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

#131
Thanks for the links, Steve. This is as good a time as any to see if the three versions, Vitali, Ponzi, and Zorli, can be reconciled, at least as far as the Pythagorean content of the work.

We have Ponzi: http://www.tarotpedia.com/wiki/D'Oncieu ... orum_Decas
Vitali and Zorli: http://www.letarot.it/page.aspx?id=293&lng=ITA
Zorli also at: http://www.tretre.it/menu/accademia-del ... cieu-1584/
Original: https://books.google.it/books?id=6JJa8o ... milarbooks

Original, for the beginning:
Image


Vitali:
Quadrata figura qua sors ludit in humanis Tessera dicta.
Quadrata quoque in cartis, inde cartae dictae: hoc idem quod
Quadruplici personarum distinctione constent, & in famosa earum trituratione quam primeriam vocant.
Quaternis paribus, quaternis imparibus, & quaternis sequacibus: quaterna autem haec omnia, terna.


La figura quadrata con la quale la sorte gioca fra gli uomini è chiamata Tessera. [Tessera è nome greco che in lingua latina designa il dado].
È quadrata anche nelle carte, per cui queste sono dette quadrate. La stessa cosa è perché consisterebbero in una quadruplice distinzione di persone [carte singole] & nella famosa pratica distruttiva di quelle carte che chiamano primiera.
Quattro ai pari, quattro ai dispari e quattro a quel che resta: d’altra parte tutta questa quaterna è anche terna.

(The four-sided figure with which fate plays among men is called the Tessera. [Tessera is the Greek name that in Latin means one of a pair of dice, one die].
Four-sided is also in cards, as these are called four-sided. The same thing is why there consists a fourfold distinction of persons [single cards] in the popular and destructive practice of those cards they call Premiera.
Four in the even [or equal], four in the odd [or unequal], and four in what remains: on the other hand all this quaternity is also a triad.)
Ponzi:
Quadrata figura qua sors ludit in humanis Tessera dicta. Quadrata quoque in cartis, inde cartae dictae: hoc idem. quod Quadruplici personarum distinctione constent, & in famosa earum trituratione quam primeriam vocant.
Quaternis paribus, quaternis imparibus, & quaternis sequacibus: quaterna autem haec omnia, terna.

[Ponzi's translation]: the squared figure with which fortune makes fun of humans is called “Tessera” [die?]. [The figure] also is squared in cards, therefore they are called “cards”. This also because they are made of four groups of persons [i.e. the suits], and because of that famous chopping^ that is called “primiera”: four even cards, four odd cards and four cards in sequence^. However all these groups of four [also] are ternary.
______________
Inde cartae dictae: According to D'Oncieu, “carta” (card) etymologically derives from “quarta” (fourth).

Trituration: The use of this term (grinding / chopping) is difficult to explain. Girolamo Zorli interprets it as “the destructive game of primiera”.

Primiera: Girolamo Zorli notes that “the author seems to allude to the main combination of the game of Primiera: 'flux', i.e. four consecutive cards of the same suit, 'primiera' i.e. four cards of different suits, '55' i.e. three cards of the same suit in a sequential hierarchical order”
Zorli's contribution must be seen in the light of his definitions of key words:
Figura: raffigurazione, cioè pezzo di gioco, quindi carta singola.
Quaternum: quarta parte o porzione omogenea del mazzo, cioè seme
Distinctio: appartenenza a un seme
Persona: carta singola
Sor-sortis: distribuzione (cfr. Folengo)
Universum: tutto, cioè il mazzo.

(Figure: representation, that is, part of the game, so a single card.
Quaternum: Fourth part or portion of the homogenous deck, i.e. suit
Distinctio: belonging to a suit
Persona: single card
Sor-sortis: distribution (see Folengo)
Universum: the whole, that is, the deck.)
So now Zorli's translation, and mine of his:
Quadrata figura qua sors ludit in humanis Tessera dicta.
Quadrata quoque in cartis, inde cartae dictae: hoc idem quod
Quadruplici personarum distinctione constent, & in famosa earum trituratione quam primeriam vocant.
Quaternis paribus, quaternis imparibus, & quaternis sequacibus: quaterna autem haec omnia, terna.


La figura quadrata che la fortuna fa giocare tra gli uomini è chiamata dado. E’ quadrata anche su carte (1), e si chiama carta da gioco: che è uguale. Quadruplice è la distinzione delle carte, anche nel loro famigerato gioco distruttivo che chiamano Primiera.
Quaterne di carte pari (uguali/dello stesso seme), quaterne impari (diverse/di seme diverso), e quaterne di carte consecutive: tutte queste sono di quattro carte, e di tre carte (2).
_________________
1) L'intuizione del pezzo da gioco fatto di diversi materiali è interessante e moderna. Oggi siamo abbastanza sicuri che le carte da gioco si sono sviluppate sulla direttrice dadi-domino-carte.
(2) L'allusione sembra alle combinazioni principali del gioco della Primiera: il flusso di quattro carte dello stesso seme, la primiera di quattro carte di seme diverso, il 55 di tre carte dello stesso seme in scala gerarchica sequenziale.

