Both of you divide the Triumphs at the Pope and Death, which gives a quite intelligible grouping of the series in three types of subject. The only "apparent" difference between your two analyses is that you focus on what is incidental, the number of images in each group, while Dummett fixed on what is essential, the type of subject in each group" (Michael Hurst, Ltarot "Alain's 1 + 4 + 7 + 10 theory")

What Mr. Hurst considers incidental, the Number, and as essential, the Image, is not important here - even if Hurst's belief in the primacy of Signified (Image) over Signifying (the Number) raises subjectivity over objectivity: how else to account for the sequence 22 when it comes to the poems of Boiardo or 22 Figures of the Sola Busca?

Nothing prevents us from thinking that the final predominance of the structure of 78 cards, broken down into 22 Trumps, 56 cards (4 × 10 + 4 × 4), belongs to so random a register of contingency - these numbers would then be purely incidental and random. Nonetheless, it will be understood, I do not share this opinion. Is it not important that the arithmology of the pentagonal Number 22 (quantitative aspect) coincides, not incidentally, with the symbolic and historical analysis of the allegorical series of Triumphs (qualitative)?

T. Depaulis examines 12 different orders of "existing games now," "old games" and "literary sources".

The analysis of the 12 orders led to the development in the sequence of Triumphs of 3 "blocs" – provided we "ignore the 3 Virtues" (Temperance, Justice and Force):

Séquence 1 :
Bateleur, Pape/Papesse, Impératrice/Empereur (with some variations)

Séquence 2 :
Amoureux, Chariot, Roue de Fortune, Ermite, Pendu (with some variations)

Séquence 3 :
Mort, Diable, Maison-Dieu, Etoile, Lune, Soleil, Monde, Jugement (with reversal possible for the last two).

Apart from the positioning of the Bateleur (and the one, not mentioned, of the Math in penultimate and 22nd position), the analysis of the Trumps in 3 sequences by Dummett and Depaulis offers indeed some surprising similarities with the 4 enclosures of the pentagonal numbers 22 = 1 + 4 + 7 + 10.

The arithmological disposition of the 22 allegorical subjects of the classical Tarot appears reconcilable with two of the three major typologies presented by Dummett and Depaulis: Type B ( "the earliest known", Depaulis T., op, cit.) And C ("that of the Tarot de Marseille and its descendants, like the Tarot of Besançon and the Tarocco Piemontese", Depaulis T., op cit.).

"The position of the 3 Virtues among these 3 successive blocs permits grouping the 12 different orders into in 3 main types" called A, B, C.(T. Depaulis, op. cit.)


- [Bagat ?]
- Impératrice/Empereur, Papesse/ Pape
- [Tempérance] Amoureux, Chariot, [Force] Roue de Fortune, Ermite, Pendu [would lack + 2 Triumphs or 2 Virtues perhaps like Tempérance and Force for example?]
- Mort, Diable, Maison-Dieu, Etoile, Lune, Soleil, Jugement, [Justice], Monde, [would lack +2 Triumphs (Fol]


It poses no major problems.

- Bateleur
- Papesse, Impératrice, Empereur, Pape
- Amoureux, Chariot, Justice, Ermite, Roue de Fortune, Force, Pendu
- Mort, Tempérance, Diable, Maison-Dieu, Etoile, Lune, Soleil, Jugement, Monde, Fol

Nota bene:

However, this would be to exclude from the scope of such a structure Type A, corresponding to "current Tarocchino Bolognese, the Sicilian Tarot (with modifications, the Minchiate (id.), the tarot of Charles VI and some other ancient games" ( T. Depaulis, op. cit.)

The alpha and omega of the allegorical sequence: Bagat and Math?
Iconographically, the Pythagorean arrangement of the 22 allegories in four enclosures raises a double question: the places of the alpha and omega of the sequence of triumphs - namely the Magician at alpha and the Fol at omega in the sequence .

It should be noted that the Sermones, of Order B, positions the Bagat in 1st position and places the Math on the twenty-second line after the World in 21st position.

Prof.. Vitali in «Tarocchi: Arte e Magia» examines the 12 oldest orders of the Tarot from the 16th century, from 1500 to 1585.

