- The Prince, Inventor of the Ludus Triumphorum
- The Traitor
- The Hospital of Incurable Madman
- Mundus Alter et Idem
- La Cassaria by Ariosto
- The Theatre of Brains
- The Mystical Staircase
- The History of the Tarot
- Bologna and the invention of the Triumphs
- Symbolic Suits
- Castel del Monte
- Nativitas
- The astral origin of the Soul
- Tarot in Literature I
- Tarot in Literature II
- Tarot in Literature III
- Tarot in Literature IV
- Minchiate in Literature
- The Sermons of Giusti
- Tasso and the Tarot
- The Aristotelian Telescope
- A poor Artist of the sixteenth century
- Il Malmantile Racquistato
- About the etymology of Tarocco
- The meaning of the word ‘Tarocco’
- The Order of the Triumphs
- Giordano Bruno and the Tarot
- Giulio Cesare Croce and the Tarot
- Playing Cards and Gambling
- Saint Bernardino and the Cards
- Tarot: History, Art, Magic
- Triumphs, Trionfini and Trionfetti
- The Twelve Words of Truth
- Farsa Satyra Morale
- Treatise on the Game of Minchiate
- Wise Madness, Pleasant Madness
- The Game of Final Bagatt
- My Heart has become a Taroch
- Taroch: vulgar Latin
- Taroch: nulla latina ratione
- Taroch - 1494
- Taroch in Milan in the XVIth century
- Writing and Quarreling
- Christ, the great gambler
- Rochi and Tarochi
- The Conjuration of the Tarrocco
- Allowed Triumphs, Forbidden Triumphs
- Ludere ad Triumphos
- Emperor Moon and Pope Sun
- The origin of Aces
- Tharocus Bacchus est
- Games and Magic in Ferrara
- Laudabiles et Vituperabiles
- Tarotica - 1584
- De Ludo in Statutis
- Ganellini seu Gallerini
- Men against Women
- Ruzante the Peasant
- Tarot and Inquisitors
- The renunciation of "Tarrocchi"
- I won. Played Tarot
- Sorian Days
- A Gang of Traitors
- The Castle of Malpaga
- Matti de Trionfi
- Triumphs in the Bonfire of the Vanities
- Odi et Amo [I hate and I love]
- Remedy of Game-Players
- God doesn't mind Tarocchino
- El Bagatella which is the symbol of sin
- Folly and 'Melancholia'
- De Rege Scaccorum, de Imperatore Tarocorum
- Playing Tarot in Delight - 1554
- Theroco Wind
- Winckelmann and Tarocchino
- From ‘Barocchi’ to ‘Tarocchi’
- The illicit skill of cheaters
- Officium Lusorum
- Il Torracchione Desolato
- An enigma in 'Orlando Furioso'
- May cancer come to Goffo and to Tarocco
- A clownish sermon (1529)
- Predicting the future with the tarot
- Of the Passion of Gambling
- A 'Cavaleyro' taroco (XIIIth century)
- Pleasant Dialogues – 1539
- Tarots in exhibition at Milan in 1872
- Like the 'Fool of the tarot' of Carducci
- A sonnet in Modenese dialect of the XVIth century
- Sigismondo Malatesta and the Triumphs

- Bolognese Industry and Tarots
- Tarot and Neo-Pythagoreanism
- Antoine Court de Gébelin
- Carl Gustav Jung and the Tarot
- The Wheel of Fortune
- The Popess Maifreda
- Dionysus and the Historical Tarot 1
- Dionysus and the Historical Tarot 2
- Dionysus and the Historical Tarot 3
- Dionysus and the Historical Tarot 4
- The Astral Journey of the Soul
- The Masonic origins of the esoteric Tarot
- The arithmological tarot
- In Appreciation of Alain Bougearel's "1+4+7+10=22"

By Alain Bougearel. Translation from French by Michael S. Howard

*Copyright Alain Bougearel, Member of the Scientific Committee of the Association “Le Tarot”,*

**Introduction: The mystical staircase of the 22 pictorial allegories**

At one point in history, probably at least before the end of the last quarter of the fifteenth century, the number of cards finally settled at 78, i.e. 56 + 22.