(The square [or four sided] figure with which Fortune plays among men is called a die [one of a pair of dice]. And square [or four sided] also in the cards (1), and it is called a playing card: it is the same. Fourfold is the distinction of the cards, also in their notorious destructive game called Primiera.
Quadruples of pari cards (equal / the same suit), quadruples of impari (other / different suits), and quadruples of consecutive cards: all these are of four cards and three cards (2).
___________
1) The intuition of game pieces made of different materials is interesting and modern. Today, we are pretty sure that the cards were developed in the direction dice-domino-cards.
2) The allusion seems to be to the principal combinations of the game of Primiera: the flusso [flush] of four cards of the same suit, the primiera of four cards of different suits, the 55 of three cards of the same suit in sequential hierarchy.
Zorli has a different interpretation of the part about "same" than Ponzi: not etymological ('Carte" derived from "quarto"), but geometrical. There is also the possibility that D'Oncieu means something else: the "same" in being four, i.r. participating in the archetype of fourness, of which four sides and four suits are two instances. Andrea's translation suggests that interpretation.

Then there is the reference to Primiera. Here Andrea says "quaternis sequacibus" means "four for the rest". Both Ponzi and Zorli say it means "four in sequence" and the three "foursomes" are three combinations in Primiera: four of the same suit, four of different suits, and four in sequence. Except that in Primiera it is not four in sequence, but three, according to Zorli. Then Zorli's translation of the end makes sense "four cards and three cards", and Ponzi's and Vitali's doesn't. But D'Onceiu says specifically that the sequences, if that is what he means, are quadruples, not triplets. Also pIn favor of the majority, we can easily suppose that D'Oncieu played a form with four in sequence. And since there are three such foursomes, the foursomes are ternary.

This must also be seen in light of preceding parts of the chapter.
Quaternis trinum unumq’, Deum inesse percipi posset [p. 249]
The one God is perceived as three in the quaternity.
Fortunately, we know from Augustine what D'Oncieu is talking about. The quaternity is the mundane world. It is the Triune God in the quaternity of the cross, or of the four elements, etc. It is also about us, with our inability to think except in terms drawn from our experience: we in the mundane world perceive the one God as three.

What D'Oncieu is saying, from this perspective is that the game of Primiera contains an analogy to the divine mystery: how from four comes three. And from the three come four.

However there is also, earlier:
Quatuor quaternae numeri pares 2, 4, 6, 8 ac impares 1,3,5,7 [p. 244, but with paribus]
Four even 1,3,5,7 and odd 2,4,6,8 numbers of the quaternity.
Here "pari" and "impari' meant "even" and "odd". In that case, however, what would the other four be? 9, 10, 11, and 12? But why would 12 be so privileged? Did Primiera have 12 cards per suit? Unless that can be answered, I am inclined to think that "pari" must mean "the same" rather than "even". There is also the question of "sequacibus" --is it the ablative singular or the dative plural. If singular, it would mean "that which follows in sequence". If plural, then "those that follow in sequence", so "sequences". I have no idea.

So, from Vitali:
The four-sided [or square] figure with which fate plays among men is called the Tessera. [Tessera is the Greek name that in Latin means one of a pair of dice, one die].
Four-sided [or square] is also in cards, as these are called four-sided. The same thing is why there consists a fourfold distinction of persons [single cards] in the popular and destructive practice of those cards they call Premiera.
Four in the even [or equal], four in the odd [or unequal], and four in what remains: on the other hand all this quaternity is also a triad.
Ponzi:
the squared figure with which fortune makes fun of humans is called “Tessera” [die?]. [The figure] also is squared in cards, therefore they are called “cards”. This also because they are made of four groups of persons [i.e. the suits], and because of that famous chopping^ that is called “primiera”: four even cards, four odd cards and four cards in sequence^. However all these groups of four [also] are ternary.
Zorli (with my comments in brackets and italics):
The square [or four sided] figure with which Fortune plays among men is called a die [one of a pair of dice]. And square [or four sided] also in the cards (1), and it is called a playing card: it is the same. Fourfold is the distinction of the cards, also in their notorious destructive game called Primiera.
Quadruples of pari cards (equal / the same suit), quadruples of impari (other / different suits), and quadruples of consecutive cards: all these are of four cards and three cards
And now me, from them:
The four-sided figure with which fate plays with men is called a die [one of a pair of dice].
Four-sided also in the cards, thus called a card; thus the same. which
Fourfoldness is the distinction of the cards [in suits], also in their notorious destructive game called Primiera.
Quadruples of equals [of the same suit; or: of evens], quadruples of unequals [of different suits; or: of odds], quadruples of what follows in the sequence. However these quadruples all, ternary.
That seems suitably ambiguous, just enough and no more. It ends in the style of Augustine talking about the cross, or the seven days of the week, or (if he did) the mystery of the Trinity. The Latin again:
Quadrata figura qua sors ludit in humanis Tessera dicta.
Quadrata quoque in cartis, inde cartae dictae: hoc idem.quod
Quadruplici personarum distinctione constent, & in famosa earum trituratione quam primeriam vocant.
Quaternis paribus, quaternis imparibus, & quaternis sequacibus: quaterna autem haec omnia, terna.
Any suggestions?