The order of the Triumphs in the documents of the 16th century (p. 120)

The proposed provision is found to comply with the earliest orders. dated circa 1500 "Sermones de ludo" and the 1521 "Pasquinata"

Anonymous, Sermones de ludo, circa 1500

1 El bagatella
2 Imperatrix
3 Imperator
4 La papessa
5 El papa
6 La temperantia
7 L’amore
8 Lo caro trimphale
9 La fortezza
10 La rota
11 El gobbo
12 Lo impichato
13 La morte
14 El diavolo
15 La sagitta
16 La stella
17 La luna
18 El sole
19 Lo angelo
20 La justicia
21 El mondo
22 El Matto

P. Aretino, Pasquinata, 1521

1 il bagatella
2 l’imperatrice
3 l’imperadore
4 la bella papessa
5 il papa
6 la temperantia
7 l’amore
8 il carro
9 la fortezza
10 la ruota di fortuna
11 il vecchio
12 il traditore
13 la morte
14 il diavol
15 la casa
16 la stella
17 la luna
18 il sol
19 l’angelo
20 la justicia
21 il mondo
22 il matto


- The position of the Pope in Vth position is also reflected in the order of the 1565 F. Piscina "Discorso".

- The position of the 'Math' in the XXIInd position is also reflected in the orders of 1534 "Triomphi" of Troilo Pomeran, an anonymous "Motti" ca. 1525-1540, another anonymous ca. 1530-1560 "Trionfi di Tarocchi" likewise in the order of 1585, T. Garzoni "Piazza Univerzale".

- The position of "La Mort" XIII is confirmed in the "Sermones de Ludo" (circa 1500), Pasquinata (1521) and the Catelin Goefroy (1557).

- The position of the Bagat I, which is found on the "Sermones de Ludo" (circa 1500) and "Pasquinata" 1521 is confirmed at the alpha of the Trumps sequence in the Tarot of Catelin Goefroy 1557. This will be the order of the Tarot de Marseille starting with the Tarot de Marseille of Jean Noblet 1650.

- In addition, the Maison académique (1654-1659) assigns the number 1 spot to the Little One and the Excuse to the twenty-second line, after 21. In this connection, it will be remembered that the oldest Rule, 1637, states that there are 22 triumphs, and cites as the 3 High, the World, the Math and the Bagat. Knowing that the Bagat is the first and World the twenty-first, we deduce that Math is the twenty-second. Not so surprising, if one conceives that the object of the game is to win all the tricks. Now, what happens in the case if a Slam? The Petit is played in the penultimate round, and the Excuse is played last.

The Position of the Fol at the Omega of the sequence after the World does not mean the triumph of the Math over the World, but suggests the idea of a Madman falling perhaps into divine madness, also the playful and subversive theme of the medieval feasts of Fools.
"The other side of the Mass of Fools in the Middle Ages is the wonderful innocence personified by the FOU, eliminating the chaos. The 'crazy one', the village idiot, the most deprived, the youngest of the community - embodied and fixed in the TRUE CENTER, and it is through him that we hunt the scapegoat.

"A Mass of Fools takes place in the cathedral, ideal because its architecture meets all the medieval theological grandeur and life of the masses who have congregated to be elevated. Nevertheless we know from the work of Julio Caro Banoja that the Feasts of Fools quickly made the street: the people participating in these festivals were not the sole prerogative of cleric-insiders. Mass religious movements of in the Middle Age were mostly mobilized by disease, starvation or despair; they left little trace on institutions or medieval thought. Yet the shifting crowd in search of the supernatural and miraculous 'were immensely sure of themselves and contemptuous of traditional disciplines and restraints. In their zeal they swamped the ordinary organization of the church, broke through the barrier between the illiterate populace and the learned rulers of society, and spoke with certainty about things to come' (R. W. SOUTHERN, Western Society and the Church in the Middle Ages, p. 308). The Mass of Fools will also gather the creative energy of this people without writing."
Berry Hayward, La Messe des Fous.

Placed in a carnival perspective, the figure of the jester would affix itself to the festive triumphal processions of the second half of the fifteenth century.