(Andrea VITALI: http://letarot.it/cgi-bin/pages/mostra_ ... r_sito.pdf

I. The earliest literary source known: Anonymous, Sermones de ludo, circa 1500

(Andrea Vitali, op. cit.)

He must overcome desire by practicing the virtue of Temperance and likewise thirst for power (Chariot) by the mistress of Strength. He learns the transitory character of human ambition (Wheel of Fortune).(A. BOUGEAREL*, Origines et histoire du Tarot,* p. 21, Editions Envol, Toulouse, France, 1997)

He must overcome desire by practicing the virtue of Temperance and likewise thirst for power (Chariot) by the mistress of Strength. He learns the transitory character of human ambition (Wheel of Fortune).(A. BOUGEAREL

Note: In the Tarot, the Fool's presence subsequently acquires a deeper meaning: the fool possessing reason but not being a believer, was to become, through the teachings expressed by the Mystical Staircase, the Fool of God, as Francis, the most popular saint, will become, named 'Holy Minstrel of God and Holy Fool of God'."

These 78 cards include 56 emblematic cards (40 numeral [10x4] + 16 courts [4x4]) and 22 allegorical subjects.

The Pythagorean arithmology of Nichomachus of Gerasa, like that of Iamblichus or of Theon of Smyrna (Cf.: Note 1), is one that mathematically defines triangular, square, and pentagonal numbers, teaching that:

Preliminary explications of the numbers depicted:

(Th. Henri MARTIN, Dean of the Faculty of Arts of Rennes, France, Corresponding Member of the Academy of Sciences of Berlin, Germany.

Series of polygonal numbers (which can be triangular, square or pentagonal)

"...

Natural series of numbers noted on the bottom side of the diagrams:

Triangular......................................1 2 3 4

Square...........................................1 2 3 4

Pentagonal....................................1

Series of component numbers or “differences” noted on the lower left and above each diagram

Triangular......................................1 2 3 4

Square.......................................... 1 3 5 7

Pentagonal....................................**1 4 7 10**

Series of polygonal numbers noted above each figure:

Pentagonal....................................

Series of polygonal numbers noted above each figure:

Triangular......................................1 3 6 **10**

Square.......................................... 1 2 9**16**

Pentagonal................................... .**1 5 12 22 **

..."

(H. MARTIN, op. cit.)

Square.......................................... 1 2 9

Pentagonal................................... .

..."

(H. MARTIN, op. cit.)

Geometrical configuration of triangular, square, and pentagonal numbers:

The small lines connecting all the dots pertaining to each of the component numbers were superimposed by hand to figures that are arithmological in origin, i.e. diagrams of triangles, squares and pentagons - and to highlight these numbers, which, in being added, form each polygonal number.

Cf: http://remacle.org/bloodwolf/erudits/ni ... etique.htm.

Cf: http://remacle.org/bloodwolf/erudits/ni ... etique.htm.

The arithmological arrangement of the 22 allegorical subjects of the Tarot is that of the Pythagorean generation of the Pentagonal Number 22: 1 + 4 + 7 + 10 = 22.

The points in the arithmological diagram have been replaced by small diamonds.

The lines were superimposed by hand in order to connect:

- The component numbers, in order to highlight them;
- The successive Four Enclosures of the component numbers together so as to emphasize visually their order of succession: first 1, then 4, then 7 and finally 10.

It is inserted into the overall arithmological layout of the 78:

The 78 cards of the Tarot (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12) are represented by diamonds arranged in an isosceles right triangle (Cf. note at bottom of page, at the end: definition and construction).

- 40 numerals [10x4]: 10 is a Triangular Number of base 4

- 16 figures [Court Cards--trans.] [4x4]): 16 is a Square Number of base 4.

- 22 allegorical subjects [1 = 4 = 7 = 10]: 22 is a Pentagonal Number of base 4.

The methodology requires that the Triumphs be arranged as if one ignored their iconography or ludic value, taking into account only their ordinal value i.e. from the first to the twenty-second position in the order of the generation of the Pentagonal number.

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 [Atouts] renders complex and delicate the replacement of the ordinal numbers of the Pentagonal Number 22 by the corresponding allegorical subject of the Triumphs.