So endeth the first mystery. I will continue.

Added later: looking online at Primero on Wikipedia, I see that there were many variations in how many cards there were per suit. In Rome the game seems to have been played with a deck of 13 cards per suit, Ace through Nine and the four courts. A French deck would have only three courts, so possibly using 12 per suit, which would support the "even" and "odd" interpretation of "paribus" and "imparibus". But I have no idea, actually. There is also a primero term "rest", which has to with the smaller-denomination cards. In any case, it is Savoy and Eastern France we are concerned with, not anywhere where Italian was spoken. The book was written in Savoy and published in Lyon.

Re: Le Tarot arithmologique - Gosselin 1582

#132
Rough transcription moyen français - français moderne

Dedidace et Epistre pp 1-10

Page 1
La signification de l ancien jeu des chartes pythagorique et la signification des deux doubtes qui se trouvent en comptant le jeu de la Paume

Lesquelles connaissances ont été longtemps cachées par ci-devant : mais depuis peu de jours, furent retrouvées , et expliquées par I. G

Page 3

[Dédicace]
A Monseigneur (...) d' Esparnon, Duc, Pair de France, Premier Gentilhomme de la chambre du Roy, et Colonel général de l' Infanterie Française

EPISTRE
Page 3
Monseigneur,
Les Mathématiques, à raison de l'utilité, et du contentement, qu'elles apportent aux hommes, ont été anciennement en si grande estime qu'on les faisait apprendre aux enfants aussi qu'ils avaient quelque

Page 4
peu de jugement
auparavant qu'ils commencent à étudier aux autres sciences humaines. Suivant laquelle coutume, nul n'était reçu pour disciple capable de la philosophie divine de Platon, s 'il n'était suffisamment savant en Mathématique, pour laquelle cause, le dit philosophe divin, avait fait écrire sur l'entrée de son Académie cette sentence : 'Que) Nul ignorant en géométrie n'entre (ici)
Et à la vérité, il n'est pas possible de bien entendre aucune science quelle qu'elle soit, sans la connaissance des Mathématiques. Pareillement, l' homme ne peut bien faire aucune action corporelle, qu'il ne pratique (suivant sa lumière naturelle) quelque raison ou opération de Mathématique ; [...]

Page 7
Et d'autant Monseigneur que je connais la bonne affection que vous avez aux Mathématiques, et le grand plaisir que vous prenez à les entendre, je me suis (décidé) de mettre par écrit, une certaine cogitation et recherche, que j'avais faite par ci-devant sur l'ancien jeu des chartes : afin d'en faire un présent (cadeau) à votre excellence ; lequel présent en apparence (est) peu de choses : mais si on y veut regarder de près, on trouvera qu il découvre de très beaux secrets de Mathématiques lesquels ont été cachés aux hommes depuis longtemps jusqu'à présent.
J'estime que ceux qui entendront ce mien discours, auront l'occasion d'en savoir gré à votre excellence.
Or, il convient de noter que les personnes qui jouent en ce jeu des chartes tâchent chacun pour sa part à retirer à soi les nombres, qui sont paints aux chartes par images et caractères : afin qu'ils puissent réduire et disposer, en certaines proportions et harmonies, les plus grandes qu'il est possible

Page 8
d'être aux dits nombres : voulant en cela imiter Nature, laquelle selon certaines proportions et harmonies des qualités élémentaires, produit toute chose naturelle; et la conserve en son être sans lesquelles proportions et harmonies, aucune chose naturelle ne peut durer.
Nous appelons (comme le fait Aristote) chose naturelle, tout ce qui est composé de matière Elémentaire, et de forme : comme sont les hommes, les bêtes, les plantes, les pierres et autres choses.
je peux dire avec quelque raison que ce jeu des chartes est venu de l' intuition de quelques Philosophes Pythagoriques : et que c'est chose digne d'être considérée, comment les Anciens avaient les mathématiques si familiaires, qu'ils s'en aidaient en toutes leurs affaires d'importance, et davantage quand ils voulaient jouer, ils s'appliquaient à quelque jeu rempli des fruits de(s) Mathématiques, tels que le dit jeu des Chartes, lequel représente par nombres proportionnels, la composition et tempérament de chaque chose naturelle.
L' Arithmomachie, laquelle représente une bataille entre les nombres pairs et les nombres impairs : qui tendent chacun à cette fin, de pouvoir gagner par nombres proportionnels une très grande victoire; et aussi le jeu de Paume
(...)
Page 10 fin Epistre
http://www.sgdl-auteurs.org/alain-bouge ... Biographie

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

#133
Since Alain is now posting his translation of Gosselin into modern French, I will hurry up with my examination of the three translations of D'Oncieu to see if the Pythagoreanism is really there. In this post I will deal with the next part, after what I quoted in my last post (posting.php?mode=reply&f=11&t=1102#pr17189).

