Propositiones ad Acuendos Juvenes/Problems/25 - De Campo Rotundo

Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $25$

A round field is $400$ perches in circumference.

How many acres does it contain?

The fourth part of the field's $400$ perches in circumference is $100$.

Multiply this by itself to get $10 \, 000$.

Divide this in $12$ parts; the result is $833$.

Divide this into $12$ parts again; the result if $69$.

This is the number of acres in the field.

$\blacksquare$

The area $\AA$ of a circle in terms of its circumference is:

$\AA = \dfrac {C^2} {4 \pi}$

However, what Alcuin has done is used a value for $\pi$ of $4$.

The actual value (assuming $144$ square perches to the acre) is approximately $88.4$ acres.

Another translator uses a tortuous method to obtain $\AA = 96$ acres, but this uses a value for $\pi$ of $3$.