Propositiones ad Acuendos Juvenes/Problems/50 - De Vino in Vasculum
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Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $50$
- De Vino in Vasculum
- Wine in Flasks
- How many sextarii are there in $100$ metri of wine,
- and how many meri are there in the same $100$ metri?
Solution
- $4800$ sextarii
which is:
- $28 \, 800$ meri.
Proof
There are $48$ sextarii to the metra.
There are $6$ meri to the sextarius.
Thus the number of sextarii in $100$ metri is:
- $48 \times 100 = 4800$
and the meri in $100$ metri is:
- $6 \times 4800 = 28 \, 800$
$\blacksquare$
Historical Note
The original text from Alcuin gives that there are $289$ meri to the metra, rather than the $288$ that are obtained by straightforward multiplication.
It is not clear whether this is what the exact number of them is, or whether Alcuin made a mistake in his arithmetic when multiplying $48$ by $6$.
Sources
- c. 800: Alcuin of York: Propositiones ad Acuendos Juvenes ... (previous) ... (next)
- 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