"Is the jester not supposed to operate outside of the carnival procession, following it and moving about along the parade" like the Fool of the so-called Charles VI Tarot?

Copyright Alain Bougearel

For a full biography of the author, part of the Association Le Tarot, click here:

Note on July 28, 2016: In the quote within a quote by Southern, I substituted the original English, from Southern's book, for my translation of a translation. What I originally put was ""came alive with great confidence in itself, displaying contempt for all traditional discipline and coercion. Its zeal led it to ignore the structures of the Church, to break the barriers between the illiterate people and the literate powerful, it did not hesitate to denounce things to come " I made a rather serious error in translating the French "denonce" as "denounce". It should have been "declaimed", which corresponds roughtly to Southern's "spoke with certainty".

Also, I should point out that Southern's reference is to popular religious movements that arose in response to famine, disease, or other disasters, but he says nothing, at least on pp. 307-9, about their being "in search of the supernatural or miraculous". For more on the "mass of the fools" see Andrea Vitali, "Officium Lussorum", translated into English at ... 35&lng=ENG.

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

I want to make a few comments in appreciation of Alain's essay.

It has been notoriously difficult to put the cards of the tarot sequence into groups that actually have something in common, as opposed to a hodgepodge. What does the Bagat have in common with the Emperor and the Pope? In Game of Tarot (1980) and Il Mondo e l'Angelo (1993) Dummett does not even try to characterize the groups, content to simply name the cards. In his FMR article (1986) he does make an effort. But he does not even attempt to unite the first with the other four in tht group (he excludes the Fool as not technically a trump). They are just the Bagat and then "the papal and imperial cards" ( ... 600/46.jpg 3rd column). That is three groups! After him, others, such as Hurst, have said that, including the Fool, they have in common their being opposites in society, high and low. OK, that works, after a fashion: if the Fool is added, there are two low-lifes. Many early lists actually did have the Fool first, as can be seen in MM Filesi's lists at viewtopic.php?f=11&t=552&hilit=susio#p7877 Exactly why those two characters are included here, and not the Traitor, who is more to be reviled than either, is not said.

Then in the next group we have "conditions of human life". For Dummett in FMR, that includes Death ( ... 600/47.jpg). Others, including Dummett himself before and after the FMR article, have decided that Death belongs in the next group. Why "conditions of human life" excludes the Bagat and the Fool but does include the Traitor is not said. The final group is again hard to unite. What do death, the devil, the moon, and the Last Judgment have in common, so as to make them a group? Dummett in FMR says "spiritual and celestial powers". Well, that is two groups. Is Death really one or the other of these? Perhaps so, since it is shown as a walking skeleton. Dummett in the FMR article conveniently makes Death part of the second group, thus avoiding the question.

It seems to me that Alain's division 1 + 4 + 7 + 10 gives a certain rationale--not the only one possible, to be sure--to the order and interpretation of the cards in each group, if the meanings of these numbers, in Pythagorean terms, is given with them.

We know from Guillaume D’Oncieu,1584 Savoy (, how some in the Renaissance approached the meaning of numbers: by thinking of examples of groups consisting of that number, both as ordinal and cardinal ... &q&f=false). Tarot is listed under the number 4, but also partakes of other numbers, such as 3 and 5.

