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

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

#562
Paccioli and games :
The games he wrote about were :
A (lost) Treaty on Chess rediscovered 2006
De ludo scacchorum
Times online : Renaissance chess master and the Da Vinci decode mystery
New York Times : Checkmate again for Leonardo? Chess book's diagrams are linked to artist

Magic trick cards
De viribus quantitatis, (1496-1508)
Mathknow: Mathematics, Applied Science and Real Life (Sous la direction de Michele Emmer et Alfio M. Quarteroni) page 193 (Editions Springer)

Maybe also the Treaty on Abacus was related to Boethius ?
Never published -Vatican Library codice Vaticano Urbinate 3129
http://www.sgdl-auteurs.org/alain-bouge ... Biographie

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

#563
mikeh wrote:

The question is, were Pentagonal Numbers part of the standard quadrivium of the time or not? If so, anybody could have applied the numbers connected with them to the cards.
1. "were Pentagonal Numbers part of the standard quadrivium of the time or not?"

Yes.

What is sure is that Boethius was well aware of them.
viewtopic.php?f=11&t=1102&start=550#p18861

BOETHIUS "arithmology" (arithmetic and harmonies) related to the "philosopher's game" in late medieval times and Italian Renaissance

Anne E. MOYER, The Philosopher's game, Rithmomachia in Renaissance and Medieval Europe, University of Michigan Press, 2001
viewtopic.php?f=11&t=1102&p=18487#p18487

2. "If so, anybody could have applied the numbers connected with them to the cards. "

Yes.
And in the "anybody" , I include Paccioli....
http://www.sgdl-auteurs.org/alain-bouge ... Biographie

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

#564
You wrote :
"What is then important is the number 5, for pentagonal. It is for the fifth suit, the one that shows the way to God, an especially sacred number, of the Pope card and of the various sacred associations to the number that made it particularly holy. For example Augustine: the five wise virgins, who have abstained from unlawful use of the five senses (http://www.newadvent.org/fathers/160343.htm); the "five books of Moses", the "five porches containing the sick folk", the "five loaves feeding the five thousand" (https://books.google.com/books?id=wIp0A ... ve&f=false), and the five stigmata of Christ, the same repeated for Francis of Asissi (https://en.wikipedia.org/wiki/Stigmata).

But perhaps some author emphasized pentagonal numbers for some reason. If so, the relevant passage needs to be found."

Yes again

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)
"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)

The members of the Neoplatonic academy in Florence (1459-1521) could not ignore it or others ...

Boethius presents the sequence of Pentagonal Numbers as :
1,5, 12. 22

See :« De institutione arithmetica » https://archive.org/details/aniciimanliitor01friegoog

See Eclairs sur le Moyen Age : http://www.apmep.fr/IMG/pdf/03_Eclairs_ ... -Age_I.pdf)
http://www.sgdl-auteurs.org/alain-bouge ... Biographie

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

#565
Also 56 is sum of triangular numbers (or has it already been mentioned?) :

1*1
2**3
3***6
4****10
5*****15
6******21

1 + 0 = 1
2 + 1 = 3
3 + 3 = 6
4 + 6 = 10
5 + 10 = 15
6 + 15 = 21

0+1+3+6+10+15+21 = 56
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

#567
SteveM wrote:Also 56 is sum of triangular numbers (or has it already been mentioned?) :

1*1
2**3
3***6
4****10
5*****15
6******21

1 + 0 = 1
2 + 1 = 3
3 + 3 = 6
4 + 6 = 10
5 + 10 = 15
6 + 15 = 21

0+1+3+6+10+15+21 = 56
Hi Steve

Thank you also for your always pertinent observations;
No it had not been mentionned - so as far as I know.
The Triangular sequence is also in Boethius incunable 1499 : 1,3,6, 10, 15, 21 ...

See : Eclairs sur le Moyen Age : http://www.apmep.fr/IMG/pdf/03_Eclairs_ ... -Age_I.pdf

Nota
So, we have now the two sequences...
22 : 1,5,12,22 that is "gnomons or differences" 22 =1+4+7+10
56 = 1+3+6+10+15+21

Reminder :
56
4 Tetractys of 1+2+3+4+5+6+7+8+9+10 numerals
4 Tetrads of Honours (game value counted as 1-2-3-4)
http://www.sgdl-auteurs.org/alain-bouge ... Biographie

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

#568
Line of thought ...
Conceptually , I am considering the hypothesis of seing the Arithmological Structure as similar to an elaborate Abacus

Thinking about Paccioli's Treaty on Abacus possibly related to Boethius ?
Never published -Vatican Library Codice Vaticano Urbinate 3129

Reminds me of a discussion with Huck about Gregor Reisch's Arithmetica, 1503
1503

About Boethius, Abacus and the "Philosopher's game" in late Middle ages and Renaissance :
The Philosophers' Game: Rithmomachia in Medieval and Renaissance Europe ...by Ann Elizabeth Moyer,William Fulke

Nota

What if the Trionfi's played on a board similar to Chess or Rythmomachia instead of staring at it- becoming tarrocchi?
Israhel van Meckenem (vers 1445 – 10 novembre 1503)
https://fr.wikipedia.org/wiki/Israhel_van_Meckenem
http://www.sgdl-auteurs.org/alain-bouge ... Biographie

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

#569
SteveM wrote:Also 56 is sum of triangular numbers (or has it already been mentioned?) :

1*1
2**3
3***6
4****10
5*****15
6******21

1 + 0 = 1
2 + 1 = 3
3 + 3 = 6
4 + 6 = 10
5 + 10 = 15
6 + 15 = 21

0+1+3+6+10+15+21 = 56
& 0+ 21+ 56 = 77 (+0)
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

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