Propositiones ad Acuendos Juvenes/Problems/35 - De Obitu Cuiusdam Patrisfamilias/Historical Note
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Historical Note on Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $35$: De Obitu Cuiusdam Patrisfamilias
David Eugene Smith discusses the general testament problem in his History of Mathematics, Volume 2 of $1925$.
He explains this type of problem and its legal origins in the law of the Roman Empire.
Commentators have argued that Alcuin's solution shows that he does not understand the law.
David Wells's take on this refers back to the "original translator", who suggests adding the original fractions they expected.
Thus we have:
- $\dfrac 3 4 + \dfrac 7 {12} + \dfrac 1 3$ (which was the mother's average expectation) for a total of $\dfrac 5 3$.
Multiplying their original expectations by $\dfrac 3 5$, this leaves:
- the mother with $432$ shillings
- the boy with $336$ shillings
- the girl with $192$ shillings.
Sources
- 1925: D.E. Smith: History of Mathematics: Volume $\text { 2 }$
- 1992: John Hadley/2 and David Singmaster: Problems to Sharpen the Young (Math. Gazette Vol. 76, no. 475: pp. 102 – 126) www.jstor.org/stable/3620384
- 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): 'Propositions to Sharpen Up the Young': $84$