Subject: Re: [HM] Division of Stakes
From: Ivo Schneider (Ivo.Schneider@UniBw-Muenchen.de)
Date: Wed Feb 23 2000 - 07:28:42 EST
I have checked the source books in Mathematics of David Eugene Smith
(published originally in 1929 with reprints by Dover) who has a chapter on
probability theory which begins with the Pascal-Fermat correspondence and
of D. J. Struik (Harvard UP 1969). Neither contains the desired translations.
The same holds for John Fauvel and Jeremy Gray, The history of mathematics
- a reader, Macmillan Education and Open University 1987) and of F. N.
David, Games, Gods & Gambling, Hafner 1969. However there is a German
Source book which I edited in 1988 (Ivo Schneider (ed.), Die Entwicklung
der Wahrscheinlichkeitstheorie von den Anfaengen bis 1933, Wissenschaftliche
Buchgesellschaft Darmstadt 1988) which contains not only a German
translation of the relevant passage of Pacioli's Summa but also the
solution of the problem of stakes contained in the Manuscript Magl. Cl. XI,
120 of the National Library in Florence, Italy, which is the same as the
one to which Jim Kiernan hinted. In addition my source book contains the
relevant texts of Cardano's Practica (1539), Cardano's De Ludo Aleae (ca.
1564), and Tartaglia's General Trattato (1556). In my article "The market
place and games of chance in the fifteenth and sixteenth centuries"
(published in Cynthia Hay, Mathematics from Manuscript to print 1300-1600,
Clarendon Press Oxford, 1988, p. 220-235, I have dealt with the problem of
stakes and given especially the relevant passages of the Florentine
manuscript from ca. 1400 in English.
I mention this since it annoys me and frustrates me quite a bit that the
wheel has to be invented again and again only because the available
bibliographical tools in this case even for an English article are not used.
Let me add that the editor of the Harvard Source Book series asked me when
I prepared my German Source Book if I would like to do the same in English.
Since I am no native speaker and since Harvard could not fund the English
translation of the texts I had selected I had to turn down the offer.
Perhaps somebody on the list is interested to help with the translation of
these texts into English, some of which like those of de Moivre, Bayes or
Kolmogorov are written in English or already translated.
Ivo Schneider
[Jim Kiernan]
>
> I know of no readily available English translations of the
> Italian sources. I have used quotations from Hacking and Burton
> and they seem to differ slightly:
> Hacking 5:2 and Burton 5:3 . Since Cardano and Tartaglia discuss
> the latter case, I have used that more frequently in talks.
> Perhaps, there are several versions.
> I have an article on this topic coming out in the Mathematics
> Teacher in Nov.( I hope). The article also discusses an "abacist"
> manuscript c.1400 which is currently in the Biblioteca Nationale
> in Florence. I had the opportunity to see this manuscript last
> summer. Unfortunately, my command of renaissance Italian is not
> great. However, I did find the passage and it was quite a thrill.
> I had a short time with the other Italian works up in Toronto,
> but could not find the relevant passages.
> Tell me what your working on.
[David Kullman]
>
>
> Pacioli, _Summa_ (1494), may have been the first mathematician to
> publish a solution (incorrect) to the problem of "fair division of
> stakes." Cardano, _Practica arithmeticae generalis_ (1539), and
> Tartaglia, _Tratto generale di numeri e misure_ (1556), criticized
> Pacioli's solution and offered their own (also incorrect) solutions.
>
> Can anybody supply an English translation of the passages from
> Pacioli, Cardano, and/or Tartaglia that pertain to this problem (or
> else point to a readily available English source)?
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