mikeh wrote: One thing I am not sure about is "familierement" as "clearly". But I think that is what must be meant. make clear = make familiar; but adding the "-ly", as is needed with "explain", doesn't work in English.
What do people think?
In a transcription, I do not think the punctuation should be changed, because it is a clue to how it should be punctuated in a translation. I do not know how the punctuation would go in modern French, only modern English. It would be something like this:Après avoir expliqué le plus familièrement qu'il nous a été possible, les proportions des nombres, les consonances et Harmonies qui en proviennent: il convient declarer les secrets qui sont cachés en ce jeu des cartes - lequel a été inventé et mis en usage par quelques hommes savants en Philosophie Pythagorique: Attendu que les Pythagoriques affirmaient qu'il y a de très grands secrets de nature cachés sous les nombres; Et aussi, [31]que la plus grande victoire du jeu des cartes consiste au nombre de trente et un, lequel selon ses parties contient une très excellente Harmonie comme nous le démontrons présentement.
The two dependent clauses at the end cannot, grammatically, be considered separate sentences, even if in modern English that is sometimes done. It does not seem to be Gosselin's intention. In English the result is a very long sentence, but not impossibly so. I think it is clearer in the original punctuation myself, although I might remove the capital letters. But given that I have not removed the capital letters elsewhere in the text, I leave them here. It seems to me that in transcribing Gosselin's text, one should say it is with modernized spelling, but otherwise the same as the original. It is the spelling that confounds me as a reader and translator.After having explained, as clearly as has been possible for us, the proportions of numbers and the consonances and Harmonies that arise from them, it is appropriate to declare the secrets hidden in this game of cards - which was invented and put into use by a few men learned in Pythagorean philosophy, considering that the Pythagoreans say that there are very great secrets of nature hidden in numbers, and also that the greatest victory in the game of cards consists in the number thirty-one, which by its parts contains a most excellent Harmony, as we demonstrate presently.
Of these, the Theolgumena Arithmeticae, although clearly including the four elements among the manifestations of the tetrad (Waterfield translation, p. 58) and in print then from a Parisian publisher, was available only in Greek. The Enneads had been translated by Ficino; it is not Pythagorean, but perhaps refers to the Pythagoreans explicitly here, I don't know. The other two were readily available in Latin. Diogenes was originally in Greek, but I see on WorldCat that a Latin translation was published in 1490 Venice; then in the 1550s and 1560s there were multiple reprintings in various places. (https://www.worldcat.org/search?q=au%3A ... dblist=638)Four is also the number of the square (60), and is represented in the elements, the seasons, the 4 elements of man, the 4 principles of a reasonable animal, the lunar phases, and the 4 virtues. (61)
________________
60. Plutarch, De animae procreatique, 1.
61. Diogenes Laertius, Biography of Pythagoras, 19, 7; Theolog. Arith., 22. Enneads, VI, 6, 16. Capella, op. cit. VII.
The "Alexander" referred to is Alexander Polyhistor, 1st century b.c., the translator tells us in a note, p. 241. You can read this with the note, at http://www.perseus.tufts.edu/hopper/tex ... hapter%3D1.Alexander in his Successions of Philosophers says that he found in the Pythagorean memoirs the following tenets as well. ... from the monad and the undefined dyad spring numbers, points; from points, lines; from lines, plane figures, from plane figures, solid figures; from solid figures, sensible bodies, the elements of which are four, fire, water, earth, and air...
