Greek Anthology Book XIV: Metrodorus: 139

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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.


Solution

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.

$\blacksquare$


Source of Name

This entry was named for Metrodorus.


Sources