I am indebted to Michael Hurst, in his "critical examination" of my theory of the sequence of Trumps 1 + 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 [Atouts]” by Thierry Depaulis in

The four enclosures of the Pentagonal Number structure the 22 allegorical subjects of the Tarot into Four successive groups:

1 + 4 + 7 + 10 = 22

The ordinal progression is then:

1, 5, 12, 22

First enclosure:

Second enclosure:

2, 3, 4,**5**

2, 3, 4,

Third Enclosure:

6, 7, 8, 9, 10, 11,**12**

6, 7, 8, 9, 10, 11,

Fourth Enclosure:

13, 14, 15, 16, 17, 18, 19, 20, 21,**22**

13, 14, 15, 16, 17, 18, 19, 20, 21,

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 the 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 Triumphs and 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 aspect)?

In fact, the only difference between the sequence of pentagonal Number 22 as 1 + 4 + 7 + 10 and Dummett’s analysis into 3 groups is that one member of the whole constitutes a group of one by itself (The Bateleur [Magician] at Alpha) and the Fool is added to the end of the fourth group, in the last position, as twenty second in the sequence.

T. DEPAULIS for his part examines 12 different orders out of "

Sequence 1:

Bateleur, Pope/Popess, Empress/Emperor (with some variations)

Sequence 2:

Lover, Chariot, Wheel of Fortune, Hermit, Hanged Man (with some variations)

Sequence 3:

Death, Devil, Tower, Star, Moon, Sun, World, Judgment (with some inversions in the order for the last two)

The arithmological arrangement positions the 3 sequences in 4 enclosures:

Enclosure 1:

Bateleur

Enclosure 2:

Pope/Popess, Empress/Emperor (with some variations)

Enclosure 3:

Lover, Chariot, Wheel of Fortune, Hermit, Hanged Man (with some variations)

Enclosure 4:

Death, Devil, Tower, Star, Moon, Sun, World, Judgment (with some inversions in the order for the last two)

The analysis of the 12 orders leads to putting the orders of the sequence of Triumphs into 3 "blocs" (Cf. Note 3)

.

However, T. Depaulis's analysis of 1984 as presented in the *Tarot, jeu and magic* exposition, BNF, has been, in 2013, updated and corrected by the author in *Le Tarot révélé: une histoire du tarot d’après les documents* [The Tarot Revealed: A History of the Tarot According to the Documents], 2013, ISBN 9782883750135.

T. Depaulis (op. cit.) gives some particular variations in Tarot enclosures 2 and 3 (according to whether that order is of Bologna or Florence).

1. Bateleur/

2. Empress / Emperor / Popess / Pope / (with some variations)

3. Lover / Chariot / Temperance / Justice / Strength / Wheel of Fortune / Hermit / Hanged Man / (with some variations)

4. Death / Devil / Tower / Star / Moon / Sun / World / Judgment /

Remark:

The difficulty is that enclosure 3 has 8 triumphs, not 7, while enclosure 4 has 8 or 9, not 10, even if the Fool was added, despite the lack of documentation on this subject.

Note: M. Howard (Cf: http://letarot.it/page.aspx?id=608&lng=ENG) has, however, expressed reservations, in my view relevant, on the non-suitability of the arithmological division 22 = 1 + 4 + 7 + 10 with the A order- excluding from it the late Sicilian Tarot and positioning the Hanged Man as the alpha of the fourth enclosure. I translate verbatim below.

F

But if the Hanged Man is made the beginning of the 4th group, then everything comes out OK. Is that wrong, conceptually? The theme of the last section is ascent to heaven. In the early type A cards (the “Charles VI”, the Rosenwald Sheet, the Rothschild Sheet), the man is shown clutching bags of coins. That suggests Judas and his “30 pieces of silver” for which he betrayed Christ. But Judas's betrayal is what leads to the crucifixion, and without the crucifixion, there is no admittance to heaven. In that way the card is not only the moment of failed trial of types B and C, but also involved in the ascent to heaven, which is the theme of the last section. The division 1 + 4 + 7 + 10 in that case still holds for the A order.

