mikeh wrote:I have removed the reference to the Timaeus from my Addition, as it now seems to me irrelevant. However before it is added to yours on Andrea's site I want to make sure it is what I want to say.


have removed the reference to the Timaeus from my Addition, as it now seems to me irrelevant. However before it is added to yours on Andrea's site I want to make sure it is what I want to say. I have also added references to Capella and Diogenes Laertes earlier.
Dont acte.
After reading your "update", I deleted in my citation of your reference to Gosselin the "irrelevant" relation to Plato(s Timeus.
As for your Addition, please send to Vitali the last version updated

As I failed to make me understand by you, and consecutively to our misunderstanding, followed by your deletion, I ve decided to reformulate some phrase of my orignal text
As you'll see, I still maintain that Gosselin gives a Pythagorean lecture of the ordinary game in ocformity with the order of the Elements as given in the Timeus.
Let's say that we'll agree that we desagree on this specific point.
Ite misa es...



I have also added references to Capella and Diogenes Laertes earlier.
Yes. this is valuable.


The doctrine of the four elements is attributed to Empedocles. I do not think he counts as a Pythagorean, but I'm not sure. The order of the elements - earth, water, air, fire - is part of the Ptolemaic worldview which most people took for granted without having any idea where it came from. As far as I know, it comes from noticing that beneath the water is earth, and above the water is air, and lightning comes from up high in the sky.

Could be . I emitted the hypothesis that it was inherited from the Corpus platoniciens identified as Elements as in Plato's Timeus. But you are not ok with this. ...

It seems to me highly unlikely that the king's library would not have had Capella--a major textbook about the liberal arts all through the Middle Ages, in Latin. WorldCat shows 33 extant printed editions between 1490 and 1580. This library would have had several manuscript editions as well. Diogenes Laertius was even more popular in the 16th century. Lives of the Eminent Philosophers was reprinted in Latin numerous times, I'm not sure how many; WorldCat lists 291 editions of Laertius's works before 1580. The majority would have been of the Lives. On WorldCat one 16th century editor of Laertius's Lives is shown as the famous Parisian printer Henry Estienne, who surely would have been known to Gosselin. In contrast, there are only 53 listed for the Timaeus for the same period, including those with only excerpts and those included as part of the "collected works" of Plato or Cicero (who had done a translation). Laertius would have been perfect for a librarian, as it is just easily read summaries of all the various classical philosophers and anecdotes about them. The only question for me is whether he knew Greek as well as Latin, something that might have been expected for a king of France's librarian. A few Pythagorean works were available only in Greek, notably the Theologumena Arithmeticae, in only one printed edition, Paris 1543.

Yes. That's what I suggested in another recent opost to you about Gosselin being Bibliothecaire du Roi;
It is highly probable that he had access to these docuemnts as you say...

About him knowung Greek, it coUld well be
A point to inquire

Ok?
I ll read your updates with the inclusions you mentionned with interest as soon as I have slept a little!

" It's been a hard day's night"

"Cent fois sur le métier, remettez votre ouvrage" : https://docs.google.com/document/d/1MTP ... mCoA8Y/pub

Article en cours de rédaction : version provisoire en date du 14 septembre 2016
1582 Gosselin Jean : "La signification de l 'ancien jeu des chartes pythagoriques..."
La plus ancienne référence française explicite connue d' une analyse pythagoricienne du Jeu de cartes ordinaires
- suivi d'une discussion à propos de la conformité ou non de la correspondance des 4 Couleurs d'avec la genèse des 4 Eléments du Timée de Platon

Mises à jour sur :
https://docs.google.com/document/d/1MTP ... mCoA8Y/pub

My apologies to eventual readers ...
I'm not able to offer a translation in English.

https://translate.google.com/m/translate?hl=fr

It suddenly occurred to me that Gosselin's source for the four elements might have been one that also talked about the series of doubles, 1, 2, 4, 8, 16. There were probably many sources that talked about both, even close together in the same work. One such is not hard to find: Nichomachus, Introduction to Arithmetic. He discusses the four elements, in the order "fire, water, air, and earth", in Book II, Chapter 1, p. 230 of the D'Ooge translation. Note also D'Ooge's note: "The ordinary list for practically all Greek philosophy." Nichomachsus discusses the series of "doubles" (D'Ooge's translation), which goes 1, 2, 4, 8, 16, 32, 64, on the "first line", with 16 is the "fourth double" a few pages later: Book II, Chapter 3, on p. 232 of the D'Ooge translation. His application to music seems to be on p. 276, in Chapter 26.

