Propositiones ad Acuendos Juvenes/Problems/22 - De Campo Fastigioso/Historical Note

Historical Note on Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $22$: De Campo Fastigioso

Alcuin's solution to this is suspect in a number of places.

$(1): \quad$ Fractions are rounded inconsistently:

At one point $\dfrac {160} 3 = 53 \tfrac 1 3$ is rounded to $53$.

At another point $\dfrac {5200} {12} = 441 \tfrac 2 3$ is truncated to $441$.

At yet another point $\dfrac {441} {12} = 36 \tfrac 3 4$ is rounded up to $37$.

However, the actual value of $\dfrac {16 \, 000} {3 \times 12 \times 12} = 37.037 \ldots$ is actually remarkably accurate.

$(2): \quad$ The method of averaging the $50$s and $60$s to get $\dfrac {160} 3$ is dubious.

If the field is a double trapezoid, then the mean width is $55$.

$(3): \quad$ The length given is measured along the side, which may not be the true length.

Sources

• 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