mikeh wrote:With original punctuation, here is the sentence in question:In a transcription, I do not think the punctuation should be changed, because it is a clue to how it should be punctuated in a translation. I do not know how the punctuation would go in modern French, only modern English. It would be something like this:Après avoir expliqué le plus familièrement qu'il nous a été possible, les proportions des nombres, les consonances et Harmonies qui en proviennent: il convient declarer les secrets qui sont cachés en ce jeu des cartes - lequel a été inventé et mis en usage par quelques hommes savants en Philosophie Pythagorique: Attendu que les Pythagoriques affirmaient qu'il y a de très grands secrets de nature cachés sous les nombres; Et aussi, [31]que la plus grande victoire du jeu des cartes consiste au nombre de trente et un, lequel selon ses parties contient une très excellente Harmonie comme nous le démontrons présentement.The two dependent clauses at the end cannot, grammatically, be considered separate sentences, even if in modern English that is sometimes done. It does not seem to be Gosselin's intention. In English the result is a very long sentence, but not impossibly so. I think it is clearer in the original punctuation myself, although I might remove the capital letters. But given that I have not removed the capital letters elsewhere in the text, I leave them here. It seems to me that in transcribing Gosselin's text, one should say it is with modernized spelling, but otherwise the same as the original. It is the spelling that confounds me as a reader and translator.After having explained, as clearly as has been possible for us, the proportions of numbers and the consonances and Harmonies that arise from them, it is appropriate to declare the secrets hidden in this game of cards - which was invented and put into use by a few men learned in Pythagorean philosophy, considering that the Pythagoreans say that there are very great secrets of nature hidden in numbers, and also that the greatest victory in the game of cards consists in the number thirty-one, which by its parts contains a most excellent Harmony, as we demonstrate presently.
As far as justifying the four elements as part of Pythagorean philosophy, a referral to the Timaeus is not enough, because there has always been a distinction between "Platonism" and "Pythagoreanism". even if the two philosophies borrowed from each other, and even if it is Gosselin's likely source. Here is what V. F. Hooper says in Medieval Number Theory, with his references (pp. 42-43), in his chapter ""Pythagorean Number Theory":Of these, the Theolgumena Arithmeticae, although clearly including the four elements among the manifestations of the tetrad (Waterfield translation, p. 58) and in print then from a Parisian publisher, was available only in Greek. The Enneads had been translated by Ficino; it is not Pythagorean, but perhaps refers to the Pythagoreans explicitly here, I don't know. The other two were readily available in Latin. Diogenes was originally in Greek, but I see on WorldCat that a Latin translation was published in 1490 Venice; then in the 1550s and 1560s there were multiple reprintings in various places. (https://www.worldcat.org/search?q=au%3A ... dblist=638)Four is also the number of the square (60), and is represented in the elements, the seasons, the 4 elements of man, the 4 principles of a reasonable animal, the lunar phases, and the 4 virtues. (61)
________________
60. Plutarch, De animae procreatique, 1.
61. Diogenes Laertius, Biography of Pythagoras, 19, 7; Theolog. Arith., 22. Enneads, VI, 6, 16. Capella, op. cit. VII.
I do not have Diogenes 19, unless it is the same as what the Loeb edition calls Book VIII, Ch. 1, section 25 (pp. 240-243 of Loeb edition). Here is the translation, pp. 241 and 243 (the Greek is on pp. 240 and 242)The "Alexander" referred to is Alexander Polyhistor, 1st century b.c., the translator tells us in a note, p. 241. You can read this with the note, at http://www.perseus.tufts.edu/hopper/tex ... hapter%3D1.Alexander in his Successions of Philosophers says that he found in the Pythagorean memoirs the following tenets as well. ... from the monad and the undefined dyad spring numbers, points; from points, lines; from lines, plane figures, from plane figures, solid figures; from solid figures, sensible bodies, the elements of which are four, fire, water, earth, and air...
I find Martianus Capella, Marriage of Philology and Mercury referring to the four elements in the section on Arithmetic, p. 278, and again on p. 279, of Stahl and Johnson translation,
https://books.google.com/books?id=nZ-Z9 ... ts&f=false, in much the same way as Diogenes Laertius. This book was in Latin and well known. Whether it explicitly says that this doctrine is Pythagorean, I don't know, as the page it would be on (275 or 276) is omitted from Google's selection. You might find it in a French translation. But it would be understood as Pythagorean.
Le me see. The Remaque is this (https://docs.google.com/document/d/1MTP ... mCoA8Y/pub:I don't think that the main argument should be rejected.
But I do have a kind of intuition that :
- the Remark could be controversial
- the Extention judged speculative at best, audacious by some or farfetched by others
I.e.:Remarque :
L’identification des idées pythagoriciennes dans Platon ne fait pas consensus.
