Greek Anthology Book XIV: Metrodorus: 140

Arithmetical Epigram of Metrodorus

Blessed Zeus, are these deeds pleasing in thy sight that the Thessalian women do in play?

The eye of the moon is blighted by mortals; I saw it myself.

The night still wanted till morning twice two-sixths and twice one-seventh of what was past.

Solution

Let $t$ be the time since sunset.

It is assumed that the night is $12$ hours long.

We have:

\(\ds 12 - t\)

\(=\)

\(\ds 2 \times \dfrac {2 t} 6 + \dfrac {2 t} 7\)

\(\ds \leadsto \ \ \)

\(\ds 21 \times 12 - 21 t\)

\(=\)

\(\ds 14 t + 6 t\)

multiplying through by $42$ to clear the fractions

\(\ds \leadsto \ \ \)

\(\ds 21 \times 12\)

\(=\)

\(\ds 41 t\)

\(\ds \leadsto \ \ \)

\(\ds t\)

\(=\)

\(\ds \frac {252} {41}\)

\(\ds \)

\(=\)

\(\ds 6 \frac 6 {41}\)

So $6 \frac 6 {41}$ hours have passed since sunset.

That leaves $12 - 6 \frac 6 {41} = 5 \frac {35} {41}$ hours remaining till sunrise.

$\blacksquare$

Source of Name

This entry was named for Metrodorus.

Historical Note

In his $1918$ translation of The Greek Anthology Book XIV, W.R. Paton points out that Thessalian women means witches in this context.

Sources

• 1918: W.R. Paton: The Greek Anthology Book XIV ... (previous) ... (next): Metrodorus' Arithmetical Epigrams: $140$