I will grant you, however, that Gosselin's order of presentation is different:

D'abord que le Feu, la Terre, l'Eau et l'Air soient des corps, cela est sans doute évident pour quiconque.

This is the order fire, earth, water, and air. In the Timaeus, Plato first presents Fire and Earth, and then argues that there must be two means between them. These, he says, are Water and Air. The order of presentation is the same as Gosselin's, even if their order in the cosmos is different. To that degree, it might well be that Gosselin had the Timaeus in front of him when writing this passage. Perhaps that was your point, I don't know. On the other hand, Plato does not take the series of doubles as far as 16: he stops at 8.

Nichomachus was the basis for other texts that included arithmetic and music: Boethius and Capella, among others. I do not know in what order the four elements are presented in Boethius. I cannot see that Capella mentions them by name. Laertius presents them in the order "fire, water, earth and air".

Hi Mikeh


1.
In chapter III, Gosselin focuses on the harmonic progression from unity (1) of the Four diapasons :
1+2+4+8+16 = 31 specific of the game le Trente et Un. (Rabelais's Trente et Ung).
viewtopic.php?f=11&t=1102&start=160#p17344

It is Nicomachus Book I Chapter 8
Translation and drawing of the Harmonic proportion : pp 192 - 196 in
https://drive.google.com/file/d/0B5Hg6j ... sp=sharing

Nicomachus of Gerasa, Introduction to Arithmetic, English translation by Martin Luther D’Ooge,
with Studies in Greek Arithmetic, by Fank Egleston Robbins and Louis Charles Karpinski,
London: Macmillan and Company, Ltd., 1916.
https://ia600709.us.archive.org/27/item ... hmetic.pdf

Did Gosselin refer implicitely to Nicomaque or translators or commentators when he mentions in his Epistre the "quelques Philosophes Pythagoriques"?


2.
In reality Gosselin's presentation of Numbers and Musical intervals is more complex and exhaustive than the last Harmonic proportion from Nicomaque's Book I Chapter 8 applied to the Game of Trente et Un of the 52 ordinary cards :

1+2+4+8+16 ....

Before in Chapters I and II, he offers a more complex and detailled presentation of proportions of Numbers and their relations to musicals intervals

Gosselins Pythagorean presenation of proportions and musicals intervals and Nicomaque de Gerase , see my post on :
viewtopic.php?f=11&t=1102&p=17250&hilit=gosselin#p17250
Followed by your's :
viewtopic.php?f=11&t=1102&p=17250&hilit=gosselin#p17256

Specifically Gosselin's writing :
1. Les Nombres et leurs 7 proportions ( en réalité 14 en comptant les sous-proportions à chaque fois)
viewtopic.php?f=11&t=1102&p=17211&hilit=gosselin#p17211

2. Proportions des Nombres en relation avec les intervalles musicaux
viewtopic.php?f=11&t=1102&p=17235&hilit=gosselin#p17235


These seems taken directly from Nicomaque

Numbers and proportions

Book I chapter XVII to XXIII

Book II
chapter I -V

chapter XVIII- XXIX



3.
In his EPISTRE Gosselin lists 3 sources for his work : PLATON, Aristote and "quelques philosophes Pythagoriques".

Quote in extenso :
[traduction libre et approximative en Français modernisé] :

[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

This enumeration is identical in Nicomaque listing in his Arithmetic Book II chapter XXII

CHAPTER XXII
I "The first three proportions[Note],' then, which are acknowledged by all
the ancients, Pythagoras, Plato, and Aristotle, are the arithmetic,
geometric, and harmonic; and there are three others subcontrary to
them, which do not have names of their own, but are called in more
general terms the fourth, fifth, and sixth forms of mean; after which
the moderns discover four others as well, making up the number ten,l
which, according to the Pythagorean view, is the most perfect possible.
It was in accordance with this number indeed that not long ago the ten
relations 2 were observed to take their proper number, the so-called ten
categories,3 the divisions and forms of the extremities of our hands and
feet, and countless other things which we shall notice in the proper
place.'