The ordinal "First", with the cardinal "One", is the number, in monotheism, Pythagorean or otherwise, of God the Father, the Prima Causa and Creator. It is the beginning of everything. The Pythagorean basis of this idea is well stated by Vincent Foster Hopper in his Medieval Number Theory, 1938 (reprinted 2000), p. 38:
Hence it is very natural that the Pythagoreans should have considered the monad as the first principle from which the other numbers flow (20). Itself not a number, it is an essence rather than a being (21) and is sometimes, like the duad, designated as a potential number, since the point, though not a plane figure, can originate plane figures (22) As first originator, the monad is good and God (24). It is both even and odd, male and female (24), for when added to odd it produces even, and when added to even it produces odd (25). It is the basis and creator of number, but, although it is actually the great Even-Odd, its nature is considered to be more akin to masculine oddness than to feminine evenness. In short, it i always taken to represent all that is good and desirable and essential, indivisible and uncreated. (26)
If 1, the point, is the Father of number, it follows that the duad, the line, is the Mother of number (27)...
20. Nichomachus, Introduction [to Arithmetic, II, vi, 3; Plotinus, Enneads, V, I, y; Photius, Biography of Pythagoras, 7; Proclus, Elements of Theology, A; C, 21.
21. Plotinus, Enneads, VI, 9, 3.
22. Nichomachus, op. cit. II, vi, 3.
23. Enneads, VI, I; 9, 6; V, I, 7.
24. Macrobius, In Somn. Scip. I, 6.
25. De E apud Delphos, 8.
26. Capella, De nuptiis, VII.
27. Capella, ibid.; Plutarch, De animae procreatione in Timaeo, II.
I include the footnotes because it is important to know if this account would have been known during the Renaissance. Nichomachus. Macrobius, and Capella weres known throughout the Middle Ages, in Latin. These alone would have been enough to convey the basic principles. Plotinus was translated by Ficino, as was Proclus. Macrobius and Capella were in Latin and known throughout the Middle Ages. Plutarch was known in Greek at least from the 1420s and in Latn after 1500. There was also, for some, the Theologumena Arithemtica, in Greek only, brought to Italy by Bessarion, available in Rome in the 1460s, Venice thereafter and printed in 16th century Paris. Phatius, having been a major polemicist against the Latins at the time of the "great schism", would have been studied by those interested in that issue, which surely were many given the conclave of reconciliation of 1438-39 in Florence.

Since in Christianity God the Father is also God the Son, God is also one of the physically weakest and lowest of his own creation, at least among humanity. So besides the Bagat's association with the number One, there is also his position in the hierachy, as the "little one".

We need not go into the significance of the number 2, that of the Popess (and the A and C orders)or the Empress (in the B order), we are concerned only with groups as generated by Alain's sequence 1, 4, 7, 10.

The number 4 is in Pythagoreanism the number of the three-dimensional universe. It takes a minimum of 4 points to define a solid (as opposed to 1 for a point, 2 for a line, and 3 for a plane figure). So we have the four elements, the four winds, the four directions, the four humors, the four qualities. Even the four gospels, which Irenaeus argued arithmologically could not be more or less, pertain to God's existence in the three-dimensional world. So we have in the tarot two pairs, spiritual and temporal, who hold sway over this domain. Here again is Hopper, pp. 83-84:
The principal Christian innovation in number science was the identification of this spiritual-temporal dualty with the archetypal numbers, 3 and 4. Four, by the known analogues of the 4 winds, the 4 elements, the 4 seasons, and the 4 rivers, is specifically the number of the mundane sphere; and, as the first 3 days of creation foreshadow the Trinity, so the fourth is the "type of man." (56) Mystically, the fact that man in a tetrad is evidenced in the name, Adam, whose letters are the 4 winds (81) For this reason, knowledge of divine things is disseminated throughout the world by the 4 gospels, evangelists or beasts, emblemized by the 4 extremities of the cross (58), the 4-fold division of Christ's clothing, and the 4 virtues, or forms of love, as Augustine names them (59). "It is not possible," says Irenaeus, "that the gospels can be either more or fewer than they are." (60)
56. Theophilus of Antioch, To Autolycus; AN III, 82; also Ambrose, De fide II, Introduction; Augustine, On John, IX, 14.
57. Augustine, On John, IX, 14; see above, p. 31.
58. The cross was conceived to have 4 or 5 points--5 if the intersection was included. As the image of 4, it is encompassed man in the universe. As an emblem of 5, it coincided with the 4 wounds in providing the salvation of man, with his 5 senses, or of those living under the Old Dispensation of the Pentateuch.
59. Of the Morals of the Catholic Church, XV, 25.
60 Against Heresies, III, 11, 8.
The number 7 is that of the virtues, the vices, and many other things pertaining to the world of humans' and their choices for good or evil:
From the triune principle of God and the quadruple principle of man are produced the universal symbols, 7 and 12. The addition of 3 and 4, spiritual and temporal, produces 7, which is therefore the first number which implies totality (61). It is the number of the universe and of man, signifying the creature as opposed to the Creeator (62). Seven gifts of the Holy Spirit were derived from Isaiah XI: 1-3 (63) The Lord's Prayer was found to contain 7 petitionns (64). Similarly, the Beatitudes were found to be 7, and by the principle of contraries these septenaries were balanced by the 7 deadly sins ((66). Later, the addition of the 3 theological virtues (Faith, Hope, Charity) to the 4 cardinal virtues produced one of the best known heptads of Catholicism. The habit of presenting these spiritual entities in precise numerical groupings indicates that a relationship was felt between them, but it remained for Augustine to show the precise connection of the 7 petitions of the Lord's Prayer to the 7 beatitudes, whch in turn relate to the 7 gifts of the spirit or to the 7 steps to wisdom (67). Seven is the number of the Sabbath and Salvation, but it is also the number of sn (68). Necessarily the churches on earth are 7, formng a likeness of the universe (69).
61. Augustine, Civ. Dei, XX, 5.
62. Augustine, On the Sermon on the Mount, II, 10, 36; Letter LV, 15, 28.
63. Tertullian, Against Marcion, V, 8; Victorinus, On Creation.
64. Cyprian, On the Lord's Prayer; Tertullian, On Prayer, II. 8.
6. Augustine, On the Sermon on the Mount, II, 10-11.
66. Tertullian, Against Marcion, IV, 9; Augustine, Harmony of the Gospels, VI, 13.
67. On the Sermn on the Mount, II, 10-11. Contra Faustum, XII, 15; On Christian Doctrine, II, y, 9-11.
68. Augustine, Harmony of the Gospels, VI, 13.
69. Augustine, Letter LV, 5, 9.
Seven, it seems to me, is the number of humanity's being tested for worthiness. This group of tarot subjects, besides including at least two of the four virtues, show the situations in which people are tested: love, triumph, fortune, shame, and the limits of time (you never know when the proctor will call "time"). The Bagat, as the tester, is easily excluded.

