D'Oncieu:Numeralium Locorum Decas
Guillaume d'Oncieu commented the numerical structure of Tarot in his 1584 work “Numeralium locorum decas, in omni fere scientiarum genere mysticis referta propositionibus” (“The ten numeric positions, replete with mystical sentences from almost all kinds of science”). Tarot is mentioned in the chapter about number four.
The relevance of the book to tarot history has been pointed out by Andrea Vitali. Girolamo Zorli has translated most of the passage into Italian and provided an extensive comment. The following Latin transcription is based on Vitali's. The English translation includes most of Zorli's proposed interpretations.
Vitali's page introducing this passage: http://www.letarot.it/page.aspx?id=293
Zorli's page with Italian translation and comments: http://www.tretre.it/menu/accademia-del-tre/documenti-e-articoli/i-tarocchi-e-la-primiera-di-doncieu-1584/
D'Oncieu on Google books: http://books.google.it/books?id=aFr_Mx6VqhQC&dq=guillaume+d'oncieu+numeralia&hl=it&source=gbs_navlinks_s
Transcription and translation
Quatuor labyrinti, primus in Aegipto, secundus in Creta, tertius in Lemno, quartus in Italia. sed non abs re ad labyrinti materiam accedat, 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. Sed tamen Quaterna distinctio perfectior imò 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 tantum figurae fatui sub effigie, videtur eo quaternum ternum: 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 damni obtigerit cuique, agnositur certò. atqui addendum quinaria distributione quina, velut quinta quadam essentia formam dari terno quaternoque, magna eorum numerorum inter se cohaerentia. 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 triumphorum 21. proinde & quoad eos triplicatis septenariis; idémque & una carta personata fatui habitu: aeque cuilibet trium distribui potest, quodcumque est in universo defalcatis mutuo velut symbolo tribus nempe pro virili, una à quolibet non autem quatuor aut quinque, constare ludus potest: namque ullo modo ab his aut ulterioribus numeris aequè partiri posibile est eum 28. numerum. Itaque licet potuerit aequè dividi tribus, defalcatur una pars à quolibet, ac seorsum constituitur, aequa in quemlibet sortis formidine, ac ne aequè distributis minoris esset ingenij à verisimiliore notitia caeterarum quae condivisoribus obvenerunt sed si contra in quatúor rem facias iam cum primum impari triumphorum omnimodo sorte, 39. cuilibet distributis, supererunt due de trahendae, ut ita in duos tantum versari
sors possit: atqui illud ad aequalitatis iudicium referendum, ut aequa formidine sortis teneatur quilibet. & licet vix accidat pares omnimodo omnes esse, à fortuna id tamen possibile esse, ut quo magis dignoscatur tum fortunam tum ingenium maximè in ludo huiuscemodi versari non alterutrum solum. sed enim & illud obiter occurrit observandum, aequalitatis singulari iudicio eum numerum ut est 78, individuorum, itidem esse in universum aestimatione, ratione habita alterius ad alterum. ex quo subtilis inventor, faceta sub demonstratione reliquit omniū acta in theatro humano vita, eadem fore urnam omniumque tandem aliquando futurum suum numerum aequalem.
obseruavit praeterea, septenarij cum uno individuo proportionem huiusmodi, ut decem septenariis & uno, possit lucrum forè unius in utrumque ex duobus reliquis multiplicatis denario numero, ordinario priore sortis iudicio: ac demum possit in universum septem quaternis numeris (quos in 27. supra denominari plerisque diximus magna eius numeri emphasi) &
[p.265] uno individuo scilicet. 189. constare lucrum uni nec possit amplius preter fraudem aut imperitiam progredi, quamquidem à sex in unum tantùm fieri contigeret.
[p.261] ... There are four labyrinths: the first in Egypt, the second in Crete, the third in Lemno, the fourth in Italy. But without changing subject to that of the labyrinth, 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”:
[p.262] four even cards, four odd cards and four cards in sequence^. However all these groups of four [also] are ternary. 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. 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. [Such is] the great coherence of those numbers between themselves. 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=2*7*4]; 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. This can be dealt equally [i.e. with an even probability] to any one of the three . The game can start with all the cards of the deck, after the players have discarded, mutually or in turn (?), three cards, not four of five. Indeed it is impossible to divide number 28^ equally in any way by these or the following numbers. So, it is granted that [the seventy eight cards] can be divided equally by three, one card being discarded by everyone and separately kept, with an equal exposure to risk for everyone, in order to avoid that [the game] required less intelligence when the cards are equally distributed, because of the knowledge of the likelihood of the other [cards] being dealt to other players. But if on the contrary you play in four, there is at first an uneven chance of the trumps, 39 (19^) cards are dealt to each [player or couple of players?], two cards are left over after drawing, so that chance can be limited to only two [players?].
[p.264] And it must be referred in judging of fairness that everyone is kept in the same exposure to risk. And it is unlikely that all are equal in all respects, still fortune makes this possible, so that in a game of this kind it is maximally evident being versed in both fortune and skill, not only one of the two.
But indeed also this occurs that must be observed: that number of seventy eight cards, with a singular choice of equality, corresponds to the total number of points and to the established relation of one to the other. With this the subtle inventor, under a clever demonstration, bequeathed the actions of all men in life, the human theatre, and [affirmed] that the urn [i.e. the lot] of everyone will be the same, when at last his number will be up.
Moreover he observed that the proportion of the septenary with an individual is such as ten septenaries and one. The gain of one with respect to the other two can be the remaining two multiplied by number ten, with the regular initial judgement of the lot: and the total gain of one can consist of seven quaternary numbers (above we said that they are named in 27^ by many, with great emphasis of this number) [p.265] and one individual, that is 189. And it cannot increase any further, by fraud or incompetence, than what six can turn out against one.
inde cartae dictae
According to D'Oncieu, “carta” (card) etymologically derives from “quarta” (fourth).
The use of this term (grinding / chopping) is difficult to explain. Girolamo Zorli interprets it as “the distructive game of 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”.
Quaterna distinctio Tarotica
Girolamo Zorli notes that the Latin adjective “Tarotica” is derived from the French “Tarot”.
terne extra reponuntur
Girolamo Zorli interprets this expression as a reference to the practice of discarding three cards at the beginning of each hand. It could also describe how tricks where stored during the game.
quinaria distributione quina
Girolamo Zorli translates this as “five cards are distributed for five times” (each player receives 25 cards).
Girolamo Zorli notes that the 78 cards were distributed giving 25 cards to two of the players and 28 to the third one (who had to discard three).
Girolamo Zorli notes that “39” likely is a typo for “19”. 19 cards are distributed to the players and 2 are discarded (19*4+2=78).
itidem esse in universum aestimatione
Literally “it is similar to the value in the whole”. In ancient tarot, 78 points were at stake. 26 were granted to the tricks in a hand. 40 were associated to the court cards (4 points to the king, 3 to the queen, 2 to the knight, 1 to the page). 4 each to the World, the Pagat and the Fool. It seems likely that D'Oncieu is commenting the “singular equality” between the number of cards in the deck and the number of points in the game.
Number 27 is extensively discussed in the text (e.g. p.242-246). At p.350 it is defined "the most mystical quaternary number”. Apparently, D'Oncieu calls “quaternary” cube numbers because they are the fourth step in a sequence starting from 1 (e.g. 1, 3, 9, 27). Since 27 is the quaternary number, D'Oncieu is saying that 189=7*27, but the overall meaning of the sentence is quite obscure.