Greek Anthology Book XIV: Metrodorus: 139

Arithmetical Epigram of Metrodorus

Diodorus, great glory of dial-makers, tell me the hour since when the golden wheels of the sun leapt up from the east to the pole.

Four times three-fifths of the distance he has traversed remain until he sinks to the western sea.

Let $t$ be the time since dawn.

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

We have:

$\ds 12 - t$

$=$

$\ds 4 \times \dfrac {3 t} 5$

$\ds \leadsto \ \ $

$\ds 60 - 5 t$

$=$

$\ds 12 t$

multiplying through by $5$ to clear the fraction

$\ds \leadsto \ \ $

$\ds 17 t$

$=$

$\ds 60$

$\ds \leadsto \ \ $

$\ds t$

$=$

$\ds \frac {60} {17}$

$\ds $

$=$

$\ds 3 \frac 9 {17}$

So $3 \frac 9 {17}$ hours have passed since dawn.

That leaves $12 - 3 \frac 9 {17} = 8 \frac 8 {17}$ hours remaining till sunset.

$\blacksquare$

This entry was named for Metrodorus.

1918: W.R. Paton: The Greek Anthology Book XIV ... (previous) ... (next): Metrodorus' Arithmetical Epigrams: $139$