Propositiones ad Acuendos Juvenes/Problems/50 - De Vino in Vasculum

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