My sources are
Ponzi: http://www.tarotpedia.com/wiki/D'Oncieu ... orum_Decas
Vitali and Zorli: http://www.letarot.it/page.aspx?id=293&lng=ITA
Original: https://books.google.it/books?id=6JJa8o ... milarbooks

So now the next two sentences. It is not clear on the page whether the "at quidem" (but indeed") at the end belongs here or with the next part. Given the precedent of the preceding "sed tamen", it would seem to go with the next part, and "at" means the same as "sed", i.e. "but" ; on the other hand, the "quidem" has a period after it, unlike the previous "sed". To cover both possibilities I will include it in the Latin both places.
sed tamen
Quaterna distinctio perfectior imó mirabilior Tarotica: nam quadrata cum sit figura, tùm quaterna personarum distinctio in universum inest; & singularim quaternae cuilibet quaternum figurae genus. sed
Quaternum illud uniforme in suo quaterno duabus admixtis diversis partibus, scilicet altera, quae sit triumphorum. 21 postrema unius tātum figurae fatui sub effigie, videtur eo quaternum ternum: at quidem.

Here is Vitali, with my translation, my comments in brackets and italics:
Tuttavia la distinzione per quattro dei Tarocchi è la più perfetta anzi la più mirabile: dal momento che la figura è quadrata, la distinzione per quattro delle figure entra nell’universo: e singolarmente a qualsiasi quaterna corrisponde una quadruplice tipologia di figura. Ma questo è uniforme nei suoi quattro elementi con in più l’aggiunta di due diverse parti: cioè l’una che consiste di 21 Trionfi e l’ultima soltanto di una sola figura sotto specie di folle; perciò certamente il quaterno sembra terno.

(However, the distinction by four is the most perfect, even the most admirable, [in what pertains to the Tarot --accidentally not translated into Italian!]: from the moment that the figure is made four, the distinction by four of the figures [personae] enters into the universe, and singularly in any quaternity corresponds a fourfold typology of the figures. But this is uniform in its four elements with the addition of two different parts: namely the one that consists of 21 Triumphs and last only a single figure under the species of Fool; so the quaternity certainly seems trinitary.)

Ponzi:
But the four-fold division of Tarot truly is more perfect and wonderful. Indeed, not only the figures are squared, but a quaternary distinction of persons is in the whole [deck]; and a quaternary rank of figures in whatever suit. The suits of this deck [the tarot] are the same [as an ordinary deck of playing cards], to which are added two other parts, one of which is composed of 21 trumps and the other a single figure portrayed as a fool, thus it is a deck with three parts.

And Zorli; in this case, for ease in comparison, I am putting the English first, then the Italian:
(The best distinction, also the most admirable, of the fourfold distinctions (the four suits) is that of the Tarot (3): in fact the fourfold distinction is included in the whole (universum, for us the deck), and individually fourfold is the genus of any quarter of the cards. The fourth part of the deck (the suit) is uniform and fourfold. Mixing in the other two parts, one of which is composed of 21 triumphs and the other of a single figure portrayed as a fool, results in a triplicity from quadruplicity.)
_________________
(3) “Tarotica” is a neologism found here for the first time. D’Oncieu invented it from the French term “tarot”. The Italian version would have been the less elegant "tarocchità.")

La distinzione migliore anzi la più mirabile della distinzione quadruplice (i quattro semi) è quella dei Tarocchi: infatti la distinzione quadruplice è inserita nel tutto (universum, per noi il mazzo), e singolarmente è quadruplice il genere di qualsiasi quarta parte delle carte. La quarta parte del mazzo (il seme) è uniforme e quadruplice. Mescolandovi due altre parti, di cui una è composta di 21 trionfi e l’altra di una sola figura effigiata come un folle, ne risulta una triplicità della quadruplicità.
__________________
3) Tarotica è neologismo che trovo qui per la prima volta. D'Oncieu l'ha inventato dal termine francese tarot. La versione italiana sarebbe stata la meno elegante "tarocchità".

Here I think the Pythagoreanism comes out best in the last few words. The Latin is "videtur eo quaternum ternum", literally "it is observed I go quaternity ternary." Then the "at quidem" means "but indeed".

Here both Vitali and Zorli seem close to getting a proper translation. Vitali has "so the quaternity certainly seems trinitary". Here the "seems" seems too weak: "is observed" is what is actually being argued. Zorli's "results in a triplicity from quadruplicity" seizes on the "eo", which can be translated as "I result". How he gets a third-person verb out of this first-person form I do not understand; perhaps someone who knows Latin can explain. Vitali seems to ignore the "eo" and use the "at quidem" for his "certainly".

Ponzi's "thus it is a deck with three parts" I do not understand at all. "Quaternum" cannot be made into "parts" or even "deck in parts". The last sentence is meant to sum up what has come before, which is that the quaternity is now a triplicity. I also have trouble with his conversion of "quaterno" to "squared", which is an interpretation rather than a translation. Also, it dilutes the Pythagorean language. It does seem, however, to be a valid interpretation, in that cards are four-sided.