[Note]
Iamblichus adds concerning the history of the proportions (p. 100, 19): "But of old there
were but three means in the days of Pythagoras and the mathematicians of his time, the arithmetic,
the geometric, and the third in order, which was once called the subcontrary, but had its
name forthwith changed to hannonic by the schools of Archytas and Hippasus, because it seemed
to embrace the ratios that govern the harmonized and tuneful. And it was formerly called subcontrary
heeause its character was somehow subcontrary to the arithmetic. . •. After this name
had been changed, those who came later, Eudoxus and his school, invented three more means,
and called the fourth properly subcontrary because its properties were subcontrary to the harmonic
_ . • and the other two they named simply from their order, fifth and sixth. The ancients
and their successors thought that this number, i.e., six, of means could be set up; but the modems
have found four more in addition, devising their formation from the terms and the intervals."
Cf. also p. tI3, 16 tf. He adds (p. II6, I if.) that the first six were in use from Plato's time to
Eratosthenes, and that the other four were devised by Myonides and Euphranor, both Pythagoreans,
who lived later. Apparently Moderatus of Gades, as well as Nicomacbus, employed all
ten forms (see Proclus, In Tim., H. 18. 29 ff. Diehl).


Maybe I missed some other correlations.

What seems more and more likely is that Gosselin had these references at hand in his Royal Library.

Theon de Smyrne also gives these results ...



Exhaustive bibliographic references


Nicomachus of Gerasa, Introduction to Arithmetic, English translation by Martin Luther D’Ooge,
with Studies in Greek Arithmetic, by Fank Egleston Robbins and Louis Charles Karpinski,
London: Macmillan and Company, Ltd., 1916.
https://ia600709.us.archive.org/27/item ... hmetic.pdf


About Nicomaque de Gerase editions, I noted the followings :

Translators and commentators : Chapter IX

Manuscrts and tetxs of the Arithmetic : Chapter XI

Aparte

In my article in Italian, some years ago :
Tarocchi e Neopitagorismo
http://letarot.it/page.aspx?id=83

about the Tetractys and harmonicals proportions, I noticed this detail of Raphael's School of Athena painted 1505





:


figura_1.jpg[/img]

Additif :

https://en.wikipedia.org/wiki/Major_sec ... =648802339


Pythagore est entouré de trois disciples, dont l'un tient une représentation de l'epogdoon, et dont un autre est Averroès, reconnaissable à son turban blanc,

connu pour avoir donné ou plus exactement redonné (après Boèce) à l'Europe accès aux connaissances grecques - largement repliées à Byzance après la partition de l'Empire Romain2 - ainsi qu'orientales, toutes diffusées dans l'Empire musulman par le biais de la langue arabe


« [Epogdoos] est le ratio 9/8 qui correspond au ton, [hêmiolios est] le ratio 3/2 qui est associé avec la quinte musicale, et [epitritos est] le ratio 4/3 associé avec la quarte musicale. Il est commun de traduire « epogdoos » en « ton » [seconde majeure]2




Selon certains spécialistes, Boece serait aussi représenté en 4
https://upload.wikimedia.org/wikipedia/ ... ed.svg.png

L’Institution arithmétique : dans ce livre Boèce reprend l’Introduction à l'arithmétique de Nicomaque de Gérase, sous forme de paraphrase libre plutôt que de traduction rigoureuse. Le grand nombre de manuscrits témoigne de l'importance de ce livre dans l'enseignement du Moyen Âge et de la Renaissance.
(Traduit par Jean-Yves Guillaumin, Les Belles Lettres, 1995).

Plotin est représenté : voir 30 sur



En savoir plus : http://profhistoire.webnode.fr/l'ecole- ... internet)/



Au deuxième plan, au centre et au point de fuite de la peinture, sont représentés les philosophes Platon et Aristote. Ceux-ci portent la toge romaine et ont une attitude majestueuse.
Platon tient dans sa main l'un de ses dialogues3, qui s'appelle le Timée


tandis qu'Aristote a son Éthique à la main.

Les gestes des deux philosophes - le premier tend sa main vers le ciel tandis que le second désigne la terre - offrent une représentation symbolique de leurs conceptions philosophiques. Raphaël marque ici clairement l'opposition entre la théorie platonicienne (qui explique les origines du monde) et le rationalisme ainsi que l'empirisme prônés par Aristote. Platon est représenté sous les traits de Léonard de Vinci, ce dernier étant venu au Vatican à la recherche d'un travail.