In fact Dummett's rationale for his three groups cannot specify by itself which group the Hanged Man is in, any more than it can specify which group Death is in. Dummett says (1980 p. 394):

In this case Depaulis, 2013, gives only one order.

1. Bateleur/

2. Empress / Emperor / Popess / Pope /

3. Temperance / Lover / Chariot / Strength / Wheel of Fortune / Hermit / Hanged Man /

4. Death / Devil / Tower / Star / Moon / Sun / Judgment / Justice / World/

Remark:

Note again that the *Sermones*, of Order B, positions the Bagatella (Bateleur) in 1st position and places the Matto (Math), while giving it the epithet "nulla", on the twenty-second line, after the World, in the 21st position*. Sermones de ludo*, circa 1500.

In this case Depaulis 2013 gives

- inversions of the Empress and the High Priestess (in enclosure 2)

- and the same between the Hermit and Strength (in enclosure 3),

depending on whether the order C is of Italy (Pavia) or France.

Below, the Order of the so-called "Tarot de Marseille", France.

1. Bateleur/

2. Popess / Empress / Emperor / Pope/

3. Lover / Chariot / Justice / Hermit / Wheel of Fortune / Strength / Hanged Man /

4. Death / Temperance / Devil / Tower / Star/ Moon / Sun / Judgment / World /

Remark:

The oldest *Rules of the Game of Tarot* in France, transcribed by T. Depaulis (Cf. Note 4) and dated to 1637 (*) enumerate 22 Triumphs (Cf. Note 5): This pack, which is composed of seventy-eight Cards, can be divided into five groups, the first and noblest of all called triumphs, which number twenty-two..." (Anonymous, *Les Règles du Jeu des Tarots* - very probably written by the Abbé de Marolles at Nevers and published by Jean FOURRÉ at Nevers in 1637 - were inspired by Louise Marie de GONZAGUE-NEVERS **)

* 1637: http://www.tarock.info/depaulis.htm.

** Louise Marie de GONZAGUE NEVERS, “inspirer” of the*Rules* of 1637:

* 1637: http://www.tarock.info/depaulis.htm.

** Louise Marie de GONZAGUE NEVERS, “inspirer” of the

The Fool, analogous to a Triumph, would therefore be the twenty-second (the World, the 21st and the Bagat the 1st).

Enclosure 3 includes 7 Triumphs and enclosure 4, 10 Triumphs.

In the scholastic thought of the Church, the number 22 makes sense.

(Cf: Steve Mangan on THF : viewtopic.php?f=11&t=1102&start=340#p17660 )

Thus Origen, one of the Fathers of the Church, was first, before being ordained a priest, a student of Ammonius Saccas, the teacher of Plotinus - the founder of Roman Neoplatonism, whose writings in their entirety were published by his disciple Porphyry of Tyre under the name of the

Origen, historically regarded as the Father of Biblical exegesis, defined the Number 22 in these terms:

"In the order of the numbers, each individual number contains some strength and power over things. The Creator of the Universe has made use of this power and strength, either for the constitution of the universe itself or to express the nature of each thing as it appears. It follows, according to the Scriptures, that we must observe and calculate these aspects which belong to the numbers themselves. And in truth, the books of the Bible itself, such as the Jews have transmitted them, are [in number] twenty-two, equal to the number of Hebrew letters, and this is not without reason. Indeed, twenty-two letters [that] seem to be the introduction to God's wisdom and the knowledge of the world."

(Select in Ps I - PG 12, 1084)

(Cf : A. Quacquarelli, s.v. Numeri, in DPAC, pages 2447-2448)

(Cf : A. Quacquarelli, s.v. Numeri, in DPAC, pages 2447-2448)

The members of the Neoplatonic academy in Florence (1459-1521) could not ignore it, whether Marsilio Ficino, Giovanni Pico della Mirandola, Giralomo Benivieni or others ...