The first sentence in the passage seems to me to be extolling the tarot deck for something not found in the Primiera deck (which has four suits and four-sided cards), but also not going beyond the quaternity. The only thing I can think of is the deck's four court cards per suit, as opposed to fewer in Primiera (probably the three of French cards), and so a fourfold quaternity across the deck. Nothing could please a Pythagorean more. Otherwise I have no idea what all the fournesses could be, besides the four suits and perhaps the four-sidedness of the cards, which are not special to Tarot.

Of these, I think either Vitali's or Zorli's--I am not sure which--is the best, both for accuracy and for bringing out the Pythagorean language of the text.

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

#134
Now the next section (including the "at quidem", i.e. "but indeed", which could go either either with this section or the previous one):
at quidem.
Quaternum ternum à triplici quaterna rei natura, tum enim triplex cartarum est distinctio ut diximus, secundò terne extrà reponuntur, tertiò ternis lusoribus experiendum, Quartò à terna divisione quid lucri quídue dāni obtigerit cuiq’;, agnositur certò. atqui addendum quinaria distributione quina, velut quinta quadam essentia formam dari terno quaternoq’;, magna eorum numerorum inter se cohaerentia.
Vitali:
Il quaterno è terno a causa della triplice natura quaterna di questo, poi in effetti la distinzione delle carte è triplice come abbiamo detto; in secondo luogo sono date a tre a tre; terzo, è da sperimentare con tre giocatori. Quarto, dalla divisione per tre si conosce per certo quale guadagno o danno sia toccato a chiunque e bisogna aggiungere alla divisione per cinque la cinquina come se si desse una certa forma di Quinta Essenza al terno e al quaterno, essendo grande la corrispondenza reciproca dei numeri.

(The quaternity is triple because of the threefold nature of this quaternity, thus in fact the distinction of the cards is threefold as we have said, and second are given three by three, and thirdly, is experienced with three players. Fourth, from the division by three is known for certain what gain or loss happens to anyone, and there needs to be added the distributions by five, the quintinary as if bestowing a certain form of the Fifth Essence to the trinary and quaternary the mutual correspondence of the numbers being great.
Ponzi:
But certainly this four-fold ternary comes from the quaternary nature of a ternary. Indeed, as we said, there is a threefold distinction of cards; second, they are put aside three by three^; third, it must be experienced by three players; fourth, what gain or loss befalls to everyone is defined with certainty by means of a division by three. And five must be added, because of the five-fold dealing by five^, almost as if a quintessence was given to the ternary and quaternary.
And Zorli, putting my translation of his Italian first:
(The triplicity of the fourfold is in the triple nature of the fourfold. In fact, as we have said, (in the Tarot) the division of the cards is threefold, in the second place three cards are discarded, thirdly the game is played by three players, in fourth place at the end of the game note is taken of the three portions of receipts and penalties (4) obtained by each of the three players. Added to this is that the distribution is five cards for five times, which is a form of quintessence given to the triplicity and quadruplicity.
___________________
(4) The text does not clearly leave room for conjecture that at the end of the hand the three divide in proportion to the points they attain. The word “dannum” for damages, penalties, loss, power seems to allude to negative scores, of which we know nothing.)

La triplicità del quadruplice è nella natura triplice del quadruplice. Infatti, come abbiamo detto, (nei Tarocchi) la divisione delle carte è triplice, in secondo luogo sono tre le carte che vengono scartate, in terzo luogo si gioca in tre giocatori, in quarto luogo si prende atto a fine gioco delle tre porzioni di incassi e penalità (4) conseguiti da ciascuno dei tre giocatori. A questo va aggiunto che la distribuzione è di cinque carte per cinque volte, ossia una certa forma di quint’essenza viene data alla triplicità e alla quadruplicità.
_________________
(4). Il testo non chiaro lascia spazio alla congettura che a fine smazzata i tre dividessero in proporzione al punteggio ottenuto. La parola dannum, per danno, penalità, perdita, sembra potere alludere a punteggi negativi, di cui non sappiamo nulla.
The first difference pertains to the translation of "secundò terne extrà reponuntur", whether meaning the discard or the dealing of the cards: "repontur", literally "put back", and "extra", literally "beyond", would seem to suggest the three extra cards after each player is dealt 25 (the "distributions by five", in Vitali's words later). Zorli says explicitly it refers to the discard: if the dealer has 28 cards, 3 are extra.

Probably Zorli is right about how the score is arrived at, in three portions; otherwise the "division by three" in Ponzi and Vitali is not clear. We know about penalties from the Rules of 1537.

In any case, all this pertains to the ludic aspect, not of concern here. What is relevant from a Pythagorean standpoint is the point about the "distributions by five" that is "a form of the quintessence", a reference to the mysterious fifth element which somehow transcends the four. Since all three translators find "quintessence" here, the Pythagorean point - "Pythagorean" in a sense that includes later numerologists--is surely in the text. Also, the progression from 3 and 4 to 5 relates to the so-called Pythagorean theorem, with 5 as the hypotenuse.

So here I slightly favor Zorli's translation above the others.

I find now that the next passage also pertains to the structure of the deck more than the method of play and introduces one more mystical element from Pythagoreanism, namely the septenary. I will cover that next.