Dans l'attroupement à gauche de Platon, se trouve Socrate, le maître de Platon. Le chef athénien Alcibiade ou Alexandre le Grand (qui fut lui-même élève d'Aristote), en soldat romain, ainsi que le poète Xénophon (en bleu), discutent avec Socrate, qui semble compter sur ses doigts des arguments de sa dialectique, procédé caractéristique de sa philosophie.

As far I know it, there is no guarantee, that Pier Antonio Viti knew Boiardo personally. Naturally there is even less probability, that Timoteo Viti knew Boiardo.
Pier Antonio was some time in Ferrara, but likely in a time, when Boiardo was not usually present there.

We don't know, how Pier Antonio became aware of the poem. Boiardo died 1494, Pier Antonio Viti in 1500. The action, which led to the realized card game was estimated to have taken place 1496/97 ... Boiardo was dead then.

Some suspicion is given, that a person "Emilia Pia da Montefeltro" was active in the matter. She was close to Elisabetta Gonzaga, duchessa of Urbino, who herself was close friend (and sister-in-law) of Isabella d'Este. Isabella d'Este loved cards, that's very sure.



It's not clear to me, how Emilia Pia was related to the Pio family. She is not mentioned as a daughter of Federico Montefeltro.

The relationship between Pio family and Boiardo wasn't a good one.
So likely the connected lady-team engaged in the production. The Viti brothers (likely) got a commission, likely not more.

Emilia Pia appeared in the story of the courtier Castiglione, who wrote a famous book.
https://de.wikipedia.org/wiki/Baldassare_Castiglione
Cards appear also in the book ...
http://trionfi.com/0/p/40/

... but that's later, I think, this plays around 1507 (if I remember correctly).



Elisabetta Gonzaga looks even similar to Emilia Pia.

Once more Isabelle d'Este ...
Many threads finaly leading to her!

After Louise Marie de Gonzagues lineage, now this one :
Some suspicion is given, that a person "Emilia Pia da Montefeltro" was active in the matter. She was close to Elisabetta Gonzaga, duchessa of Urbino, who herself was close friend (and sister-in-law) of Isabella d'Este. Isabella d'Este loved cards, that's very sure.

Eariier d'Este : Biographie
Lionel d' Este

Naissance
21 janvier 1407
Ferrare
Décès
1er octobre 1450(à 43 ans)Voghiera
Nom de naissance
Leonello d’Este
Père
Nicolas III d'Este
Frères
Hercule Ier d'Este
Meliaduse d'Este
Sigismondo d'Este
Ugo d'Este
Borso d'Este
Sœur
Ginevra d'Este
Conjoints
Margherita Gonzaga
Maria d'Aragona
Enfant
Niccolò d'Este

Leonello d' Este d'Este, I'll add now the Muse URANIA
Studio di Leonello d'Este, un tempo al Palazzo di Belfiore di Ferrara, raffigurante la Musa Urania


Nore 3 :http://letarot.it/page.aspx?id=83

Lionel d'Este
He maries in 1435 with a Gonzague , Marguerite .
il s'est également distingué comme un homme cultivé. Leon Battista Alberti écrit son De Re Aedificatoria sous le mécénat de Lionel, et de nombreux artistes travaillent à la cour d'Este : Pisanello, Jacopo Bellini, Andrea Mantegna, et le flamand Rogier van der Weyden. Durant son règne, l'Université de Ferrare obtient une renommée européenne.

About Alberti; and the Temple of Malatesta in architecture see the note of O' Neill I give :
"Potrebbe essere utile studiare un sistema simbolico neo-platonico tacciato d'infamia risalente agli inizi del XV secolo. Il Tempio Malatestiano fu costruito da Sigismondo Pandolfo Malatesta (1419-1468).

Se il Tempio non si rivela utile come modello dei primi tarocchi, esso fornisce non di meno un esempio di un altro sistema simbolico neo-platonico dell'epoca.

L'importanza del Tempio sta nel fatto che vi sono incorporati dei simboli scaturiti da una varietà di fonti diverse messe insieme in un sistema sintetico-esoterico e spirituale.

Il risultato è un sistema sincretistico e simbolico che sembra possedere le stesse basi dei primi tarocchi"