The 22 pictorial allegories and the 21 Tarots + the Math:

Many lists of Tarots consider the Math not to be part of the 21 Tarots, even if they position it in the 0 position before the Bagat, with an ordinal progression of:

0 and 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21

Hence a count of:

0 [Math] + XXI Tarots

The

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,12, 13, 14, 15, 16, 17, 18, 19, 20, 21 and 0

Hence a count of:

XXI Tarots + NULLA

The 1637 Rules, the oldest in France, count XXII Triumphs:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,1 2, 13, 14, 15, 16, 17, 18, 19, 20, 21 and 22

Hence a count of:

XXII Triumphs = XXI tarots + 1 (The Excuse).

These ordinal progressions in no way conflict with the arithmological generation of the Pentagonal Number 22 of 1 + 4 + 7 + 10.

Beyond knowing whether there are 21 or 22 Triumphs, the ordinal progressions are justly subject to perceiving the 22 pictorial allegories as arranged in a circle depicting an Ouroboros.

or indeed:

- from 0 to the 21st allegory: the Math is the 0th Triumph; the Bagat is the first, and the World, twenty-first.

In summary:

- the Math is the 22nd in ordinal position in a count of 1 to 22

or

- the Math is 0th in ordinal position in a count from 0-21

The position of the Fool [Fol] at Omega in the B and C orders after the World does not signify the Matto's triumph over the World but suggests the idea of a Madman [Fou] falling perhaps into divine madness, even the playful and subversive theme of the medieval Festivals of Fools.

Berry Hayward,

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.

● "The Order of the Triumphs, In ancient tarot cards and in 16th century documents"

By Andrea VITALI

Translation by Michael S. HOWARD

http://letarot.it/page.aspx?id=221

● Nicomachus of Gerasa,

English translation by Martin Luther D’Ooge, with

London: Macmillan and Company, Ltd., 1916.

https://ia600709.us.archive.org/27/item ... hmetic.pdf

https://ia600709.us.archive.org/27/item ... hmetic.pdf

● "The astral origin of the Soul, A Neoplatonic myth in the iconography of a few cards of the Triumphs"

By Andrea VITALI: http://letarot.it/page.aspx?id=197&lng=ENG

● "The Astral Journey of the Soul, Porphyry and Plutarch in the context of the medieval cosmograph"

....

Platonic Syncretism is massively enriched by contributions from Byzantine philosophers (a) fleeing Constantinople just before it was finally taken in 1453 by the Ottoman Turks led by Mehmed II the Conqueror.

Indeed, in the years 1438-1439, the Congress of Ferrara-Florence sees the growing exchange between Byzantine and Latin intellectuals.

*"... The contacts between Greeks and Latins are growing (...) Many scholars and Byzantine scholars emigrated to the West early in the 15th century and foremost to Italy, where the Congress of Florence was an exceptional meeting point.*

*'*[The latter] *carried with them many manuscripts, the majority of ancient works ... the contributions permitted the undertaking of the rediscovery of Antiquity "*

(A. DUCELLIER,* Les Byzantins*)

(A. DUCELLIER,

(a) Thus, among the most famous:

- Jean Argyrotopoulos, co-founder of the Academy of Constantinople who removes himself to Italy in 1434 and teaches in Florence
- Gemistos Plethon, who journeys there in 1440, whose theses close to absolute Platonism inspired humanist Marsilio Ficino, founder of the Platonic Academy.

Michael Hurst:

*"I recommend Alain Bougearel's 78-card analysis as particularly attractive, conceptually neat, generally charming, and quite devoid of explanatory value."* (Tarot History Forum)

(T. DEPAULIS,

Transcription from the original, kept in the Bibliothèque Nationale de France, by Thierry DEPAULIS of

The book is printed in Nevers, France, in 1637.

The author is anonymous; however T. DEPAULIS ascribes authorship to Abbé de Marolles.

The "Rules of the game of Tarot" were "inspired" by the Princess Marie Louise Gonzaga-Nevers, daughter of the Duke of Mantua during the stay of Michel de Marolles in Nevers who wrote them during the summer 1637 and gave them to Jean FOURRÉ who edited them at Nevers the same year.

(Episode related by T. DEPAULIS in the Introduction to "Quand l’abbé de Marolles jouait au Tarot", Le Vieux Papier, July 2002: http://www.academia.edu/15316947/_Quand ... p._313-326

See pp. 209-214 of

T. DEPAULIS (op. cit.) corrects the Notice thus:

[MAROLLES, Michel de],* Regles dv iev des tarots*, s.l. [Nevers]: s.n. [Jean Fourré], s.d. [1637]

(BnF, Mss., Dupuy 777, f° 94-97.)