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

#135
Now for the final passage of D'Oncieu of interest here.

Here is the Latin for the next passage, which introduces the septenary:
Siquidem cum septuagenus octavus sit universus numerus, tripliciter distinctus partibus aequalibus, quarum quelibet sit viginti sex, ac porro triplici qua diximus distinctione, quarum prior sit quinquaginta sex quadratarum quippe cartarum principalium, quadratis septenariis duplicatis: altera triumphorū 21. proinde & quoad eos triplicatis septenariis; idémque & una carta personata fatui habitu:
First Andrea, with my translation following:
Se è vero che il numero totale dell’universo è 78 diviso in tre parti uguali, di cui una qualunque è 26, e proseguendo per quella triplice distinzione che abbiamo detto, di cui la prima parte è di 56, che è effettivamente il numero delle principali carte quadrate, con il raddoppio dei quadrati settenari: l’altra parte è di 21 Trionfi per cui e per quanto riguarda essi essendo moltiplicati per tre settenari; parimenti una carta sola con abito da folle;

(If it is true that the total number of the universe is 78 divided into three equal parts, of which any one is 26, and continuing for the threefold distinction that we have said, of which the first part is 56, which is indeed the number of main fourfold cards, doubling the quadruple septenary, the other part is the 21 Triumphs, which can be regarded as the septenary being multiplied by three; also one card alone dressed as a Fool; ...)
Ponzi:
The total number [of cards] is seventy eight, [p. 263] distinct in three equal parts, each of which is twenty six. And again [they can be divided] by the triple distinction we spoke of, the first of which obviously consists in the fifty six four-fold main cards, doubling a septenary square [56=2x7x4]; the second one are the twenty one trumps, which in the same way are a triple septenary; and similarly a single card personified by the character of the fool.
And Zorli:
(If it is true that the total number of cards in the deck is 78, dividing this number into three equal parts we get 26. Continuing with its three orders we have said, the first of which is 56 pieces, this number is actually the number of ordinary cards. But 56 is the double of four septenaries (4x7x2 = 56). The second part is of 21 triumphs, which is equivalent to three septenaries (3x7 = 21), and the third one is a card with the dress of the Fool,..)

Se è vero che il numero totale delle carte del mazzo è 78, dividendo questo numero in tre parti uguali otteniamo 26. Proseguendo su quei tre ordini che abbiamo detto, di cui il primo è di 56 pezzi, questo numero è di fatto il numero delle carte ordinarie. Ma 56 è il doppio di quattro settenari (4x7x2=56). La seconda parte è di 21 trionfi, numero che equivale a tre settenari (3x7=21); la terza è una carta sola con abito da folle, ...
Here the three accounts are substantially the same, except that Zorli has "this number is actually the number of ordinary cards", while Andrea has "which is indeed the number of main fourfold cards" and Ponzi " the first of which obviously consists in the fifty six four-fold main cards". Zorli has put in "ordinary" while the other two have "main", for the Latin "principalium". On the other hand, both Zorli and Vitali retain the language of "quaternity" and "septenary" dear to the Pythagoreans, whereas Ponzi dilutes it with "square", which makes no sense in the context. Here it seems to me that Andrea's translation is perfect.

The point is that in Pythagorean theory the septenary is a mystical number of trial and redemption, i.e. winning at the end. D'Oncieu sees septenaries throughout the tarot deck, not only in its suits but also its triumphs.

The rest of the account deals with the playing of the game. D'Oncieu is dealing with the different roles played by ingenuity and chance for the competing players. The problem seems to be that in discarding three cards and taking the three remaining after each player gets 25, the dealer seems to have an unfair advantage. However if the dealership is rotated among the three, the advantage is shared. It is a way in which the game imitates life, where in fact both ingenuity and chance play a role, and some have more knowledge and opportunity than others in some ways, but not in others. These aspects are not particularly Pythagorean, although they certainly pertain to the mathematics of probability and in that way, governed by number, they could be seen as a new extension of number theory, arithmology, in which Cardano (1501-1576), who sometimes supported himself gambling (https://en.wikipedia.org/wiki/Gerolamo_Cardano), was a pioneer in his work on games (Liber de ludo aleae ("Book on Games of Chance"), written around 1564 but not published until 1663, according to Wikipedia).

To sum up this comparison of the three translations: Vitali's is very accurate about the Pythagorean language, but there are some questions about the ludic aspects. Ponzi has a tendency to downplay the Pythagorean language for the sake of making the ludic aspects, many derived from Zorli, clearer. Zorli manages to be more plausible for the ludic aspects than Vitali while retaining the Pythagorean language. There remain questions of interpretation in all three.

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

#136
mikeh wrote:... I will hurry up with my examination of the three translations of D'Oncieu to see if the Pythagoreanism is really there.
The clearest and most obvious Pythagorean influence does not require translation, it is illustrated by the Pythagorean Tetraktys, or Platonic Lambda* (from Timaeus). Pythagorus begins with three quaternaries, addition 1+2+3+4, then multiplication of even and of odd numbers, with odd numbers down one side of the triangle, and even down the other (in an inverted V shape, like Greek Lambda, hence Plato’s Lambda). Hence his reference to the quarternary number 27, (1 3 9 27).