En effet, très peu de références à Pythagoras dans son oeuvre.
Toutefois, même si la théorie des Eléments n’est pas en soi explicitement pythagoricienne dans Platon, la formation des corps platoniciens à partir d’eux et notamment l’insistance sur le Triangle semblerait une confirmation implicite d’une influence sous-jacente pythagoricienne que l’on devrait pas sous-estimer ...
D’abord que le Feu, la Terre, l’Eau et l’Air soient des corps, cela est sans doute évident pour quiconque.
Or, l’essence du corps possède aussi toujours l’épaisseur.
Mais toute épaisseur enveloppe nécessairement la nature de la surface.
ET toute surface de formation rectiligne est composée de triangles”
(Le Timée)
But this does not require there be fire, earth, air, and water. This justification is too speculative.The identification of Pythagorean ideas in Pythagoras has no consensus.
Actually, very few reference to Pythagoras in his works.
However, just as the theory of the Elements is not in itself explicitly Pythagorean in Plato, the formation of the Platonic corpus departs from them; notably, the insistence on the Triangle would seem an implicit affirmation of an underlying Pythagorean influence that cannot be underestimated ...
First, Fire, Earth, Water and Air are the body, as is probably obvious to anyone.
But the essence of the body also still has thickness.
But any thickness necessarily involves the nature of surface.
And every surface of rectilinear formation is composed of triangles "
I.e.:Sous la réserve d’établir une correspondance non sujette à discussion Couleurs du Jeu de cartes ordinaires / Emblèmes du Tarot, la conséquence sur la plan du Tarot Arithmologique :
posting.php?mode=edit&f=11&t=1102&p=17455
serait que les 4 Tetractys emblématiquss des 40 cartes numérales (4X10), à savoir les quatre Décades représentées géométriquement sous sous du nombres triangulaire figuré 10 :
1
2+3
4+5+6
7+8+9+10
seraient, dans cette hypothèse, à percevoir comme des Triangles platoniciens spécifiques des Eléments Terre Eau, Air, Feu.
Le Triangle Terre à la base de la formation du Cube (Jeu des 4 Couleurs : Décade des Carreaux)
Le Triangle Eau, celle de l’ Icosaèdre.(Jeu des 4 Couleurs : Décade des Trèfles)
Le Triangle Air, celle de l’ Octaèdre (Jeu des 4 Couleurs : Décade des Coeurs)
Le Triangle Feu, celle du Tétraèdre.(Jeu des 4 Couleursécade des Trèfles)
Néanmoins, en l’état actuel de la recherche, ces correspondances sont uniquement celle du Jeu des Chartes Pythagoriques de Gosselin
I haActually, the matches with the solids is only in Plato, neither Gosselin nor the Pythagoreans. Frankly, I see no reason to invoke Plato at all in relation to Gosselin. I cannot imagine that Gosselin is thinking about arrangements of triangles in relation to the four suits and their assignment to elements. He does give an allegorical justification, and it is neither Platonic nor Pythagorean. In your diagram, all the Tetratkyses look identical, with nothing suggesting different solids about them. Or am I missing your point?With the reservation, not under discussion, of matching the elements with the suits of ordinary playing cards/ Emblems of the Tarot, the impact on the level of the arithmological Tarot:
posting.php?mode=edit&f=11&t=1102&p=17455
would be that the 4 emblematic Tetractys, 40 numeral cards (4X10), namely four Decades represented geometrically as in the triangular numbers figured as 10:
1
2 + 3
4 + 5 + 6
7 + 8 + 9 + 10
would, in this case, be to perceive as specific Platonic Triangles, the Elements Earth, Water, Air, Fire.
The Triangle Earth to the basic arrangement of the Cube (Deck of 4 Suits: Decade of Tiles)
The Triangle Water, that of the icosahedron (Deck of 4 Suits: Decade of Clovers).
The Triangle Air, that of the octahedron (Deck of 4 Suits: Decade of Hearts)
The Triangle Fire, that of the tetrahedron (Deck of 4 Suits: Decade of Clovers).
However, in the present state of research, these matches are uniquely only in the Jeu des Chartes Pythagoriques of Gosselin.