The number 10 is that of the cycle of the basic numbers, after which one can go on forever. It also is that which returns to the One. Here is Hopper (p. 84):
Ten had long been recognized in the image of unity, but it was Augustinian Pythagoreanismm that produced it by adding the Trinity of the Creator to the hebdomad of the created (75). In Christian usage, its great type is always the 10 Commandments, whose traditional division into 2 groups of 5 was soon to be altered to 3 and 7, in recognitin of this doctrine.
75. Augustine, Against the Epistle of Manicaeus, Called Fundamental, X, 11.
In the Tarot, the cycle here begins in the sphere of the earth, at death, and ends in heaven, the Empyrian; it is the course of the soul from underground to eternity, through the medieval cosmograph of concentric circles, although not all are represented.. One card in the sequence, the Star (representing the Fixed Stars, and/or Venus), is out of order. That is for the sake of the players. It is easier to remember a sequence of increasing light than it is the Ptolemaic universe.
I have elaborated on this cosmographic progression in the essay to which Alain, at viewtopic.php?f=11&t=1102#p16911, graciously gave a link, "The Astral Journey of the Soul", For an exposition of the entire sequence in the interpretation which I am overlaying onto Alain's structure, see my "Platonism and the Tarot", at

It is important also to understand the Christian style of incorporating Pythagorean number theory into a text. It is not by citing Pythagoras by name; it is merely enough to use the principles, which were known as Pythagorean by all ealready already. For example, Hopper quotes Augustine (p. 81):
That the flood came 7 days after Noah entered the ark, as we are baptised in the hope of future rest, which was denoted by the 7th day...
This is is an essay (Contra Faustem) in which Augustine discusses one number after another, for its Christian significance. So also D’Oncieu, discussing the meaning of 3, 4, and 5 in the game of tarot, does not have to mention Pythagoras specifically to be seeing the game in a Pythagorean way.