Image

From Numeralium Locorum Decas, p.243

... videtur eo quaternum ternum: at quidem. ...look at the four of three! (taking at quidem as emphasis, translated by exclamation!) Of which one might say Il quaterno è terno a causa della triplice natura quaterna...

SteveM

*The text specifically refers to Plato in Timaeus, in which the Lambda is discussed.
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

#137
I did not find that particular array, or even any one of the sequences, in D'Oncieu's book, at least not in the part on cards. Perhaps you mean it as a primary example of how the idea of quaternity/quartenary is physically significant. Plato himself does not use the term "quaternary/quaternity/fourness" here.

https://books.google.com/books?id=mwZOB ... ls&f=false

He is somehow generating the musical scale of seven tones; maybe there is also something about the seven planets. However it is certainly an example of doubles/ternaries/quaternities/septenaries in action.

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

#138
mikeh wrote:I did not find that particular array, or even any one of the sequences, in D'Oncieu's book,
The illustraton is from d'Oncieu's book. And he references Plato's Timaeus (wherein we find Plato's Lambda).

At the end of the Tarotica section he writes:

...ac demum possit in universum septem quaternis numeris (quos in 27. supra denominari plerisque diximus magna eius numeri emphasi) & uno individuo scilicet. 189.

(The 27 "mentioned above" I think refers to the discussion that accompanies the Lambda illustration on p.243. So though he doesn't make much of a direct use of it in the Tarotica section, he does refer to the discussion of it made previously in the book.)

27 on the lamba is a quaternis numeris in that it is fourth in sequence 1 3 9 27.

I mentioned this in the previous thread I linked to, and Marco included a note with the illustration at the bottom of his translation on Tarotpedia.

Here is one of his references to Plato on p.252, also 253 and 254 on which page he mentions Pythagorus/Pytagoreis. This is hardly surprising in a book on the places of the ten numerals, and does not by its inclusion mean he applies such to the tarotica, excepting to his reference to the discussion of 27 referring back to this section:

Image


Image


Image


Following pages go on to discuss 27 etc.
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

#139
Very good, Steve. This time around, I only looked at what Andrea linked to. Three years ago, when I was doing the translation that never got posted, I see from my notes that I did look on p. 245 and wrote about the number 27 precisely what you wrote (perhaps based on what you wrote). The number 27 occurs in a rather dense part of the "tarotica" section, which I preferred not to examine closely this time around. But yes, I could have saved myself some trouble, if I'd chosen to just take his remark on the number 27 out of context and related it to his reference to p. 245.

Added later: and the way in which 27 is one of seven quaternity numbers, as D'Oncieu says (septem quaternis numeris) is by beings one of the 7 numbers generated by doubling on the one hand and tripling on the other, three times starting from 1, which is the number common to both sets.

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

#140
I now have a translation for pp. 1-10 of Gosselin. First the original, then the translation:
BOUGEAREL Alain wrote:Rough transcription moyen français - français moderne

Decidace et Epistre pp 1-10

Page 1
La signification de l ancien jeu des chartes pythagorique et la signification des deux doubtes qui se trouvent en comptant le jeu de la Paume

Lesquelles connaissances ont été longtemps cachées par ci-devant : mais depuis peu de jours, furent retrouvées , et expliquées par I. G

Page 3

[Dédicace]
A Monseigneur (...) d' Esparnon, Duc, Pair de France, Premier Gentilhomme de la chambre du Roy, et Colonel général de l' Infanterie Française

EPISTRE
Page 3
Monseigneur,
Les Mathématiques, à raison de l'utilité, et du contentement, qu'elles apportent aux hommes, ont été anciennement en si grande estime qu'on les faisait apprendre aux enfants aussi qu'ils avaient quelque

Page 4
peu de jugement
auparavant qu'ils commencent à étudier aux autres sciences humaines. Suivant laquelle coutume, nul n'était reçu pour disciple capable de la philosophie divine de Platon, s 'il n'était suffisamment savant en Mathématique, pour laquelle cause, le dit philosophe divin, avait fait écrire sur l'entrée de son Académie cette sentence : 'Que) Nul ignorant en géométrie n'entre (ici)
Et à la vérité, il n'est pas possible de bien entendre aucune science quelle qu'elle soit, sans la connaissance des Mathématiques. Pareillement, l' homme ne peut bien faire aucune action corporelle, qu'il ne pratique (suivant sa lumière naturelle) quelque raison ou opération de Mathématique ; [...]

