Greek Anthology Book XIV: Metrodorus: 124

Arithmetical Epigram of Metrodorus

The sun, the moon, and the planets of the revolving zodiac spun such a nativity for thee;

for a sixth part of thy life to remain an orphan with thy dear mother,

for an eighth part to perform forced labour for thy enemies.

For a third part the gods shall grant thee home-coming, and likewise a wife and a late-born son by her.

Then thy son and wife shall perish by the spears of the Scythians,

and then having shed tears for them thou shalt reach the end of thy life in twenty-seven years.

Solution

Let $n$ be the length in years of the subject's life.

$\dfrac n 6$ is spent as an orphan

$\dfrac n 8$ is spent as a slave

$\dfrac n 3$ is spent at home with a wife and son

$27$ years remain.

We have:

\(\ds n\)

\(=\)

\(\ds \dfrac n 6 + \dfrac n 8 + \dfrac n 3 + 27\)

\(\ds \leadsto \ \ \)

\(\ds 24 n\)

\(=\)

\(\ds 4 n + 3 n + 8 n + 24 \times 27\)

multiplying through by $24 = \lcm \set {6, 8, 3}$ and simplifying

\(\ds \leadsto \ \ \)

\(\ds \paren {24 - 4 - 3 - 8} n\)

\(=\)

\(\ds 24 \times 27\)

\(\ds \leadsto \ \ \)

\(\ds 9 n\)

\(=\)

\(\ds 24 \times 27\)

\(\ds \leadsto \ \ \)

\(\ds n\)

\(=\)

\(\ds \dfrac {24 \times 27} 9\)

\(\ds \)

\(=\)

\(\ds 72\)

So the subject lived $72$ years, of which:

$12$ years were spent as an orphan

$9$ years were spent as a slave

$24$ years were spent as a family man at home

and $27$ years remained before his death.

$\blacksquare$

Source of Name

This entry was named for Metrodorus.

Sources

• 1918: W.R. Paton: The Greek Anthology Book XIV ... (previous) ... (next): Metrodorus' Arithmetical Epigrams: $124$