In Alain's diagram, the 1 is in the center, with the 4, 7, and 10, as concentric enclosures, U-shaped, around it. If the tops are joined, they can be seen as concentric squares, each enclosed in its own circle passing through the four vertices of each. In the center is the Creator, a kind of "big bang" point. The authorities in this world get their legitimacy from that center; they are the divinely appointed earthly representatives of that Creator. Beyond that are humans in general, all confronted with the situations of the middle section. Beyond that is the cosmograph, now represented as dots on a U, or square, or circle. Enclosing all is the "infinite circle whose center is everywhere and whose circumference is nowhere", a definition of God of uncertain origin that Nicholas of Cusa ( revived in the mid-15th century.

On July 28 I modified this post by adding the quotes from Hopper now embedded in the post.

One other addition: I wrote about d'Oncieu as using Pythagoreanism in relation to the tarot at viewtopic.php?f=11&t=767&p=14694&hilit=tarotica#p14694. However I did not quote d'Oncieu, as opposed to paraphrasing him. I was hoping for some clarity about what the translation should be of the . Well, three translations were produced, of all or part (Andrea, Zorli, Marco), somewhat contradictory and none of which makes complete sense or is easy to translate into English that makes sense.

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

Another thought: it is not totally clear that the type-A tarot is an exception to the division 1 + 4 + 7 + 10. Applied to the type A tarot, the last group begins with the Hanged Man rather than Death. Is that so bad? The Hanged Man is not dead, but he is on the point of death. The theme of the last section is ascent to heaven. Without the crucifixion, there is no admittance to heaven. In the type A cards, the man is shown clutching bags of coins. If that reminds us of Judas, the number 12, invariably associated with the card (except in Minchiate, which is not tarot, and the Sicilian, which is derivative from Minchiae), is also associated with Judas, the so-called 12th disciple. Judas's betrayal of Jesus is what leads to the crucifixion. So the card changes from being a "condition of life" in types B and C to a condition of salvation in A. The division 1 + 4 + 7 =10 in that case still holds. However it is a rather radical idea, that Judas is a condition of salvation, perhaps too radical for the time. In which case Alain is right that his way of dividing the sequence doesn't hold for type A.

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

For the Hanged Man as the 12th card, here is what was on the shame poster of the hanged man posted in 1412 by anti-pope John XXIII (from Andrea's essay "A Gang of Traitors:,
“Per ordine del Signor nostro Papa fu dipinto su tutti i ponti e su tutte le porte di Roma, sospeso pel piede destro alla forca, quale traditore della Santa Madre Chiesa, Sforza Attendolo e teneva una zappa nella mano destra, e nella mano sinistra una scritta che diceva così: Io sono Sforza vilano de la Cotignola, traditore, che XII tradimenti ho facti alla Chiesa contro lo mio honore, promissioni, capitoli, pacti aio rocti” (By order of our Lord Pope is to be depicted on all the bridges and on all the gates of Rome, suspended by the right foot from a gallows, as a traitor to the Holy Mother Church, Sforza Attendolo, holding a hoe in his right hand (2) and in his left hand a sign saying: I am Sforza peasant of Cotignola, traitor, who twelve times have betrayed the Church against my honor: promises, compacts, agreements have I broken" [aio rocti = ho io rotti])
There is also Alciato's designation of the card as "crux", a reference to the cross made by the man's legs but also to the crucifixion. And on the CY Hope card, the rope on the bottom around a figure's head, labeled "Judas".

A problem is that in the type A tarot, the Hanged Man is not the 12th trump; it is the 13th. Yet it was still, at some point, numbered 12, as indicated by the little numbers on the Charles VI deck. Either by then a card had been removed, such as the Popess, or the Bagat was unnumbered, making the Popess number 1 and so on (or the "Papi" numbers 1-4, as at some point in Bologna). Either would seem to have been a later development, not in type A when it first had 22 special cards, in the latter case because it is so strange. If so, it would not have been the deck in which the Hanged Man first appeared, as it is rather evidently associated with the number 12--unless, it must be conceded, it is pure coincidence that the Hanged Man is 12 in B, C, and later A. Alain's hypothesis only fits type A decks in which it was the 13th trump, perhaps numbered 12 due to the practice of not numbering the Bagat.