Page 7
Et d'autant Monseigneur que je connais la bonne affection que vous avez aux Mathématiques, et le grand plaisir que vous prenez à les entendre, je me suis (décidé) de mettre par écrit, une certaine cogitation et recherche, que j'avais faite par ci-devant sur l'ancien jeu des chartes : afin d'en faire un présent (cadeau) à votre excellence ; lequel présent en apparence (est) peu de choses : mais si on y veut regarder de près, on trouvera qu il découvre de très beaux secrets de Mathématiques lesquels ont été cachés aux hommes depuis longtemps jusqu'à présent.
J'estime que ceux qui entendront ce mien discours, auront l'occasion d'en savoir gré à votre excellence.
Or, il convient de noter que les personnes qui jouent en ce jeu des chartes tâchent chacun pour sa part à retirer à soi les nombres, qui sont paints aux chartes par images et caractères : afin qu'ils puissent réduire et disposer, en certaines proportions et harmonies, les plus grandes qu'il est possible

Page 8
d'être aux dits nombres : voulant en cela imiter Nature, laquelle selon certaines proportions et harmonies des qualités élémentaires, produit toute chose naturelle; et la conserve en son être sans lesquelles proportions et harmonies, aucune chose naturelle ne peut durer.
Nous appelons (comme le fait Aristote) chose naturelle, tout ce qui est composé de matière Elémentaire, et de forme : comme sont les hommes, les bêtes, les plantes, les pierres et autres choses.
je peux dire avec quelque raison que ce jeu des chartes est venu de l' intuition de quelques Philosophes Pythagoriques : et que c'est chose digne d'être considérée, comment les Anciens avaient les mathématiques si familiaires, qu'ils s'en aidaient en toutes leurs affaires d'importance, et davantage quand ils voulaient jouer, ils s'appliquaient à quelque jeu rempli des fruits de(s) Mathématiques, tels que le dit jeu des Chartes, lequel représente par nombres proportionnels, la composition et tempérament de chaque chose naturelle.
L' Arithmomachie, laquelle représente une bataille entre les nombres pairs et les nombres impairs : qui tendent chacun à cette fin, de pouvoir gagner par nombres proportionnels une très grande victoire; et aussi le jeu de Paume
(...)
Page 10 fin Epistre
Here is what I come up with. Some of the comments in brackets are Alain's and some are mine.:
[start page 1]
The meaning of the ancient game of Pythagorean cards and meaning of two doubts that are found in counting the game of Tennis

Which knowledge has been long hidden heretofore, but a few days ago has been found and explained by I. G

At Paris, at the sign of Hope, before the College of Cambray.
MDLXXXII

[page 2 blank; start page 3, with the numeral II in the upper right corner of the page]

[Dedication]
To Monsignor (...) of Esparnon, Duke, Peer of France, First Gentleman of the Chamber of the King, and Colonel General of the French Infantry

[Epistle]
My lord,
Mathematics, due to the utility and contentment it brings to men, was from ancient times in such high esteem that it is taught to children even when they have

[start of p. 4] little judgment and before they start studying other human sciences. Following that custom, no one was received as a disciple capable of divine philosophy by Plato, if he was not sufficiently learned in Mathematics, for which cause, says the divine philosopher, he had written on the entrance to his Academy this sentence: “Let no one ignorant of geometry enter (here)”
And in truth, it is not possible to understand any science whatsoever without acquaintance with Mathematics. Similarly, man can do no good corporeal action, unless he practices (according to his natural light) some reasoning or operation of Mathematics. [...]

[the rest of p. 4, all of p. 5--which has the numeral III in the upper right--and most of p. 6 discuss the use of mathematics in history, mainly warfare]

[bottom of p. 6]
....And inasmuch as I know, Monsignor, the good affection you have for Mathematics

[start of p. 7, with a "IV" on upper right of page]

and the great pleasure you take in understanding it, I have (decided) to put into writing a certain cogitation and investigation that I have made heretofore on the ancient game of cards: in short, to make a present (gift) to your excellency; which present in appearance (is) little: but if one wants to look closely, one finds that he discovers quite beautiful Mathematical secrets which have been hidden so long before now. I believe that those who will hear this my discourse will have occasion to be grateful to your Excellency.
However, it should be noted that people who play this game of cards strive each in turn to withdraw to himself the numbers painted on the cards in images and characters: so they can reduce and dispose, in certain proportions and harmonies, the the largest that can

[start of p. 8]
be of said numbers: wanting in this to imitate Nature, which in certain proportions and harmonies of elementary qualities, produces every natural thing; and conserves it in its being, without which proportions and harmonies, no natural thing can endure.
We call (as does Aristotle) natural, everything made of Elementary matter and of form: as are men, animals, plants, stones and other things.
I can say with some reason that this game of cards has come from the intuition of some Pythagorean Philosophers: and this is something worthy of consideration, how the Ancients, being so familiar with mathematics that they were helped by it in in all their important business, and when they wanted to play, they applied themselves to

[start of p. 9, V in upper right] some game filled with the fruit(s) of Mathematics, such as the game called Cards, by which is represented, in proportionate numbers, the composition and temperament of every natural thing.

The Arithmomachy, which depicts a battle between the even numbers and the odd numbers: which tend each to this end, of being able to win by proportionate numbers a great victory; and also the Game of Tennis [Paume], ...

[rest of p. 9 concerns tennis, to the conduct of which he says mathematics applies, and a closing statement]

[p. 10]
....Your most humble and affectionate servant,
I. Gosselin

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