(BnF, Mss., Dupuy 777, f° 94-97.)

Nonetheless, it will be noted that from 1585, in the

(http://www.academia.edu/15317283/_%C3%8 ... p._386-392)

**(5) **In the Rules of 1637 (probably in use in the last quarter of the 16th century: see Note 4), the Fool is necessarily made part of the 22 Triumphs:

It is systematically cited after the World and before the Bagat:

[Translator's note: for a translation, with notes, of the first paragraph, see http://www.trionfi.com/0/p/1637.html.]

The Math serving as Excuse is considered as being part of the 7 Tarots:

(...) trois Tarots, Monde, Math, & Bagat"

Comment:

Why was the Math specifically named as one of the triumphs, in bringing their number to 22, and cited after the World and before the Bagat among the Highs - while retaining its specific function of Excuse?

Math serving as excuse is described as "not taking and not being taken".

In subsequent rules there will be listed 21 Trumps [Atouts] + the Excuse.

The contradiction is only apparent, if one takes into account the following hypothesis:

- of a reminiscence of the old value of the Matto to which is awarded the epithet "nulla" in the B Order, circa 1500, where it is positioned on a twenty-second line, after the World and before the Bagat.

- that the ultimate strategy of the game was to score the most points, and if possible all of them - which will be the case for the player who has the Excuse in his hand, if he plays it at last trick as in the case of the Slam [Chelem].

Thus the Math, if it cannot take and cannot be taken, however, then takes away the last trick.

One can rationally infer that this particular function of the Math, serving as Excuse, winning the last trick (and therefore all the tricks as in case of the Slam [Chelem]) was possibly in use in 1637 or before (1580) - although in the current state of historical research, the documents are missing.

Thus, for example, we now know that playing tarot was a "family tradition" of Henry of Navarre. (http://www.academia.edu/15317283/_%C3%8 ... p._386-392).

It is almost impossible that in the course of all these hands played the opportunity will not present itself for a player with the excuse in his hand to win all the tricks.

The only way to achieve what is later called the Slam [Chelem] is to play the Excuse as the last trick after le Petit [the Little One, i.e. the Bagat--trans.] in the next to last trick.

That the drafters of the Rules did not note this ultra-winning strategy does not prevent, in my opinion, empirical knowledge of this specification by serious players ...

In addition, knowing that players’ practice always precedes published rules and that these are published circa 1580 throughout France, the probability is reduced to zero, for at least one player, considering the number of hands played and number of players in the kingdom, for not winning all the tricks with the Excuse in his hand.

The *rarity *of what will be subsequently called the Slam [Chelem] (nomenclature of our time, with mandatory announcement) therefore does not invalidate in any case the multiplicity of hands with the Fool acting as Excuse winning the last trick as a Triumph (and what is even more beautiful: all the tricks then being won) – taking into account, in France at the time, the large number of players and therefore the high number of hands played.

_____________

1. Reference at the bottom of the page

**Definition:**

_____________

1. Reference at the bottom of the page

An isosceles right triangle, also called right isosceles, has a right angle with two adjacent sides of the same length, with, therefore, two 45° angles at the base.

Geometric construction of a triangular number from a square cut diagonally:

Geometric construction of the triangular number of base 12 = 78.

The geometric production of triangular numbers is made from a square cut diagonally.

The geometrical production of the triangular number of base 12 (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 78) is obtained from a square of base 12: [12 squared = 144], cut diagonally.

Then the diagonal divides the initial square into two unequal triangular numbers: 78, of base 12, and 66, of base 11 - [78 + 66 = 144].

The larger of the two is that of the triangular number 78 of base 12.

(Thanks to Jean Michel DAVID for these clarifications: http://www.tarotforum.net/showthread.php?t=29707&page=4)

[Translator's note: I have written my own thoughts on Alain's essay at http://www.associazioneletarot.it/page.aspx?id=608&lng=ENG.; My essay also appears at http://tarotarithmologique.blogspot.com/ ]